@inproceedings{addanki2020efficient,
	title        = {{Efficient Intervention Design for Causal Discovery with Latents}},
	author       = {Addanki, Raghavendra and Kasiviswanathan, Shiva and Mcgregor, Andrew and Musco, Cameron},
	year         = 2020,
	booktitle    = {Proceedings of the 37th International Conference on Machine Learning},
	publisher    = {PMLR},
	series       = {Proceedings of Machine Learning Research},
	volume       = 119,
	abstract     = {We consider recovering a causal graph in presence of latent variables, where we seek to minimize the cost of interventions used in the recovery process. We consider two intervention cost models: (1) a linear cost model where the cost of an intervention on a subset of variables has a linear form, and (2) an identity cost model where the cost of an intervention is the same, regardless of what variables it is on, i.e., the goal is just to minimize the number of interventions. Under the linear cost model, we give an algorithm to identify the ancestral relations of the underlying causal graph, achieving within a $2$-factor of the optimal intervention cost. This approximation factor can be improved to $1+\eps$ for any $\eps > 0$ under some mild restrictions. Under the identity cost model, we bound the number of interventions needed to recover the entire causal graph, including the latent variables, using a parameterization of the causal graph through a special type of colliders. In particular, we introduce the notion of $p$-colliders, that are colliders between pair of nodes arising from a specific type of conditioning in the causal graph, and provide an upper bound on the number of interventions as a function of the maximum number of $p$-colliders between any two nodes in the causal graph.},
	keywords     = {Intervention Design}
}
@article{ahmed2020causalworld,
	title        = {{CausalWorld: A robotic manipulation benchmark for causal structure and transfer learning}},
	author       = {Ahmed, Ossama and Tr{\"a}uble, Frederik and Goyal, Anirudh and Neitz, Alexander and Bengio, Yoshua and Sch{\"o}lkopf, Bernhard and W{\"u}thrich, Manuel and Bauer, Stefan},
	year         = 2020,
	journal      = {arXiv preprint arXiv:2010.04296}
}
@inproceedings{ahuja2022weakly,
	title        = {{Weakly Supervised Representation Learning with Sparse Perturbations}},
	author       = {Ahuja, Kartik and Hartford, Jason and Bengio, Yoshua},
	year         = 2022,
	booktitle    = {Advances in Neural Information Processing Systems 35, NeurIPS}
}
@inproceedings{andreassen1991a,
	title        = {{A model-based approach to insulin adjustment}},
	author       = {Steen Andreassen and Roman Hovorka and Jonathan Benn and Kristian G. Olesen and Ewart R. Carson},
	year         = 1991,
	booktitle    = {Lecture Notes in Medical Informatics},
	publisher    = {Springer},
	address      = {Germany},
	series       = {Lecture Notes in Medical Informatics},
	volume       = 44,
	note         = {Conference date: 24-06-1991 Through 27-06-1991}
}
@article{ba2016layer,
	title        = {{Layer Normalization}},
	author       = {Lei Jimmy Ba and Jamie Ryan Kiros and Geoffrey E. Hinton},
	year         = 2016,
	journal      = {CoRR},
	volume       = {abs/1607.06450},
	eprinttype   = {arXiv},
	eprint       = {1607.06450}
}
@inproceedings{beinlich1989the,
	title        = {{The ALARM Monitoring System: A Case Study with two Probabilistic Inference Techniques for Belief Networks}},
	author       = {Beinlich, Ingo A. and Suermondt, Henri Jacques and Chavez, R. Martin and Cooper, Gregory F.},
	year         = 1989,
	booktitle    = {AIME 89},
	publisher    = {Springer Berlin Heidelberg},
	address      = {Berlin, Heidelberg},
	isbn         = {978-3-642-93437-7},
	abstract     = {ALARM (A Logical Alarm Reduction Mechanism) is a diagnostic application used to explore probabilistic reasoning techniques in belief networks. ALARM implements an alarm message system for patient monitoring; it calculates probabilities for a differential diagnosis based on available evidence. The medical knowledge is encoded in a graphical structure connecting 8 diagnoses, 16 findings and 13 intermediate variables. Two algorithms were applied to this belief network: (1) a message-passing algorithm by Pearl for probability updating in multiply connected networks using the method of conditioning; and (2) the Lauritzen-Spiegelhalter algorithm for local probability computations on graphical structures. The characteristics of both algorithms are analyzed and their specific applications and time complexities are shown.}
}
@inproceedings{belghazi2018mutual,
	title        = {{Mutual Information Neural Estimation}},
	author       = {Belghazi, Mohamed Ishmael and Baratin, Aristide and Rajeshwar, Sai and Ozair, Sherjil and Bengio, Yoshua and Courville, Aaron and Hjelm, Devon},
	year         = 2018,
	month        = {10--15 Jul},
	booktitle    = {Proceedings of the 35th International Conference on Machine Learning},
	publisher    = {PMLR},
	series       = {Proceedings of Machine Learning Research},
	volume       = 80,
	abstract     = {We argue that the estimation of mutual information between high dimensional continuous random variables can be achieved by gradient descent over neural networks. We present a Mutual Information Neural Estimator (MINE) that is linearly scalable in dimensionality as well as in sample size, trainable through back-prop, and strongly consistent. We present a handful of applications on which MINE can be used to minimize or maximize mutual information. We apply MINE to improve adversarially trained generative models. We also use MINE to implement the Information Bottleneck, applying it to supervised classification; our results demonstrate substantial improvement in flexibility and performance in these settings.}
}
@article{bellemare2013arcade,
	title        = {{The Arcade Learning Environment: An Evaluation Platform for General Agents}},
	author       = {Bellemare, Marc G. and Naddaf, Yavar and Veness, Joel and Bowling, Michael},
	year         = 2013,
	month        = {may},
	journal      = {J. Artif. Int. Res.},
	publisher    = {AI Access Foundation},
	address      = {El Segundo, CA, USA},
	volume       = 47,
	number       = 1,
	issn         = {1076-9757},
	issue_date   = {May 2013},
	abstract     = {In this article we introduce the Arcade Learning Environment (ALE): both a challenge problem and a platform and methodology for evaluating the development of general, domain-independent AI technology. ALE provides an interface to hundreds of Atari 2600 game environments, each one different, interesting, and designed to be a challenge for human players. ALE presents significant research challenges for reinforcement learning, model learning, model-based planning, imitation learning, transfer learning, and intrinsic motivation. Most importantly, it provides a rigorous testbed for evaluating and comparing approaches to these problems. We illustrate the promise of ALE by developing and benchmarking domain-independent agents designed using well-established AI techniques for both reinforcement learning and planning. In doing so, we also propose an evaluation methodology made possible by ALE, reporting empirical results on over 55 different games. All of the software, including the benchmark agents, is publicly available.},
	numpages     = 27
}
@article{belouchrani1997blind,
	title        = {{A blind source separation technique using second-order statistics}},
	author       = {Belouchrani, A. and Abed-Meraim, K. and Cardoso, J.-F. and Moulines, E.},
	year         = 1997,
	journal      = {IEEE Transactions on Signal Processing},
	volume       = 45,
	number       = 2
}
@article{bengio2013estimating,
	title        = {{Estimating or propagating gradients through stochastic neurons for conditional computation}},
	author       = {Bengio, Yoshua and L{\'e}onard, Nicholas and Courville, Aaron},
	year         = 2013,
	journal      = {arXiv preprint arXiv:1308.3432}
}
@inproceedings{bengio2020a,
	title        = {{A Meta-Transfer Objective for Learning to Disentangle Causal Mechanisms}},
	author       = {Yoshua Bengio and Tristan Deleu and Nasim Rahaman and Nan Rosemary Ke and S{\'{e}}bastien Lachapelle and Olexa Bilaniuk and Anirudh Goyal and Christopher J. Pal},
	year         = 2020,
	booktitle    = {8th International Conference on Learning Representations, {ICLR} 2020, Addis Ababa, Ethiopia, April 26-30, 2020}
}
@inproceedings{bhattacharya2021differentiable,
	title        = {{Differentiable Causal Discovery Under Unmeasured Confounding}},
	author       = {Rohit Bhattacharya and Tushar Nagarajan and Daniel Malinsky and Ilya Shpitser},
	year         = 2021,
	booktitle    = {The 24th International Conference on Artificial Intelligence and Statistics, {AISTATS} 2021, April 13-15, 2021, Virtual Event},
	publisher    = {{PMLR}},
	series       = {Proceedings of Machine Learning Research},
	volume       = 130
}
@manual{blender2021blender,
	title        = {{Blender - a 3D modelling and rendering package}},
	author       = {{Blender Online Community}},
	year         = 2021,
	address      = {Stichting Blender Foundation, Amsterdam},
	organization = {Blender Foundation}
}
@inproceedings{brehmer2022weakly,
	title        = {{Weakly supervised causal representation learning}},
	author       = {{Brehmer}, Johann and {de Haan}, Pim and {Lippe}, Phillip and {Cohen}, Taco},
	year         = 2022,
	booktitle    = {Advances in Neural Information Processing Systems 35, NeurIPS}
}
@inproceedings{brouillard2020differentiable,
	title        = {{Differentiable Causal Discovery from Interventional Data}},
	author       = {Philippe Brouillard and S{\'{e}}bastien Lachapelle and Alexandre Lacoste and Simon Lacoste{-}Julien and Alexandre Drouin},
	year         = 2020,
	booktitle    = {Advances in Neural Information Processing Systems 33, NeurIPS}
}
@inproceedings{chalpuka2015visual,
	title        = {{Visual Causal Feature Learning}},
	author       = {Chalupka, Krzysztof and Perona, Pietro and Eberhardt, Frederick},
	year         = 2015,
	booktitle    = {Proceedings of the Thirty-First Conference on Uncertainty in Artificial Intelligence},
	location     = {Amsterdam, Netherlands},
	publisher    = {AUAI Press},
	address      = {Arlington, Virginia, USA},
	series       = {UAI'15},
	isbn         = 9780996643108,
	abstract     = {We provide a rigorous definition of the visual cause of a behavior that is broadly applicable to the visually driven behavior in humans, animals, neurons, robots and other perceiving systems. Our framework generalizes standard accounts of causal learning to settings in which the causal variables need to be constructed from micro-variables. We prove the Causal Coarsening Theorem, which allows us to gain causal knowledge from observational data with minimal experimental effort. The theorem provides a connection to standard inference techniques in machine learning that identify features of an image that correlate with, but may not cause, the target behavior. Finally, we propose an active learning scheme to learn a manipulator function that performs optimal manipulations on the image to automatically identify the visual cause of a target behavior. We illustrate our inference and learning algorithms in experiments based on both synthetic and real data.},
	numpages     = 10
}
@inproceedings{chalpuka2016multilevel,
	title        = {{Multi-Level Cause-Effect Systems}},
	author       = {Chalupka, Krzysztof and Eberhardt, Frederick and Perona, Pietro},
	year         = 2016,
	booktitle    = {Proceedings of the 19th International Conference on Artificial Intelligence and Statistics},
	publisher    = {PMLR},
	address      = {Cadiz, Spain},
	series       = {Proceedings of Machine Learning Research},
	volume       = 51,
	abstract     = {We present a domain-general account of causation that applies to settings in which macro-level causal relations between two systems are of interest, but the relevant causal features are poorly understood and have to be aggregated from vast arrays of micro-measurements. Our approach generalizes that of Chalupka et. al. (2015) to the setting in which the macro-level effect is not specified. We formalize the connection between micro- and macro-variables in such situations and provide a coherent framework describing causal relations at multiple levels of analysis. We present an algorithm that discovers macro-variable causes and effects from micro-level measurements obtained from an experiment. We further show how to design experiments to discover macro-variables from observational micro-variable data. Finally, we show that under specific conditions, one can identify multiple levels of causal structure. Throughout the article, we use a simulated neuroscience multi-unit recording experiment to illustrate the ideas and the algorithms.}
}
@inproceedings{chalpuka2016unsupervised,
	title        = {{Unsupervised Discovery of El Nino Using Causal Feature Learning on Microlevel Climate Data}},
	author       = {Chalupka, Krzysztof and Bischoff, Tobias and Perona, Pietro and Eberhardt, Frederick},
	year         = 2016,
	booktitle    = {Proceedings of the Thirty-Second Conference on Uncertainty in Artificial Intelligence},
	location     = {Jersey City, New Jersey, USA},
	publisher    = {AUAI Press},
	address      = {Arlington, Virginia, USA},
	series       = {UAI'16},
	isbn         = 9780996643115,
	abstract     = {We show that the climate phenomena of El Ni\~{n}o and La Ni\~{n}a arise naturally as states of macro-variables when our recent causal feature learning framework (Chalupka et al., 2015, 2016) is applied to micro-level measures of zonal wind (ZW) and sea surface temperatures (SST) taken over the equatorial band of the Pacific Ocean. The method identifies these unusual climate states on the basis of the relation between ZW and SST patterns without any input about past occurrences of El Ni\~{n}o or La Ni\~{n}a. The simpler alternatives of (i) clustering the SST fields while disregarding their relationship with ZW patterns, or (ii) clustering the joint ZW-SST patterns, do not discover El Ni\~{n}o. We discuss the degree to which our method supports a causal interpretation and use a low-dimensional toy example to explain its success over other clustering approaches. Finally, we propose a new robust and scalable alternative to our original algorithm (Chalupka et al., 2016), which circumvents the need for high-dimensional density learning.},
	numpages     = 10
}
@inproceedings{chen2020simple,
	title        = {{A simple framework for contrastive learning of visual representations}},
	author       = {Chen, Ting and Kornblith, Simon and Norouzi, Mohammad and Hinton, Geoffrey},
	year         = 2020,
	booktitle    = {International conference on machine learning},
	organization = {PMLR}
}
@inproceedings{cherepkov2021navigating,
	title        = {{Navigating the GAN Parameter Space for Semantic Image Editing}},
	author       = {Cherepkov, Anton and Voynov, Andrey and Babenko, Artem},
	year         = 2021,
	month        = {June},
	booktitle    = {Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition (CVPR)}
}
@inbook{chickering1996learning,
	title        = {{Learning Bayesian Networks is NP-Complete}},
	author       = {Chickering, David Maxwell},
	year         = 1996,
	booktitle    = {Learning from Data: Artificial Intelligence and Statistics V},
	publisher    = {Springer New York},
	address      = {New York, NY},
	isbn         = {978-1-4612-2404-4},
	abstract     = {Algorithms for learning Bayesian networks from data have two components: a scoring metric and a search procedure. The scoring metric computes a score reflecting the goodness-of-fit of the structure to the data. The search procedure tries to identify network structures with high scores. Heckerman et al. (1995) introduce a Bayesian metric, called the BDe metric, that computes the relative posterior probability of a network structure given data. In this paper, we show that the search problem of identifying a Bayesian network---among those where each node has at most K parents---that has a relative posterior probability greater than a given constant is NP-complete, when the BDe metric is used.}
}
@article{chickering2002optimal,
	title        = {{Optimal structure identification with greedy search}},
	author       = {Chickering, David Maxwell},
	year         = 2002,
	journal      = {Journal of machine learning research},
	volume       = 3,
	number       = {Nov}
}
@article{chickering2004large,
	title        = {{Large-Sample Learning of Bayesian Networks is NP-Hard}},
	author       = {Chickering, David Maxwell and Heckerman, David and Meek, Christopher},
	year         = 2004,
	journal      = {Journal of Machine Learning Research},
	publisher    = {JMLR},
	volume       = 5,
	issn         = {1532-4435},
	abstract     = {In this paper, we provide new complexity results for algorithms that learn discrete-variable Bayesian networks from data. Our results apply whenever the learning algorithm uses a scoring criterion that favors the simplest structure for which the model is able to represent the generative distribution exactly. Our results therefore hold whenever the learning algorithm uses a consistent scoring criterion and is applied to a sufficiently large dataset. We show that identifying high-scoring structures is NP-hard, even when any combination of one or more of the following hold: the generative distribution is perfect with respect to some DAG containing hidden variables; we are given an independence oracle; we are given an inference oracle; we are given an information oracle; we restrict potential solutions to structures in which each node has at most k parents, for all k&gt;=3.Our proof relies on a new technical result that we establish in the appendices. In particular, we provide a method for constructing the local distributions in a Bayesian network such that the resulting joint distribution is provably perfect with respect to the structure of the network.},
	issue_date   = {12/1/2004},
	numpages     = 44
}
@article{christina2018invariant,
	title        = {{Invariant Causal Prediction for Nonlinear Models}},
	author       = {Heinze-Deml Christina and Meinshausen Nicolai and Peters Jonas},
	year         = 2018,
	journal      = {Journal of Causal Inference},
	volume       = 6,
	number       = 2,
	abstract     = {An important problem in many domains is to predict how a system will respond to interventions. This task is inherently linked to estimating the system’s underlying causal structure. To this end, Invariant Causal Prediction (ICP) [1] has been proposed which learns a causal model exploiting the invariance of causal relations using data from different environments. When considering linear models, the implementation of ICP is relatively straightforward. However, the nonlinear case is more challenging due to the difficulty of performing nonparametric tests for conditional independence.},
	keywords     = {causal structure learning; structural equation models; invariance}
}
@article{comon1994independent,
	title        = {{Independent component analysis, A new concept?}},
	author       = {Comon, Pierre},
	year         = 1994,
	month        = apr,
	journal      = {Signal Processing},
	volume       = 36,
	number       = 3,
	abstract     = {The independent component analysis (ICA) of a random vector consists of searching for a linear transformation that minimizes the statistical dependence between its components. In order to define suitable search criteria, the expansion of mutual information is utilized as a function of cumulants of increasing orders. An efficient algorithm is proposed, which allows the computation of the ICA of a data matrix within a polynomial time. The concept of ICA may actually be seen as an extension of the principal component analysis (PCA), which can only impose independence up to the second order and, consequently, defines directions that are orthogonal. Potential applications of ICA include data analysis and compression, Bayesian detection, localization of sources, and blind identification and deconvolution. Zusammenfassung Die Analyse unabh{\"a}ngiger Komponenten (ICA) eines Vektors beruht auf der Suche nach einer linearen Transformation, die die statistische Abh{\"a}ngigkeit zwischen den Komponenten minimiert. Zur Definition geeigneter Such-Kriterien wird die Entwicklung gemeinsamer Information als Funktion von Kumulanten steigender Ordnung genutzt. Es wird ein effizienter Algorithmus vorgeschlagen, der die Berechnung der ICA f{\"u}r Datenmatrizen innerhalb einer polynomischen Zeit erlaubt. Das Konzept der ICA kann eigentlich als Erweiterung der `Principal Component Analysis` (PCA) betrachtet werden, die nur die Unabh{\"a}ngigkeit bis zur zweiten Ordnung erzwingen kann und deshalb Richtungen definiert, die orthogonal sind. Potentielle Anwendungen der ICA beinhalten Daten-Analyse und Kompression, Bayes-Detektion, Quellenlokalisierung und blinde Identifikation und Entfaltung. R{\'e}sum{\'e} L'Analyse en Composantes Ind{\'e}pendentes (ICA) d'un vecteur al{\'e}atoire consiste en la recherche d'une transformation lin{\'e}aire qui minimise la d{\'e}pendance statistique entre ses composantes. Afin de d{\'e}finir des crit{\`e}res d'optimisation appropri{\'e}s, on utilise un d{\'e}veloppment en s{\'e}rie de l'information mutuelle en fonction de cumulants d'ordre croissant. On propose ensuite un algorithme pratique permettant le calcul de l'ICA d'une matrice de donn{\'e}es en un temps polynomial. Le concept d'ICA peut {\^e}tre vu en r{\'e}alit{\'e} comme une extention de l'Analyse en Composantes Principales (PCA) qui, elle, ne peut imposer l'ind{\'e}pendence qu'au second ordre et d{\'e}finit par cons{\'e}quent des directions orthogonales. Les applications potentielles de l'ICA incluent l'analyse et la compression de donn{\'e}es, la d{\'e}tection bayesienne, la localisation de sources, et l'identification et la d{\'e}convolution aveugles.}
}
@article{corcoll2020disentangling,
	title        = {{Disentangling causal effects for hierarchical reinforcement learning}},
	author       = {Corcoll, Oriol and Vicente, Raul},
	year         = 2020,
	journal      = {arXiv preprint arXiv:2010.01351}
}
@book{cover2005elements,
	title        = {{Elements of Information Theory}},
	author       = {Cover, Thomas M. and Thomas, Joy A.},
	year         = 2005,
	publisher    = {John Wiley and Sons, Ltd},
	isbn         = 9780471748823,
	abstract     = {Summary The prelims comprise: Half Title Title Copyright Contents Preface to the Second Edition Preface to the First Edition Acknowledgments for the Second Edition Acknowledgments for the First Edition},
	eprint       = {https://onlinelibrary.wiley.com/doi/pdf/10.1002/047174882X.fmatter}
}
@inproceedings{mian2023information,
	title        = {Information-Theoretic Causal Discovery and Intervention Detection over Multiple Environments},
	author       = {Mian, Osman and Kamp, Michael and Vreeken, Jilles},
	year         = 2023,
	series       = {AAAI-23},
        booktitle    = {Proceedings of the AAAI Conference on Artificial Intelligence}
}
@article{lesort2018state,
	title        = {State representation learning for control: An overview},
	author       = {Timothée Lesort and Natalia Díaz-Rodríguez and Jean-Frano̧is Goudou and David Filliat},
	year         = 2018,
	journal      = {Neural Networks},
	volume       = 108,
	keywords     = {State representation learning, Low dimensional embedding learning, Learning disentangled representations, Disentanglement of control factors, Robotics, Reinforcement learning},
	abstract     = {Representation learning algorithms are designed to learn abstract features that characterize data. State representation learning (SRL) focuses on a particular kind of representation learning where learned features are in low dimension, evolve through time, and are influenced by actions of an agent. The representation is learned to capture the variation in the environment generated by the agent’s actions; this kind of representation is particularly suitable for robotics and control scenarios. In particular, the low dimension characteristic of the representation helps to overcome the curse of dimensionality, provides easier interpretation and utilization by humans and can help improve performance and speed in policy learning algorithms such as reinforcement learning. This survey aims at covering the state-of-the-art on state representation learning in the most recent years. It reviews different SRL methods that involve interaction with the environment, their implementations and their applications in robotics control tasks (simulated or real). In particular, it highlights how generic learning objectives are differently exploited in the reviewed algorithms. Finally, it discusses evaluation methods to assess the representation learned and summarizes current and future lines of research.}
}
@inproceedings{curless1996volumetric,
	title        = {{A Volumetric Method for Building Complex Models from Range Images}},
	author       = {Curless, Brian and Levoy, Marc},
	year         = 1996,
	booktitle    = {Proceedings of the 23rd Annual Conference on Computer Graphics and Interactive Techniques},
	publisher    = {Association for Computing Machinery},
	address      = {New York, NY, USA},
	series       = {SIGGRAPH '96},
	isbn         = {0897917464},
	numpages     = 10,
	keywords     = {three-dimensional shape recovery, isosurface extraction, range image integration, surface fitting}
}
@article{DBN,
	title        = {{A model for reasoning about persistence and causation}},
	author       = {Dean, Thomas and Kanazawa, Keiji},
	year         = 1989,
	journal      = {Computational Intelligence},
	volume       = 5,
	number       = 2,
	abstract     = {Reasoning about change requires predicting how long a proposition, having become true, will continue to be so. Lacking perfect knowledge, an agent may be constrained to believe that a proposition persists indefinitely simply because there is no way for the agent to infer a contravening proposition with certainty. In this paper, we describe a model of causal reasoning that accounts for knowledge concerning cause-and-effect relationships and knowledge concerning the tendency for propositions to persist or not as a function of time passing. Our model has a natural encoding in the form of a network representation for probabilistic models. We consider the computational properties of our model by reviewing recent advances in computing the consequences of models encoded in this network representation. Finally, we discuss how our probabilistic model addresses certain classical problems in temporal reasoning (e. g., the frame and qualification problems).},
	eprint       = {https://onlinelibrary.wiley.com/doi/pdf/10.1111/j.1467-8640.1989.tb00324.x},
	keywords     = {temporal reasoning, causal reasoning, uncertainty, probabilistic models, probabilistic inference, belief networks, raisonnement tenmorel, raisonnement causal, incertitude, mod{\`e}les probabilistiques, inf{\'e}rence probabilistique, r{\'e}seau de croyances},
	bdsk-url-1   = {https://onlinelibrary.wiley.com/doi/abs/10.1111/j.1467-8640.1989.tb00324.x},
	bdsk-url-2   = {https://doi.org/10.1111/j.1467-8640.1989.tb00324.x}
}
@article{de2019causal,
	title        = {{Causal confusion in imitation learning}},
	author       = {De Haan, Pim and Jayaraman, Dinesh and Levine, Sergey},
	year         = 2019,
	journal      = {Advances in Neural Information Processing Systems},
	volume       = 32
}
@inproceedings{didelez2006direct,
	title        = {{Direct and Indirect Effects of Sequential Treatments}},
	author       = {Didelez, Vanessa and Dawid, A. Philip and Geneletti, Sara},
	year         = 2006,
	booktitle    = {Proceedings of the Twenty-Second Conference on Uncertainty in Artificial Intelligence},
	location     = {Cambridge, MA, USA},
	publisher    = {AUAI Press},
	address      = {Arlington, Virginia, USA},
	series       = {UAI'06},
	isbn         = {0974903922},
	abstract     = {In this paper we review the notion of direct and indirect causal effect as introduced by Pearl (2001). We show how it can be formulated without counterfactuals, using regime indicators instead. This allows to consider the natural (in)direct effect as a special case of sequential treatments discussed by Dawid & Didelez (2005) which immediately yields conditions for identifiability as well as a graphical way of checking identifiability.},
	numpages     = 9
}
@inproceedings{dinh2017density,
	title        = {{Density estimation using Real NVP}},
	author       = {Laurent Dinh and Jascha Sohl{-}Dickstein and Samy Bengio},
	year         = 2017,
	booktitle    = {5th International Conference on Learning Representations, {ICLR} 2017, Toulon, France, April 24-26, 2017, Conference Track Proceedings}
}
@article{dixit2016p,
	title        = {{Perturb-Seq: Dissecting Molecular Circuits with Scalable Single-Cell RNA Profiling of Pooled Genetic Screens}},
	author       = {Dixit, A.  and Parnas, O.  and Li, B.  and Chen, J.  and Fulco, C. P.  and Jerby-Arnon, L.  and Marjanovic, N. D.  and Dionne, D.  and Burks, T.  and Raychowdhury, R.  and Adamson, B.  and Norman, T. M.  and Lander, E. S.  and Weissman, J. S.  and Friedman, N.  and Regev, A.},
	year         = 2016,
	journal      = {Cell},
	volume       = 167,
	number       = 7
}
@inproceedings{du2019provably,
	title        = {{Provably efficient RL with rich observations via latent state decoding}},
	author       = {Du, Simon and Krishnamurthy, Akshay and Jiang, Nan and Agarwal, Alekh and Dudik, Miroslav and Langford, John},
	year         = 2019,
	booktitle    = {International Conference on Machine Learning},
	organization = {PMLR}
}
@inproceedings{eaton2007exact,
	title        = {{Exact Bayesian structure learning from uncertain interventions}},
	author       = {Eaton, Daniel and Murphy, Kevin},
	year         = 2007,
	month        = {21--24 Mar},
	booktitle    = {Proceedings of the Eleventh International Conference on Artificial Intelligence and Statistics},
	publisher    = {PMLR},
	address      = {San Juan, Puerto Rico},
	series       = {Proceedings of Machine Learning Research},
	volume       = 2,
	abstract     = {We show how to apply the dynamic programming algorithm of Koivisto and Sood [KS04, Koi06], which computes the exact posterior marginal edge probabilities p(G_ij = 1|D) of a DAG G given data D, to the case where the data is obtained by interventions (experiments). In particular, we consider the case where the targets of the interventions are a priori unknown. We show that it is possible to learn the targets of intervention at the same time as learning the causal structure. We apply our exact technique to a biological data set that had previously been analyzed using MCMC [SPP+ 05, EW06, WGH06].}
}
@inproceedings{eberhardt2005on,
	title        = {{On the Number of Experiments Sufficient and in the Worst Case Necessary to Identify All Causal Relations among N Variables}},
	author       = {Eberhardt, Frederick and Glymour, Clark and Scheines, Richard},
	year         = 2005,
	booktitle    = {Proceedings of the Twenty-First Conference on Uncertainty in Artificial Intelligence},
	location     = {Edinburgh, Scotland},
	publisher    = {AUAI Press},
	address      = {Arlington, Virginia, USA},
	series       = {UAI'05},
	isbn         = {0974903914},
	abstract     = {We show that if any number of variables are allowed to be simultaneously and independently randomized in any one experiment, log2(N) + 1 experiments are sufficient and in the worst case necessary to determine the causal relations among N ≥ 2 variables when no latent variables, no sample selection bias and no feedback cycles are present. For all K, 0 &lt; K &lt; 1/2N we provide an upper bound on the number experiments required to determine causal structure when each experiment simultaneously randomizes K variables. For large N, these bounds are significantly lower than the N - 1 bound required when each experiment randomizes at most one variable. For kmax &lt; N/2, we show that (N/kmaz -1) + N/2kmax log2(kmax) experiments are sufficient and in the worst case necessary. We offer a conjecture as to the minimal number of experiments that are in the worst case sufficient to identify all causal relations among N observed variables that are a subset of the vertices of a DAG.},
	numpages     = 7
}
@article{eberhardt2007causation,
	title        = {{Causation and intervention}},
	author       = {Eberhardt, Frederick},
	year         = 2007,
	journal      = {Unpublished doctoral dissertation, Carnegie Mellon University}
}
@inproceedings{eberhardt2008almost,
	title        = {{Almost Optimal Intervention Sets for Causal Discovery}},
	author       = {Eberhardt, Frederick},
	year         = 2008,
	booktitle    = {Proceedings of the Twenty-Fourth Conference on Uncertainty in Artificial Intelligence},
	location     = {Helsinki, Finland},
	publisher    = {AUAI Press},
	address      = {Arlington, Virginia, USA},
	series       = {UAI'08},
	isbn         = {0974903949},
	abstract     = {We conjecture that the worst case number of experiments necessary and sufficient to discover a causal graph uniquely given its observational Markov equivalence class can be specified as a function of the largest clique in the Markov equivalence class. We provide an algorithm that computes intervention sets that we believe are optimal for the above task. The algorithm builds on insights gained from the worst case analysis in Eberhardt et al. (2005) for sequences of experiments when all possible directed acyclic graphs over N variables are considered. A simulation suggests that our conjecture is correct. We also show that a generalization of our conjecture to other classes of possible graph hypotheses cannot be given easily, and in what sense the algorithm is then no longer optimal.},
	numpages     = 8
}
@article{engelcke2019genesis,
	title        = {{GENESIS: Generative scene inference and sampling with object-centric latent representations}},
	author       = {Engelcke, Martin and Kosiorek, Adam R and Jones, Oiwi Parker and Posner, Ingmar},
	year         = 2020,
	journal      = {International Conference on Learning Representations (ICLR)}
}
@article{faes2010extended,
	title        = {{Extended causal modeling to assess Partial Directed Coherence in multiple time series with significant instantaneous interactions}},
	author       = {Faes, Luca and Nollo, Giandomenico},
	year         = 2010,
	journal      = {Biological cybernetics},
	publisher    = {Springer},
	volume       = 103,
	number       = 5
}
@misc{Falcon_PyTorch_Lightning_2019,
	title        = {{PyTorch Lightning}},
	author       = {Falcon, William and {The PyTorch Lightning team}},
	year         = 2019,
	license      = {Apache-2.0},
	version      = {1.4}
}
@inproceedings{faria2022differentiable,
	title        = {{Differentiable Causal Discovery Under Latent Interventions}},
	author       = {Faria, Gon{\c{c}}alo Rui Alves and Martins, Andre and Figueiredo, Mario A. T.},
	year         = 2022,
	month        = {11--13 Apr},
	booktitle    = {Proceedings of the First Conference on Causal Learning and Reasoning},
	publisher    = {PMLR},
	series       = {Proceedings of Machine Learning Research},
	volume       = 177,
	abstract     = {Recent work has shown promising results in causal discovery by leveraging interventional data with gradient-based methods, even when the intervened variables are unknown. However, previous work assumes that the correspondence between samples and interventions is known, which is often unrealistic. We envision a scenario with an extensive dataset sampled from multiple intervention distributions and one observation distribution, but where we do not know which distribution originated each sample and how the intervention affected the system, \textit{i.e.}, interventions are entirely latent. We propose a method based on neural networks and variational inference that addresses this scenario by framing it as learning a shared causal graph among a infinite mixture (under a Dirichlet process prior) of intervention structural causal models . Experiments with synthetic and real data show that our approach and its semi-supervised variant are able to discover causal relations in this challenging scenario.}
}
@article{friedman2000using,
	title        = {{Using Bayesian networks to analyze expression data}},
	author       = {Friedman, Nir and Linial, Michal and Nachman, Iftach and Pe'er, Dana},
	year         = 2000,
	journal      = {Journal of computational biology},
	publisher    = {Mary Ann Liebert, Inc.},
	volume       = 7,
	number       = {3-4}
}
@inproceedings{fukumizu2007kernel,
	title        = {{Kernel Measures of Conditional Dependence}},
	author       = {Kenji Fukumizu and Arthur Gretton and Xiaohai Sun and Bernhard Sch{\"{o}}lkopf},
	year         = 2007,
	booktitle    = {Advances in Neural Information Processing Systems 20, Proceedings of the Twenty-First Annual Conference on Neural Information Processing Systems, Vancouver, British Columbia, Canada, December 3-6, 2007},
	publisher    = {Curran Associates, Inc.}
}
@inproceedings{germain2015made,
	title        = {{Made: Masked autoencoder for distribution estimation}},
	author       = {Germain, Mathieu and Gregor, Karol and Murray, Iain and Larochelle, Hugo},
	year         = 2015,
	booktitle    = {International Conference on Machine Learning},
	organization = {PMLR}
}
@article{glymour2019review,
	title        = {{Review of Causal Discovery Methods Based on Graphical Models}},
	author       = {Glymour, Clark and Zhang, Kun and Spirtes, Peter},
	year         = 2019,
	journal      = {Frontiers in Genetics},
	volume       = 10,
	issn         = {1664-8021},
	abstract     = {A fundamental task in various disciplines of science, including biology, is to find underlying causal relations and make use of them. Causal relations can be seen if interventions are properly applied; however, in many cases they are difficult or even impossible to conduct. It is then necessary to discover causal relations by analyzing statistical properties of purely observational data, which is known as causal discovery or causal structure search. This paper aims to give a introduction to and a brief review of the computational methods for causal discovery that were developed in the past three decades, including constraint-based and score-based methods and those based on functional causal models, supplemented by some illustrations and applications.}
}
@article{goudet2017causal,
	title        = {{Causal generative neural networks}},
	author       = {Goudet, Olivier and Kalainathan, Diviyan and Caillou, Philippe and Guyon, Isabelle and Lopez-Paz, David and Sebag, Mich{\`e}le},
	year         = 2017,
	journal      = {arXiv preprint arXiv:1711.08936}
}
@inproceedings{gresele2021independent,
	title        = {{Independent mechanism analysis, a new concept?}},
	author       = {Gresele, Luigi and von K{\"u}gelgen, Julius and Stimper, Vincent and Sch{\"o}lkopf, Bernhard and Besserve, Michel},
	year         = 2021,
	booktitle    = {Advances in Neural Information Processing Systems},
	abstract     = {Independent component analysis provides a principled framework for unsupervised representation learning, with solid theory on the identifiability of the latent code that generated the data, given only observations of mixtures thereof. Unfortunately, when the mixing is nonlinear, the model is provably nonidentifiable, since statistical independence alone does not sufficiently constrain the problem. Identifiability can be recovered in settings where additional, typically observed variables are included in the generative process. We investigate an alternative path and consider instead including assumptions reflecting the principle of independent causal mechanisms exploited in the field of causality. Specifically, our approach is motivated by thinking of each source as independently influencing the mixing process. This gives rise to a framework which we term independent mechanism analysis. We provide theoretical and empirical evidence that our approach circumvents a number of nonidentifiability issues arising in nonlinear blind source separation.}
}
@article{guo2020a,
	title        = {{A Survey of Learning Causality with Data: Problems and Methods}},
	author       = {Guo, Ruocheng and Cheng, Lu and Li, Jundong and Hahn, P. Richard and Liu, Huan},
	year         = 2020,
	journal      = {ACM Comput. Surv.},
	publisher    = {Association for Computing Machinery},
	address      = {New York, NY, USA},
	volume       = 53,
	number       = 4,
	issn         = {0360-0300},
	abstract     = {This work considers the question of how convenient access to copious data impacts our ability to learn causal effects and relations. In what ways is learning causality in the era of big data different from—or the same as—the traditional one? To answer this question, this survey provides a comprehensive and structured review of both traditional and frontier methods in learning causality and relations along with the connections between causality and machine learning. This work points out on a case-by-case basis how big data facilitates, complicates, or motivates each approach.},
	articleno    = 75,
	issue_date   = {September 2020},
	keywords     = {Causal machine learning, causal inference, causal discovery},
	numpages     = 37
}
@inproceedings{hafner2021mastering,
	title        = {{Mastering Atari with Discrete World Models}},
	author       = {Danijar Hafner and Timothy P Lillicrap and Mohammad Norouzi and Jimmy Ba},
	year         = 2021,
	booktitle    = {International Conference on Learning Representations}
}
@inproceedings{harkonen2020GANSpace,
	title        = {{GANSpace: Discovering Interpretable GAN Controls}},
	author       = {H\"{a}rk\"{o}nen, Erik and Hertzmann, Aaron and Lehtinen, Jaakko and Paris, Sylvain},
	year         = 2020,
	booktitle    = {Advances in Neural Information Processing Systems},
	publisher    = {Curran Associates, Inc.},
	volume       = 33
}
@article{hauser2012characterization,
	title        = {{Characterization and Greedy Learning of Interventional Markov Equivalence Classes of Directed Acyclic Graphs}},
	author       = {Hauser, Alain and B\"{u}hlmann, Peter},
	year         = 2012,
	journal      = {Journal of Machine Learning Research},
	publisher    = {JMLR},
	volume       = 13,
	number       = 1,
	issn         = {1532-4435},
	abstract     = {The investigation of directed acyclic graphs (DAGs) encoding the same Markov property, that is the same conditional independence relations of multivariate observational distributions, has a long tradition; many algorithms exist for model selection and structure learning in Markov equivalence classes. In this paper, we extend the notion of Markov equivalence of DAGs to the case of interventional distributions arising from multiple intervention experiments. We show that under reasonable assumptions on the intervention experiments, interventionalMarkov equivalence defines a finer partitioning of DAGs than observational Markov equivalence and hence improves the identifiability of causal models. We give a graph theoretic criterion for two DAGs being Markov equivalent under interventions and show that each interventional Markov equivalence class can, analogously to the observational case, be uniquely represented by a chain graph called interventional essential graph (also known as CPDAG in the observational case). These are key insights for deriving a generalization of the Greedy Equivalence Search algorithm aimed at structure learning from interventional data. This new algorithm is evaluated in a simulation study.},
	issue_date   = {January 2012},
	keywords     = {causal inference, interventions, graphical model, Markov equivalence, greedy equivalence search},
	numpages     = 56
}
@inproceedings{he2016deep,
	title        = {{Deep residual learning for image recognition}},
	author       = {He, Kaiming and Zhang, Xiangyu and Ren, Shaoqing and Sun, Jian},
	year         = 2016,
	booktitle    = {Proceedings of the IEEE conference on computer vision and pattern recognition}
}
@article{heckerman1995learning,
	title        = {{Learning Bayesian networks: The combination of knowledge and statistical data}},
	author       = {Heckerman, David and Geiger, Dan and Chickering, David M},
	year         = 1995,
	journal      = {Machine Learning},
	volume       = 20,
	number       = 3,
	issn         = {1573-0565},
	abstract     = {We describe a Bayesian approach for learning Bayesian networks from a combination of prior knowledge and statistical data. First and foremost, we develop a methodology for assessing informative priors needed for learning. Our approach is derived from a set of assumptions made previously as well as the assumption of likelihood equivalence, which says that data should not help to discriminate network structures that represent the same assertions of conditional independence. We show that likelihood equivalence when combined with previously made assumptions implies that the user's priors for network parameters can be encoded in a single Bayesian network for the next case to be seen—aprior network—and a single measure of confidence for that network. Second, using these priors, we show how to compute the relative posterior probabilities of network structures given data. Third, we describe search methods for identifying network structures with high posterior probabilities. We describe polynomial algorithms for finding the highest-scoring network structures in the special case where every node has at mostk=1 parent. For the general case (k>1), which is NP-hard, we review heuristic search algorithms including local search, iterative local search, and simulated annealing. Finally, we describe a methodology for evaluating Bayesian-network learning algorithms, and apply this approach to a comparison of various approaches.}
}
@article{heinze-deml2018invariant,
	title        = {{Invariant Causal Prediction for Nonlinear Models}},
	author       = {Heinze-Deml, Christina and Meinshausen, Nicolai and Peters, Jonas},
	year         = 2018,
	journal      = {Journal of Causal Inference},
	publisher    = {De Gruyter},
	volume       = 6,
	number       = 2
}
@article{hendrycks2016gelu,
	title        = {{Gaussian Error Linear Units (GELUs)}},
	author       = {Hendrycks, Dan and Gimpel, Kevin},
	year         = 2016,
	journal      = {arXiv preprint arXiv:1606.08415}
}
@book{hicks1980causality,
	title        = {{Causality in economics}},
	author       = {Hicks, John and others},
	year         = 1980,
	publisher    = {Australian National University Press}
}
@inproceedings{higgins2017beta,
	title        = {{beta-VAE: Learning Basic Visual Concepts with a Constrained Variational Framework}},
	author       = {Irina Higgins and Lo{\"{\i}}c Matthey and Arka Pal and Christopher Burgess and Xavier Glorot and Matthew Botvinick and Shakir Mohamed and Alexander Lerchner},
	year         = 2017,
	booktitle    = {5th International Conference on Learning Representations, {ICLR} 2017, Toulon, France, April 24-26, 2017, Conference Track Proceedings}
}
@inproceedings{hjelm2018learning,
	title        = {{Learning deep representations by mutual information estimation and maximization}},
	author       = {R Devon Hjelm and Alex Fedorov and Samuel Lavoie-Marchildon and Karan Grewal and Phil Bachman and Adam Trischler and Yoshua Bengio},
	year         = 2019,
	booktitle    = {International Conference on Learning Representations}
}
@inproceedings{ho2019flow,
	title        = {{Flow++: Improving Flow-Based Generative Models with Variational Dequantization and Architecture Design}},
	author       = {Ho, Jonathan and Chen, Xi and Srinivas, Aravind and Duan, Yan and Abbeel, Pieter},
	year         = 2019,
	month        = {09--15 Jun},
	booktitle    = {Proceedings of the 36th International Conference on Machine Learning},
	publisher    = {PMLR},
	series       = {Proceedings of Machine Learning Research},
	volume       = 97,
	abstract     = {Flow-based generative models are powerful exact likelihood models with efficient sampling and inference. Despite their computational efficiency, flow-based models generally have much worse density modeling performance compared to state-of-the-art autoregressive models. In this paper, we investigate and improve upon three limiting design choices employed by flow-based models in prior work: the use of uniform noise for dequantization, the use of inexpressive affine flows, and the use of purely convolutional conditioning networks in coupling layers. Based on our findings, we propose Flow++, a new flow-based model that is now the state-of-the-art non-autoregressive model for unconditional density estimation on standard image benchmarks. Our work has begun to close the significant performance gap that has so far existed between autoregressive models and flow-based models.}
}
@article{hoel2013quantifying,
	title        = {{Quantifying causal emergence shows that macro can beat micro}},
	author       = {Hoel, Erik P and Albantakis, Larissa and Tononi, Giulio},
	year         = 2013,
	month        = dec,
	journal      = {Proc. Natl. Acad. Sci. U. S. A.},
	volume       = 110,
	number       = 49,
	abstract     = {Causal interactions within complex systems can be analyzed at multiple spatial and temporal scales. For example, the brain can be analyzed at the level of neurons, neuronal groups, and areas, over tens, hundreds, or thousands of milliseconds. It is widely assumed that, once a micro level is fixed, macro levels are fixed too, a relation called supervenience. It is also assumed that, although macro descriptions may be convenient, only the micro level is causally complete, because it includes every detail, thus leaving no room for causation at the macro level. However, this assumption can only be evaluated under a proper measure of causation. Here, we use a measure [effective information (EI)] that depends on both the effectiveness of a system's mechanisms and the size of its state space: EI is higher the more the mechanisms constrain the system's possible past and future states. By measuring EI at micro and macro levels in simple systems whose micro mechanisms are fixed, we show that for certain causal architectures EI can peak at a macro level in space and/or time. This happens when coarse-grained macro mechanisms are more effective (more deterministic and/or less degenerate) than the underlying micro mechanisms, to an extent that overcomes the smaller state space. Thus, although the macro level supervenes upon the micro, it can supersede it causally, leading to genuine causal emergence--the gain in EI when moving from a micro to a macro level of analysis.}
}
@article{holtgen2021encoding,
	title        = {{Encoding Causal Macrovariables}},
	author       = {H{\"o}ltgen, Benedikt},
	year         = 2021,
	month        = nov,
	journal      = {arXiv preprint arXiv:2111.14724},
	abstract     = {In many scientific disciplines, coarse-grained causal models are used to explain and predict the dynamics of more fine-grained systems. Naturally, such models require appropriate macrovariables. Automated procedures to detect suitable variables would be useful to leverage increasingly available high-dimensional observational datasets. This work introduces a novel algorithmic approach that is inspired by a new characterisation of causal macrovariables as information bottlenecks between microstates. Its general form can be adapted to address individual needs of different scientific goals. After a further transformation step, the causal relationships between learned variables can be investigated through additive noise models. Experiments on both simulated data and on a real climate dataset are reported. In a synthetic dataset, the algorithm robustly detects the ground-truth variables and correctly infers the causal relationships between them. In a real climate dataset, the algorithm robustly detects two variables that correspond to the two known variations of the El Nino phenomenon.},
	archiveprefix = {arXiv},
	primaryclass = {cs.LG},
	eprint       = {2111.14724}
}
@article{hornik1989multilayer,
	title        = {{Multilayer feedforward networks are universal approximators}},
	author       = {Kurt Hornik and Maxwell Stinchcombe and Halbert White},
	year         = 1989,
	journal      = {Neural Networks},
	volume       = 2,
	number       = 5,
	issn         = {0893-6080},
	abstract     = {This paper rigorously establishes that standard multilayer feedforward networks with as few as one hidden layer using arbitrary squashing functions are capable of approximating any Borel measurable function from one finite dimensional space to another to any desired degree of accuracy, provided sufficiently many hidden units are available. In this sense, multilayer feedforward networks are a class of universal approximators.},
	keywords     = {Feedforward networks, Universal approximation, Mapping networks, Network representation capability, Stone-Weierstrass Theorem, Squashing functions, Sigma-Pi networks, Back-propagation networks}
}
@inproceedings{huang2018neural,
	title        = {{Neural Autoregressive Flows}},
	author       = {Chin{-}Wei Huang and David Krueger and Alexandre Lacoste and Aaron C. Courville},
	year         = 2018,
	booktitle    = {Proceedings of the 35th International Conference on Machine Learning, {ICML} 2018, Stockholmsm{\"{a}}ssan, Stockholm, Sweden, July 10-15, 2018},
	publisher    = {{PMLR}},
	series       = {Proceedings of Machine Learning Research},
	volume       = 80
}
@article{hunter2007matplotlib,
	title        = {{Matplotlib: A 2D graphics environment}},
	author       = {Hunter, John D.},
	year         = 2007,
	journal      = {Computing in Science \& Engineering},
	publisher    = {IEEE COMPUTER SOC},
	volume       = 9,
	number       = 3,
	abstract     = {Matplotlib is a 2D graphics package used for Python for application development, interactive scripting, and publication-quality image generation across user interfaces and operating systems.}
}
@article{hyttinen2013experiment,
	title        = {{Experiment selection for causal discovery}},
	author       = {Hyttinen, Antti and Eberhardt, Frederick and Hoyer, Patrik O},
	year         = 2013,
	journal      = {Journal of Machine Learning Research},
	publisher    = {Microtome Publishing},
	volume       = 14
}
@inproceedings{hyttinen2014constraint,
	title        = {{Constraint-based Causal Discovery: Conflict Resolution with Answer Set Programming}},
	author       = {Antti Hyttinen and Frederick Eberhardt and Matti J{\"{a}}rvisalo},
	year         = 2014,
	booktitle    = {Proceedings of the Thirtieth Conference on Uncertainty in Artificial Intelligence, {UAI} 2014, Quebec City, Quebec, Canada, July 23-27, 2014},
	publisher    = {{AUAI} Press}
}
@book{hyvaerinen2001independent,
	title        = {{Independent Component Analysis}},
	author       = {Hyv{\"a}rinen, Aapo and Karhunen, Juha and Oja, Erkki},
	year         = 2001,
	month        = jun,
	publisher    = {John Wiley \& Sons},
	abstract     = {A comprehensive introduction to ICA for students and practitioners Independent Component Analysis (ICA) is one of the most exciting new topics in fields such as neural networks, advanced statistics, and signal processing. This is the first book to provide a comprehensive introduction to this new technique complete with the fundamental mathematical background needed to understand and utilize it. It offers a general overview of the basics of ICA, important solutions and algorithms, and in-depth coverage of new applications in image processing, telecommunications, audio signal processing, and more. Independent Component Analysis is divided into four sections that cover: * General mathematical concepts utilized in the book * The basic ICA model and its solution * Various extensions of the basic ICA model * Real-world applications for ICA models Authors Hyvarinen, Karhunen, and Oja are well known for their contributions to the development of ICA and here cover all the relevant theory, new algorithms, and applications in various fields. Researchers, students, and practitioners from a variety of disciplines will find this accessible volume both helpful and informative.}
}
@inproceedings{hyvaerinen2017nonlinear,
	title        = {{Nonlinear ICA of Temporally Dependent Stationary Sources}},
	author       = {Hyvarinen, Aapo and Morioka, Hiroshi},
	year         = 2017,
	month        = {20--22 Apr},
	booktitle    = {Proceedings of the 20th International Conference on Artificial Intelligence and Statistics},
	publisher    = {PMLR},
	series       = {Proceedings of Machine Learning Research},
	volume       = 54,
	abstract     = {We develop a nonlinear generalization of independent component analysis (ICA) or blind source separation, based on temporal dependencies (e.g. autocorrelations). We introduce a nonlinear generative model where the independent sources are assumed to be temporally dependent, non-Gaussian, and stationary, and we observe arbitrarily nonlinear mixtures of them. We develop a method for estimating the model (i.e. separating the sources) based on logistic regression in a neural network which learns to discriminate between a short temporal window of the data vs. a temporal window of temporally permuted data. We prove that the method estimates the sources for general smooth mixing nonlinearities, assuming the sources have sufficiently strong temporal dependencies, and these dependencies are in a certain way different from dependencies found in Gaussian processes. For Gaussian (and similar) sources, the method estimates the nonlinear part of the mixing. We thus provide the first rigorous and general proof of identifiability of nonlinear ICA for temporally dependent sources, together with a practical method for its estimation.}
}
@inproceedings{hyvaerinen2019nonlinear,
	title        = {{Nonlinear ICA Using Auxiliary Variables and Generalized Contrastive Learning}},
	author       = {Hyv{\"a}rinen, Aapo and Sasaki, Hiroaki and Turner, Richard},
	year         = 2019,
	booktitle    = {Proceedings of the {Twenty-Second} International Conference on Artificial Intelligence and Statistics},
	publisher    = {PMLR},
	series       = {Proceedings of Machine Learning Research},
	volume       = 89,
	abstract     = {Nonlinear ICA is a fundamental problem for unsupervised representation learning, emphasizing the capacity to recover the underlying latent variables generating the data (i.e., identifiability). Recently, the very first identifiability proofs for nonlinear ICA have been proposed, leveraging the temporal structure of the independent components. Here, we propose a general framework for nonlinear ICA, which, as a special case, can make use of temporal structure. It is based on augmenting the data by an auxiliary variable, such as the time index, the history of the time series, or any other available information. We propose to learn nonlinear ICA by discriminating between true augmented data, or data in which the auxiliary variable has been randomized. This enables the framework to be implemented algorithmically through logistic regression, possibly in a neural network. We provide a comprehensive proof of the identifiability of the model as well as the consistency of our estimation method. The approach not only provides a general theoretical framework combining and generalizing previously proposed nonlinear ICA models and algorithms, but also brings practical advantages.}
}
@article{hyvarinen1999nonlinear,
	title        = {{Nonlinear Independent Component Analysis: Existence and Uniqueness Results}},
	author       = {Hyv\"{a}rinen, Aapo and Pajunen, Petteri},
	year         = 1999,
	month        = {apr},
	journal      = {Neural Netw.},
	publisher    = {Elsevier Science Ltd.},
	address      = {GBR},
	volume       = 12,
	number       = 3,
	issn         = {0893-6080},
	issue_date   = {April 1999},
	numpages     = 11,
	keywords     = {feature extraction, independent component analysis, blind source separation, redundancy reduction}
}
@inproceedings{hyvarinen2008causal,
	title        = {{Causal Modelling Combining Instantaneous and Lagged Effects: An Identifiable Model Based on Non-Gaussianity}},
	author       = {Hyv\"{a}rinen, Aapo and Shimizu, Shohei and Hoyer, Patrik O.},
	year         = 2008,
	booktitle    = {Proceedings of the 25th International Conference on Machine Learning},
	location     = {Helsinki, Finland},
	publisher    = {Association for Computing Machinery},
	address      = {New York, NY, USA},
	series       = {ICML '08},
	isbn         = 9781605582054,
	url          = {https://doi.org/10.1145/1390156.1390210},
	abstract     = {Causal analysis of continuous-valued variables typically uses either autoregressive models or linear Gaussian Bayesian networks with instantaneous effects. Estimation of Gaussian Bayesian networks poses serious identifiability problems, which is why it was recently proposed to use non-Gaussian models. Here, we show how to combine the non-Gaussian instantaneous model with autoregressive models. We show that such a non-Gaussian model is identifiable without prior knowledge of network structure, and we propose an estimation method shown to be consistent. This approach also points out how neglecting instantaneous effects can lead to completely wrong estimates of the autoregressive coefficients.},
	numpages     = 8
}
@inproceedings{hyvarinen2016unsupervised,
	title        = {{Unsupervised Feature Extraction by Time-Contrastive Learning and Nonlinear ICA}},
	author       = {Hyv\"{a}rinen, Aapo and Morioka, Hiroshi},
	year         = 2016,
	booktitle    = {Proceedings of the 30th International Conference on Neural Information Processing Systems},
	publisher    = {Curran Associates Inc.},
	abstract     = {Nonlinear independent component analysis (ICA) provides an appealing framework for unsupervised feature learning, but the models proposed so far are not identifiable. Here, we first propose a new intuitive principle of unsupervised deep learning from time series which uses the nonstationary structure of the data. Our learning principle, time-contrastive learning (TCL), finds a representation which allows optimal discrimination of time segments (windows). Surprisingly, we show how TCL can be related to a nonlinear ICA model, when ICA is redefined to include temporal nonstationarities. In particular, we show that TCL combined with linear ICA estimates the nonlinear ICA model up to point-wise transformations of the sources, and this solution is unique — thus providing the first identifiability result for nonlinear ICA which is rigorous, constructive, as well as very general.},
	numpages     = 9
}
@inproceedings{ioffe2015batch,
	title        = {{Batch Normalization: Accelerating Deep Network Training by Reducing Internal Covariate Shift}},
	author       = {Ioffe, Sergey and Szegedy, Christian},
	year         = 2015,
	month        = {07--09 Jul},
	booktitle    = {Proceedings of the 32nd International Conference on Machine Learning},
	publisher    = {PMLR},
	address      = {Lille, France},
	series       = {Proceedings of Machine Learning Research},
	volume       = 37,
	abstract     = {Training Deep Neural Networks is complicated by the fact that the distribution of each layer’s inputs changes during training, as the parameters of the previous layers change. This slows down the training by requiring lower learning rates and careful parameter initialization, and makes it notoriously hard to train models with saturating nonlinearities. We refer to this phenomenon as internal covariate shift, and address the problem by normalizing layer inputs. Our method draws its strength from making normalization a part of the model architecture and performing the normalization for each training mini-batch. Batch Normalization allows us to use much higher learning rates and be less careful about initialization, and in some cases eliminates the need for Dropout. Applied to a stateof-the-art image classification model, Batch Normalization achieves the same accuracy with 14 times fewer training steps, and beats the original model by a significant margin. Using an ensemble of batch-normalized networks, we improve upon the best published result on ImageNet classification: reaching 4.82% top-5 test error, exceeding the accuracy of human raters.}
}
@inproceedings{ivanov2019variational,
	title        = {{Variational Autoencoder with Arbitrary Conditioning}},
	author       = {Oleg Ivanov and Michael Figurnov and Dmitry P. Vetrov},
	year         = 2019,
	booktitle    = {7th International Conference on Learning Representations, {ICLR} 2019, New Orleans, LA, USA, May 6-9, 2019}
}
@inproceedings{jaber2020causal,
	title        = {{Causal Discovery from Soft Interventions with Unknown Targets: Characterization and Learning}},
	author       = {Amin Jaber and Murat Kocaoglu and Karthikeyan Shanmugam and Elias Bareinboim},
	year         = 2020,
	booktitle    = {Advances in Neural Information Processing Systems 33, NeurIPS}
}
@inproceedings{jang2017categorical,
	title        = {{Categorical Reparameterization with Gumbel-Softmax}},
	author       = {Eric Jang and Shixiang Gu and Ben Poole},
	year         = 2017,
	booktitle    = {5th International Conference on Learning Representations, {ICLR} 2017, Toulon, France, April 24-26, 2017, Conference Track Proceedings}
}
@article{jaynes1957information,
	title        = {{Information Theory and Statistical Mechanics}},
	author       = {Jaynes, Edward T.},
	year         = 1957,
	month        = {May},
	journal      = {Phys. Rev.},
	publisher    = {American Physical Society},
	volume       = 106,
	issue        = 4,
	numpages     = {0}
}
@article{jaynes1968prior,
	title        = {{Prior Probabilities}},
	author       = {Jaynes, Edwin T.},
	year         = 1968,
	journal      = {IEEE Transactions on Systems Science and Cybernetics},
	volume       = 4,
	number       = 3
}
@article{kalainathan2020causal,
	title        = {{Causal Discovery Toolbox: Uncovering causal relationships in Python.}},
	author       = {Kalainathan, Diviyan and Goudet, Olivier and Dutta, Ritik},
	year         = 2020,
	journal      = {J. Mach. Learn. Res.},
	volume       = 21
}
@article{ke2019learning,
	title        = {{Learning neural causal models from unknown interventions}},
	author       = {Ke, Nan Rosemary and Bilaniuk, Olexa and Goyal, Anirudh and Bauer, Stefan and Larochelle, Hugo and Pal, Chris and Bengio, Yoshua},
	year         = 2019,
	journal      = {arXiv preprint arXiv:1910.01075},
	arxivid      = {1910.01075}
}
@misc{keenan2021cow,
	title        = {{Keenan's 3D Model Repository}},
	author       = {Keenan Crane},
	year         = 2021,
	howpublished = {\url{https://www.cs.cmu.edu/~kmcrane/Projects/ModelRepository/}}
}
@inproceedings{khemakhem2020ice,
	title        = {{ICE-BeeM: Identifiable Conditional Energy-Based Deep Models Based on Nonlinear ICA}},
	author       = {Khemakhem, Ilyes and Monti, Ricardo and Kingma, Diederik and Hyvarinen, Aapo},
	year         = 2020,
	booktitle    = {Advances in Neural Information Processing Systems 33, NeurIPS}
}
@inproceedings{khemakhem2020variational,
	title        = {{Variational Autoencoders and Nonlinear ICA: A Unifying Framework}},
	author       = {Khemakhem, Ilyes and Kingma, Diederik and Monti, Ricardo and Hyvarinen, Aapo},
	year         = 2020,
	booktitle    = {Proceedings of the Twenty Third International Conference on Artificial Intelligence and Statistics},
	publisher    = {PMLR},
	series       = {Proceedings of Machine Learning Research},
	volume       = 108,
	abstract     = {The framework of variational autoencoders allows us to efficiently learn deep latent-variable models, such that the model's marginal distribution over observed variables fits the data. Often, we're interested in going a step further, and want to approximate the true joint distribution over observed and latent variables, including the true prior and posterior distributions over latent variables. This is known to be generally impossible due to unidentifiability of the model. We address this issue by showing that for a broad family of deep latent-variable models, identification of the true joint distribution over observed and latent variables is actually possible up to very simple transformations, thus achieving a principled and powerful form of disentanglement. Our result requires a factorized prior distribution over the latent variables that is conditioned on an additionally observed variable, such as a class label or almost any other observation. We build on recent developments in nonlinear ICA, which we extend to the case with noisy, undercomplete or discrete observations, integrated in a maximum likelihood framework. The result also trivially contains identifiable flow-based generative models as a special case.}
}
@inproceedings{kingma2014auto,
	title        = {{Auto-Encoding Variational Bayes}},
	author       = {Diederik P. Kingma and Max Welling},
	year         = 2014,
	booktitle    = {2nd International Conference on Learning Representations, {ICLR} 2014, Banff, AB, Canada, April 14-16, 2014, Conference Track Proceedings}
}
@inproceedings{kingma2015adam,
	title        = {{Adam: A Method for Stochastic Optimization}},
	author       = {Diederik P. Kingma and Jimmy Ba},
	year         = 2015,
	booktitle    = {3rd International Conference on Learning Representations, {ICLR} 2015, San Diego, CA, USA, May 7-9, 2015, Conference Track Proceedings}
}
@article{kingma2016improved,
	title        = {{Improved variational inference with inverse autoregressive flow}},
	author       = {Kingma, Durk P and Salimans, Tim and Jozefowicz, Rafal and Chen, Xi and Sutskever, Ilya and Welling, Max},
	year         = 2016,
	journal      = {Advances in neural information processing systems},
	volume       = 29
}
@inproceedings{kingma2018glow,
	title        = {{Glow: Generative Flow with Invertible 1x1 Convolutions}},
	author       = {Kingma, Durk P and Dhariwal, Prafulla},
	year         = 2018,
	booktitle    = {Advances in Neural Information Processing Systems},
	publisher    = {Curran Associates, Inc.},
	volume       = 31
}
@article{kipf2021conditional,
	title        = {{Conditional Object-Centric Learning from Video}},
	author       = {Kipf, Thomas and Elsayed, Gamaleldin F and Mahendran, Aravindh and Stone, Austin and Sabour, Sara and Heigold, Georg and Jonschkowski, Rico and Dosovitskiy, Alexey and Greff, Klaus},
	year         = 2022,
	journal      = {International Conference on Learning Representations (ICLR)}
}
@inproceedings{klindt2021towards,
	title        = {{Towards Nonlinear Disentanglement in Natural Data with Temporal Sparse Coding}},
	author       = {Klindt, David and Schott, Lukas and Sharma, Yash and Ustyuzhaninov, Ivan and Brendel, Wieland and Bethge, Matthias and Paiton, Dylan},
	year         = 2021,
	booktitle    = {International Conference on Learning Representations ({ICLR})},
	abstract     = {We construct an unsupervised learning model that achieves nonlinear disentanglement of underlying factors of variation in naturalistic videos. Previous work suggests that representations can be disentangled if all but a few factors in the environment stay constant at any point in time. As a result, algorithms proposed for this problem have only been tested on carefully constructed datasets with this exact property, leaving it unclear whether they will transfer to natural scenes. Here we provide evidence that objects in segmented natural movies undergo transitions that are typically small in magnitude with occasional large jumps, which is characteristic of a temporally sparse distribution. We leverage this finding and present SlowVAE, a model for unsupervised representation learning that uses a sparse prior on temporally adjacent observations to disentangle generative factors without any assumptions on the number of changing factors. We provide a proof of identifiability and show that the model reliably learns disentangled representations on several established benchmark datasets, often surpassing the current state-of-the-art. We additionally demonstrate transferability towards video datasets with natural dynamics, Natural Sprites and KITTI Masks, which we contribute as benchmarks for guiding disentanglement research towards more natural data domains.}
}
@inproceedings{kocaoglu2017cost,
	title        = {{Cost-Optimal Learning of Causal Graphs}},
	author       = {Kocaoglu, Murat and Dimakis, Alex and Vishwanath, Sriram},
	year         = 2017,
	booktitle    = {Proceedings of the 34th International Conference on Machine Learning},
	publisher    = {PMLR},
	series       = {Proceedings of Machine Learning Research},
	volume       = 70,
	url          = {http://proceedings.mlr.press/v70/kocaoglu17a.html},
	abstract     = {We consider the problem of learning a causal graph over a set of variables with interventions. We study the cost-optimal causal graph learning problem: For a given skeleton (undirected version of the causal graph), design the set of interventions with minimum total cost, that can uniquely identify any causal graph with the given skeleton. We show that this problem is solvable in polynomial time. Later, we consider the case when the number of interventions is limited. For this case, we provide polynomial time algorithms when the skeleton is a tree or a clique tree. For a general chordal skeleton, we develop an efficient greedy algorithm, which can be improved when the causal graph skeleton is an interval graph.},
	keywords     = {Intervention Design}
}
@inproceedings{kocaoglu2017experimental,
	title        = {{Experimental Design for Learning Causal Graphs with Latent Variables}},
	author       = {Murat Kocaoglu and Karthikeyan Shanmugam and Elias Bareinboim},
	year         = 2017,
	booktitle    = {Advances in Neural Information Processing Systems 30: Annual Conference on Neural Information Processing Systems 2017, December 4-9, 2017, Long Beach, CA, {USA}},
	url          = {https://proceedings.neurips.cc/paper/2017/hash/291d43c696d8c3704cdbe0a72ade5f6c-Abstract.html}
}
@inproceedings{kocaoglu2019characterization,
	title        = {{Characterization and Learning of Causal Graphs with Latent Variables from Soft Interventions}},
	author       = {Murat Kocaoglu and Amin Jaber and Karthikeyan Shanmugam and Elias Bareinboim},
	year         = 2019,
	booktitle    = {Advances in Neural Information Processing Systems 32: Annual Conference on Neural Information Processing Systems 2019, NeurIPS 2019, December 8-14, 2019, Vancouver, BC, Canada}
}
@article{kolve2017ai,
	title        = {{AI2-THOR: An interactive 3d environment for visual ai}},
	author       = {Kolve, Eric and Mottaghi, Roozbeh and Han, Winson and VanderBilt, Eli and Weihs, Luca and Herrasti, Alvaro and Gordon, Daniel and Zhu, Yuke and Gupta, Abhinav and Farhadi, Ali},
	year         = 2017,
	journal      = {arXiv preprint arXiv:1712.05474},
	note         = {Web demo \url{https://ai2thor.allenai.org/demo/}}
}
@book{korb2010bayesian,
	title        = {{Bayesian artificial intelligence, second edition}},
	author       = {Korb, {Kevin B.} and Nicholson, {Ann E.}},
	year         = 2010,
	day          = 1,
	publisher    = {CRC Press},
	address      = {Australia},
	isbn         = 9781439815915,
	abstract     = {Updated and expanded, Bayesian Artificial Intelligence, Second Edition provides a practical and accessible introduction to the main concepts, foundation, and applications of Bayesian networks. It focuses on both the causal discovery of networks and Bayesian inference procedures. Adopting a causal interpretation of Bayesian networks, the authors discuss the use of Bayesian networks for causal modeling. They also draw on their own applied research to illustrate various applications of the technology. New to the Second Edition •New chapter on Bayesian network classifiers •New section on object-oriented Bayesian networks •New section that addresses foundational problems with causal discovery and Markov blanket discovery •New section that covers methods of evaluating causal discovery programs •Discussions of many common modeling errors •New applications and case studies •More coverage on the uses of causal interventions to understand and reason with causal Bayesian networks Illustrated with real case studies, the second edition of this bestseller continues to cover the groundwork of Bayesian networks. It presents the elements of Bayesian network technology, automated causal discovery, and learning probabilities from data and shows how to employ these technologies to develop probabilistic expert systems. Web Resource The book's website at www.csse.monash.edu.au/bai/book/book.html offers a variety of supplemental materials, including example Bayesian networks and data sets. Instructors can email the authors for sample solutions to many of the problems in the text.}
}
@inproceedings{krishnamurthy1996fitting,
	title        = {{Fitting Smooth Surfaces to Dense Polygon Meshes}},
	author       = {Krishnamurthy, Venkat and Levoy, Marc},
	year         = 1996,
	booktitle    = {Proceedings of the 23rd Annual Conference on Computer Graphics and Interactive Techniques},
	publisher    = {Association for Computing Machinery},
	address      = {New York, NY, USA},
	series       = {SIGGRAPH '96},
	isbn         = {0897917464},
	numpages     = 12,
	keywords     = {B-spline surfaces, parameterization, surface fitting, dense polygon meshes, displacement maps}
}
@book{kullback1997information,
	title        = {{Information theory and statistics}},
	author       = {Kullback, Solomon},
	year         = 1997,
	publisher    = {Courier Corporation}
}
@inproceedings{kumar2018variational,
	title        = {{Variational Inference of Disentangled Latent Concepts from Unlabeled Observations}},
	author       = {Abhishek Kumar and Prasanna Sattigeri and Avinash Balakrishnan},
	year         = 2018,
	booktitle    = {6th International Conference on Learning Representations, {ICLR} 2018, Vancouver, BC, Canada, April 30 - May 3, 2018, Conference Track Proceedings}
}
@inproceedings{kumar2021disentangling,
	title        = {{Disentangling mixtures of unknown causal interventions}},
	author       = {Kumar, Abhinav and Sinha, Gaurav},
	year         = 2021,
	month        = {27--30 Jul},
	booktitle    = {Proceedings of the Thirty-Seventh Conference on Uncertainty in Artificial Intelligence},
	publisher    = {PMLR},
	series       = {Proceedings of Machine Learning Research},
	volume       = 161,
	abstract     = {In many real-world scenarios, such as gene knockout experiments, targeted interventions are often accompanied by unknown interventions at off-target sites. Moreover, different units can get randomly exposed to different unknown interventions, thereby creating a mixture of interventions. Identifying different components of this mixture can be very valuable in some applications. Motivated by such situations, in this work, we study the problem of identifying all components present in a mixture of interventions on a given causal Bayesian Network. We construct examples to show that, in general, the components are not identifiable from the mixture distribution. Next, assuming that the given network satisfies a positivity condition, we show that, if the set of mixture components satisfy a mild exclusion assumption, then they can be uniquely identified. Our proof gives an efficient algorithm to recover these targets from the exponentially large search space of possible targets. In the more realistic scenario, where distributions are given via finitely many samples, we conduct a simulation study to analyze the performance of an algorithm derived from our identifiability proof.}
}
@inproceedings{lachapelle2020gradient,
	title        = {{Gradient-Based Neural DAG Learning}},
	author       = {S{\'{e}}bastien Lachapelle and Philippe Brouillard and Tristan Deleu and Simon Lacoste{-}Julien},
	year         = 2020,
	booktitle    = {8th International Conference on Learning Representations, {ICLR} 2020, Addis Ababa, Ethiopia, April 26-30, 2020}
}
@inproceedings{lachapelle2021disentanglement,
	title        = {{Disentanglement via Mechanism Sparsity Regularization: A New Principle for Nonlinear ICA}},
	author       = {Sebastien Lachapelle and Pau Rodriguez and R{\'e}mi Le and Yash Sharma and Katie E Everett and Alexandre Lacoste and Simon Lacoste-Julien},
	year         = 2022,
	booktitle    = {First Conference on Causal Learning and Reasoning}
}
@inproceedings{lachapelle2022partial,
	title        = {{Partial Disentanglement via Mechanism Sparsity}},
	author       = {Lachapelle, S{\'e}bastien and Lacoste-Julien, Simon},
	year         = 2022,
	booktitle    = {UAI 2022 Workshop on Causal Representation Learning}
}
@article{lauritzen1988local,
	title        = {{Local computations with probabilities on graphical structures and their application to expert systems}},
	author       = {S. Lauritzen and D. Spiegelhalter},
	year         = 1988,
	journal      = {Journal of the royal statistical society series b-methodological},
	volume       = 50
}
@inproceedings{li2020acflow,
	title        = {{ACFlow: Flow Models for Arbitrary Conditional Likelihoods}},
	author       = {Yang Li and Shoaib Akbar and Junier Oliva},
	year         = 2020,
	booktitle    = {Proceedings of the 37th International Conference on Machine Learning, {ICML} 2020, 13-18 July 2020, Virtual Event},
	publisher    = {{PMLR}},
	series       = {Proceedings of Machine Learning Research},
	volume       = 119
}
@inproceedings{lippe2022citris,
	title        = {{CITRIS: Causal Identifiability from Temporal Intervened Sequences}},
	author       = {Lippe, Phillip and Magliacane, Sara and L{\"o}we, Sindy and Asano, Yuki M. and Cohen, Taco and Gavves, Efstratios},
	year         = 2022,
	booktitle    = {Proceedings of the 39th International Conference on Machine Learning, {ICML}}
}
@inproceedings{lippe2022enco,
	title        = {{Efficient Neural Causal Discovery without Acyclicity Constraints}},
	author       = {Lippe, Phillip and Cohen, Taco and Gavves, Efstratios},
	year         = 2022,
	booktitle    = {International Conference on Learning Representations}
}
@inproceedings{lippe2022icitris,
    title        = {Causal Representation Learning for Instantaneous and Temporal Effects in Interactive Systems},
    author       = {Phillip Lippe and Sara Magliacane and Sindy L{\"o}we and Yuki M Asano and Taco Cohen and Efstratios Gavves},
    year         = 2023,
    booktitle    = {The Eleventh International Conference on Learning Representations}
}
@inproceedings{lippe2022intervention,
	title        = {{Intervention Design for Causal Representation Learning}},
	author       = {Phillip Lippe and Sara Magliacane and Sindy L{\"o}we and Yuki M Asano and Taco Cohen and Efstratios Gavves},
	year         = 2022,
	booktitle    = {UAI 2022 Workshop on Causal Representation Learning}
}
@misc{lippe2022uvadlc,
	title        = {{UvA Deep Learning Tutorials}},
	author       = {Phillip Lippe},
	year         = 2022,
	howpublished = {\url{https://uvadlc-notebooks.readthedocs.io/en/latest/}}
}
@inproceedings{locatello2019challenging,
	title        = {{Challenging Common Assumptions in the Unsupervised Learning of Disentangled Representations}},
	author       = {Locatello, Francesco and Bauer, Stefan and Lucic, Mario and Raetsch, Gunnar and Gelly, Sylvain and Sch{\"o}lkopf, Bernhard and Bachem, Olivier},
	year         = 2019,
	month        = {09--15 Jun},
	booktitle    = {Proceedings of the 36th International Conference on Machine Learning},
	publisher    = {PMLR},
	series       = {Proceedings of Machine Learning Research},
	volume       = 97,
	abstract     = {The key idea behind the unsupervised learning of disentangled representations is that real-world data is generated by a few explanatory factors of variation which can be recovered by unsupervised learning algorithms. In this paper, we provide a sober look at recent progress in the field and challenge some common assumptions. We first theoretically show that the unsupervised learning of disentangled representations is fundamentally impossible without inductive biases on both the models and the data. Then, we train more than $12000$ models covering most prominent methods and evaluation metrics in a reproducible large-scale experimental study on seven different data sets. We observe that while the different methods successfully enforce properties “encouraged” by the corresponding losses, well-disentangled models seemingly cannot be identified without supervision. Furthermore, increased disentanglement does not seem to lead to a decreased sample complexity of learning for downstream tasks. Our results suggest that future work on disentanglement learning should be explicit about the role of inductive biases and (implicit) supervision, investigate concrete benefits of enforcing disentanglement of the learned representations, and consider a reproducible experimental setup covering several data sets.}
}
@inproceedings{locatello2020disentangling,
	title        = {{Disentangling Factors of Variations Using Few Labels}},
	author       = {Francesco Locatello and Michael Tschannen and Stefan Bauer and Gunnar Rätsch and Bernhard Schölkopf and Olivier Bachem},
	year         = 2020,
	booktitle    = {International Conference on Learning Representations}
}
@inproceedings{locatello2020object,
	title        = {{Object-Centric Learning with Slot Attention}},
	author       = {Locatello, Francesco and Weissenborn, Dirk and Unterthiner, Thomas and Mahendran, Aravindh and Heigold, Georg and Uszkoreit, Jakob and Dosovitskiy, Alexey and Kipf, Thomas},
	year         = 2020,
	booktitle    = {Advances in Neural Information Processing Systems},
	publisher    = {Curran Associates, Inc.},
	volume       = 33
}
@inproceedings{locatello2020weakly,
	title        = {{Weakly-Supervised Disentanglement Without Compromises}},
	author       = {Francesco Locatello and Ben Poole and Gunnar R{\"{a}}tsch and Bernhard Sch{\"{o}}lkopf and Olivier Bachem and Michael Tschannen},
	year         = 2020,
	booktitle    = {Proceedings of the 37th International Conference on Machine Learning, {ICML}}
}
@article{loewe2022complex,
	title        = {{Complex-Valued Autoencoders for Object Discovery}},
	author       = {Sindy L{\"o}we and Phillip Lippe and Maja Rudolph and Max Welling},
	year         = 2022,
	journal      = {Transactions on Machine Learning Research}
}
@book{luce1959individual,
	title        = {{Individual choice behavior}},
	author       = {Luce, R Duncan},
	year         = 1959,
	booktitle    = {Individual choice behavior.},
	publisher    = {John Wiley},
	address      = {Oxford,  England},
	abstract     = {This research monograph is devoted to a theoretical (mathematical) analysis of one of the major themes of interest to psychologists: choice. The analysis begins by stating a general axiom that may hold among the probabilities of choice from related sets of alternatives. This is shown to imply the existence of a ratio scale that is then used to analyze a number of traditional problems. The 1st subject treated is psychophysics, and covers areas involving time- and space-order effects, Fechner's equal jnd problem, power law in psychophysics and its relation to discrimination data, psychophysical interaction between 2 independent physical variables and possible correlates with Stevens' distinction between prothetic and metathetic continua, Thurston's low of comparative judgment, signal detectability theory, and ranking of stimuli. The next major theme studied is utility theory. Unusual results are obtained which suggest an experiment to test the theory. Topics in learning are analyzed in a concluding chapter which uses the stochastic theories of learning as the basic approach, with the exception that distributions of response strengths are assumed to be transformed rather than response probabilities. 3 classes of learning operators emerge, both linear and nonlinear. (PsycINFO Database Record (c) 2016 APA, all rights reserved)}
}
@article{macosko2015h,
	title        = {{Highly Parallel Genome-wide Expression Profiling of Individual Cells Using Nanoliter Droplets}},
	author       = {Macosko, E. Z.  and Basu, A.  and Satija, R.  and Nemesh, J.  and Shekhar, K.  and Goldman, M.  and Tirosh, I.  and Bialas, A. R.  and Kamitaki, N.  and Martersteck, E. M.  and Trombetta, J. J.  and Weitz, D. A.  and Sanes, J. R.  and Shalek, A. K.  and Regev, A.  and McCarroll, S. A.},
	year         = 2015,
	journal      = {Cell},
	volume       = 161,
	number       = 5
}
@inproceedings{mahmood2014weighted,
	title        = {{Weighted importance sampling for off-policy learning with linear function approximation}},
	author       = {Ashique Rupam Mahmood and Hado van Hasselt and Richard S. Sutton},
	year         = 2014,
	booktitle    = {Advances in Neural Information Processing Systems 27: Annual Conference on Neural Information Processing Systems 2014, December 8-13 2014, Montreal, Quebec, Canada}
}
@misc{makoviychuk2021isaac,
	title        = {{Isaac Gym: High Performance GPU-Based Physics Simulation For Robot Learning}},
	author       = {Viktor Makoviychuk and Lukasz Wawrzyniak and Yunrong Guo and Michelle Lu and Kier Storey and Miles Macklin and David Hoeller and Nikita Rudin and Arthur Allshire and Ankur Handa and Gavriel State},
	year         = 2021,
	journal      = {arXiv preprint arXiv:2108.10470}
}
@phdthesis{meek1997graphical,
	title        = {{Graphical Models: Selecting causal and statistical models}},
	author       = {Meek, Christopher},
	year         = 1997,
	school       = {Carnegie Mellon University}
}
@inproceedings{moneta2006graphical,
	title        = {{Graphical models for the identification of causal structures in multivariate time series models}},
	author       = {Moneta, Alessio and Spirtes, Peter},
	year         = 2006,
	booktitle    = {9th Joint International Conference on Information Sciences (JCIS-06)},
	organization = {Atlantis press}
}
@inproceedings{monti2019causal,
	title        = {{Causal Discovery with General Non-Linear Relationships using Non-Linear ICA}},
	author       = {Ricardo Pio Monti and Kun Zhang and Aapo Hyv{\"{a}}rinen},
	year         = 2019,
	booktitle    = {Proceedings of the Thirty-Fifth Conference on Uncertainty in Artificial Intelligence, {UAI}}
}
@article{mooij2020joint,
	title        = {{Joint Causal Inference from Multiple Contexts}},
	author       = {Joris M. Mooij and Sara Magliacane and Tom Claassen},
	year         = 2020,
	journal      = {Journal of Machine Learning Research},
	volume       = 21,
	number       = 99
}
@inproceedings{morshed2011simultaneous,
	title        = {{Simultaneous Learning of Instantaneous and Time-Delayed Genetic Interactions Using Novel Information Theoretic Scoring Technique}},
	author       = {Morshed, Nizamul and Chetty, Madhu and Vinh, Nguyen Xuan},
	year         = 2011,
	booktitle    = {Neural Information Processing},
	publisher    = {Springer Berlin Heidelberg},
	address      = {Berlin, Heidelberg},
	isbn         = {978-3-642-24958-7},
	abstract     = {Understanding gene interactions is a fundamental question in systems biology. Currently, modeling of gene regulations assumes that genes interact either instantaneously or with time delay. In this paper, we introduce a framework based on the Bayesian Network (BN) formalism that can represent both instantaneous and time-delayed interactions between genes simultaneously. Also, a novel scoring metric having firm mathematical underpinnings is then proposed that, unlike other recent methods, can score both interactions concurrently and takes into account the biological fact that multiple regulators may regulate a gene jointly, rather than in an isolated pair-wise manner. Further, a gene regulatory network inference method employing evolutionary search that makes use of the framework and the scoring metric is also presented. Experiments carried out using synthetic data as well as the well known Saccharomyces cerevisiae gene expression data show the effectiveness of our approach.}
}
@article{Murphy_DBN,
	title        = {{Dynamic Bayesian Networks: Representation, Inference and Learning}},
	author       = {Murphy, Kevin},
	year         = 2002,
	journal      = {UC Berkeley, Computer Science Division}
}
@phdthesis{newell1975utilization,
	title        = {{The Utilization of Procedure Models in Digital Image Synthesis.}},
	author       = {Newell, Martin Edward},
	year         = 1975,
	publisher    = {The University of Utah},
	note         = {AAI7529894},
	school       = {The University of Utah}
}
@inproceedings{ng2020on,
	title        = {{On the Role of Sparsity and DAG Constraints for Learning Linear DAGs}},
	author       = {Ng, Ignavier and Ghassami, AmirEmad and Zhang, Kun},
	year         = 2020,
	booktitle    = {Advances in Neural Information Processing Systems}
}
@inproceedings{ng2022masked,
	title        = {{Masked Gradient-Based Causal Structure Learning}},
	author       = {Ignavier Ng and Shengyu Zhu and Zhuangyan Fang and Haoyang Li and Zhitang Chen and Jun Wang},
	year         = 2022,
	booktitle    = {Proceedings of the 2022 SIAM International Conference on Data Mining (SDM)},
	chapter      = {}
}
@article{nielsen2020survae,
	title        = {{Survae flows: Surjections to bridge the gap between vaes and flows}},
	author       = {Nielsen, Didrik and Jaini, Priyank and Hoogeboom, Emiel and Winther, Ole and Welling, Max},
	year         = 2020,
	journal      = {Advances in Neural Information Processing Systems},
	volume       = 33
}
@article{nuzzi2021extending,
	title        = {{Extending the spectral decomposition of Granger causality to include instantaneous influences: application to the control mechanisms of heart rate variability}},
	author       = {Nuzzi, D and Stramaglia, S and Javorka, M and Marinazzo, Daniele and Porta, A and Faes, Luca},
	year         = 2021,
	journal      = {Philosophical Transactions of the Royal Society A},
	publisher    = {The Royal Society},
	volume       = 379,
	number       = 2212
}
@article{opgen-rhein2007from,
	title        = {{From correlation to causation networks: a simple approximate learning algorithm and its application to high-dimensional plant gene expression data}},
	author       = {Opgen-Rhein, Rainer and Strimmer, Korbinian},
	year         = 2007,
	journal      = {BMC Systems Biology},
	volume       = 1,
	number       = 1,
	issn         = {1752-0509},
	abstract     = {The use of correlation networks is widespread in the analysis of gene expression and proteomics data, even though it is known that correlations not only confound direct and indirect associations but also provide no means to distinguish between cause and effect. For "causal" analysis typically the inference of a directed graphical model is required. However, this is rather difficult due to the curse of dimensionality.}
}
@inproceedings{paszke2019pytorch,
	title        = {{PyTorch: An Imperative Style, High-Performance Deep Learning Library}},
	author       = {Adam Paszke and Sam Gross and Francisco Massa and Adam Lerer and James Bradbury and Gregory Chanan and Trevor Killeen and Zeming Lin and Natalia Gimelshein and Luca Antiga and Alban Desmaison and Andreas K{\"{o}}pf and Edward Yang and Zachary DeVito and Martin Raison and Alykhan Tejani and Sasank Chilamkurthy and Benoit Steiner and Lu Fang and Junjie Bai and Soumith Chintala},
	year         = 2019,
	booktitle    = {Advances in Neural Information Processing Systems 32: Annual Conference on Neural Information Processing Systems 2019, NeurIPS 2019, December 8-14, 2019, Vancouver, BC, Canada}
}
@book{pearl1988probabilistic,
	title        = {{Probabilistic Reasoning in Intelligent Systems: Networks of Plausible Inference}},
	author       = {Pearl, Judea},
	year         = 1988,
	publisher    = {Morgan Kaufmann Publishers Inc.},
	address      = {San Francisco, CA, USA},
	isbn         = {0934613737}
}
@book{pearl2009causality,
	title        = {{Causality: Models, Reasoning and Inference}},
	author       = {Pearl, Judea},
	year         = 2009,
	publisher    = {Cambridge University Press},
	address      = {USA},
	isbn         = {052189560X},
	abstract     = {Written by one of the preeminent researchers in the field, this book provides a comprehensive exposition of modern analysis of causation. It shows how causality has grown from a nebulous concept into a mathematical theory with significant applications in the fields of statistics, artificial intelligence, economics, philosophy, cognitive science, and the health and social sciences. Judea Pearl presents and unifies the probabilistic, manipulative, counterfactual, and structural approaches to causation and devises simple mathematical tools for studying the relationships between causal connections and statistical associations. The book will open the way for including causal analysis in the standard curricula of statistics, artificial intelligence, business, epidemiology, social sciences, and economics. Students in these fields will find natural models, simple inferential procedures, and precise mathematical definitions of causal concepts that traditional texts have evaded or made unduly complicated. The first edition of Causality has led to a paradigmatic change in the way that causality is treated in statistics, philosophy, computer science, social science, and economics. Cited in more than 3,000 scientific publications, it continues to liberate scientists from the traditional molds of statistical thinking. In this revised edition, Judea Pearl elucidates thorny issues, answers readers' questions, and offers a panoramic view of recent advances in this field of research. Causality will be of interests to students and professionals in a wide variety of fields. Anyone who wishes to elucidate meaningful relationships from data, predict effects of actions and policies, assess explanations of reported events, or form theories of causal understanding and causal speech will find this book stimulating and invaluable.},
	edition      = {2nd}
}
@article{peters2015structural,
	title        = {{Structural Intervention Distance (SID) for Evaluating Causal Graphs}},
	author       = {Peters, Jonas and B{\"u}hlmann, Peters},
	year         = 2015,
	journal      = {Neural Computation},
	volume       = 27,
	number       = 3
}
@article{peters2016causal,
	title        = {{Causal inference by using invariant prediction: identification and confidence intervals}},
	author       = {Peters, Jonas and B{\"u}hlmann, Peter and Meinshausen, Nicolai},
	year         = 2016,
	journal      = {Journal of the Royal Statistical Society. Series B (Statistical Methodology)},
	publisher    = {JSTOR}
}
@book{peters2017elements,
	title        = {{Elements of Causal Inference: Foundations and Learning Algorithms}},
	author       = {Peters, Jonas and Janzing, Dominik and Schlkopf, Bernhard},
	year         = 2017,
	publisher    = {The MIT Press},
	isbn         = {0262037319},
	abstract     = {A concise and self-contained introduction to causal inference, increasingly important in data science and machine learning. The mathematization of causality is a relatively recent development, and has become increasingly important in data science and machine learning. This book offers a self-contained and concise introduction to causal models and how to learn them from data. After explaining the need for causal models and discussing some of the principles underlying causal inference, the book teaches readers how to use causal models: how to compute intervention distributions, how to infer causal models from observational and interventional data, and how causal ideas could be exploited for classical machine learning problems. All of these topics are discussed first in terms of two variables and then in the more general multivariate case. The bivariate case turns out to be a particularly hard problem for causal learning because there are no conditional independences as used by classical methods for solving multivariate cases. The authors consider analyzing statistical asymmetries between cause and effect to be highly instructive, and they report on their decade of intensive research into this problem. The book is accessible to readers with a background in machine learning or statistics, and can be used in graduate courses or as a reference for researchers. The text includes code snippets that can be copied and pasted, exercises, and an appendix with a summary of the most important technical concepts.}
}
@article{plackett1975the,
	title        = {{The Analysis of Permutations}},
	author       = {R. L. Plackett},
	year         = 1975,
	journal      = {Journal of the Royal Statistical Society. Series C (Applied Statistics)},
	publisher    = {[Wiley, Royal Statistical Society]},
	volume       = 24,
	number       = 2,
	issn         = {00359254, 14679876},
	abstract     = {A probability distribution is defined over the r! permutations of r objects in such a way as to incorporate up to r! - 1 parameters. Problems of estimation and testing are considered. The results are applied to data on voting at elections and beanstores.}
}
@inproceedings{praun2000lapped,
	title        = {{Lapped Textures}},
	author       = {Emil Praun and Adam Finkelstein and Hugues Hoppe},
	year         = 2000,
	month        = jul,
	booktitle    = {Proceedings of ACM SIGGRAPH 2000}
}
@article{ramachandran2017searching,
	title        = {{Searching for activation functions}},
	author       = {Ramachandran, Prajit and Zoph, Barret and Le, Quoc V},
	year         = 2017,
	journal      = {arXiv preprint arXiv:1710.05941}
}
@inproceedings{reed2014learning,
	title        = {{Learning to Disentangle Factors of Variation with Manifold Interaction}},
	author       = {Reed, Scott and Sohn, Kihyuk and Zhang, Yuting and Lee, Honglak},
	year         = 2014,
	month        = {22--24 Jun},
	booktitle    = {Proceedings of the 31st International Conference on Machine Learning},
	publisher    = {PMLR},
	address      = {Bejing, China},
	series       = {Proceedings of Machine Learning Research},
	volume       = 32,
	abstract     = {Many latent factors of variation interact to generate sensory data; for example pose, morphology and expression in face images. We propose to learn manifold coordinates for the relevant factors of variation and to model their joint interaction. Most existing feature learning algorithms focus on a single task and extract features that are sensitive to the task-relevant factors and invariant to all others. However, models that just extract a single set of invariant features do not exploit the relationships among the latent factors. To address this we propose a higher-order Boltzmann machine that incorporates multiplicative interactions among groups of hidden units that each learn to encode a factor of variation. Furthermore, we propose a manifold-based training strategy that allows effective disentangling, meaning that units in each group encode a distinct type of variation. Our model achieves state-of-the-art emotion recognition and face verification performance on the Toronto Face Database, and we also demonstrate disentangled features learned on the CMU Multi-PIE dataset.}
}
@inproceedings{reizinger2022embrace,
	title        = {{Embrace the Gap: VAEs Perform Independent Mechanism Analysis}},
	author       = {Reizinger, Patrik and Gresele, Luigi and Brady, Jack and von K{\"u}gelgen, Julius and Zietlow, Dominik and Sch{\"o}lkopf, Bernhard and Martius, Georg and Brendel, Wieland and Besserve, Michel},
	year         = 2022,
	booktitle    = {Advances in Neural Information Processing Systems 35, NeurIPS}
}
@article{renyi1961random,
	title        = {{On random generating elements of a finite Boolean algebra}},
	author       = {R{\'e}nyi, A},
	year         = 1961,
	journal      = {Acta Sci. Math. Szeged},
	volume       = 22,
	number       = {75-81}
}
@inproceedings{wu2018group,
	title        = {Group normalization},
	author       = {Wu, Yuxin and He, Kaiming},
	year         = 2018,
	booktitle    = {Proceedings of the European conference on computer vision (ECCV)},
	pages        = {3--19}
}
@inproceedings{rezende2015variational,
	title        = {{Variational Inference with Normalizing Flows}},
	author       = {Danilo Jimenez Rezende and Shakir Mohamed},
	year         = 2015,
	booktitle    = {Proceedings of the 32nd International Conference on Machine Learning, {ICML}}
}
@article{robins2000marginal,
	title        = {{Marginal Structural Models and Causal Inference in Epidemiology}},
	author       = {Robins, J.M. and Hernan, M.A. and Brumback, B},
	year         = 2000,
	journal      = {Epidemiology},
	volume       = 11,
	number       = 5,
	date-added   = {2007-09-03 22:45:16 -0500},
	date-modified = {2007-09-03 22:45:16 -0500},
	interhash    = {63c7c3d9a22bd65f987ac8b4a69b271c},
	intrahash    = {716acd3701439b14f132c6aa3d7ec1b5},
	keywords     = {imported}
}
@article{rothenhausler2015backshift,
	title        = {{BACKSHIFT: Learning causal cyclic graphs from unknown shift interventions}},
	author       = {Rothenh{\"a}usler, Dominik and Heinze, Christina and Peters, Jonas and Meinshausen, Nicolai},
	year         = 2015,
	journal      = {Advances in Neural Information Processing Systems},
	volume       = 28
}
@misc{rusinkiewicz2021head,
	title        = {{Suggestive Contour Gallery}},
	author       = {Szymon Rusinkiewicz and Doug DeCarlo and Adam Finkelstein and Anothony Santella},
	year         = 2021,
	howpublished = {\url{https://gfx.cs.princeton.edu/proj/sugcon/models/}}
}
@article{sachs2005causal,
	title        = {{Causal Protein-Signaling Networks Derived from Multiparameter Single-Cell Data}},
	author       = {K. Sachs and O. Perez and D. Pe’er and D. Lauffenburger and G. Nolan},
	year         = 2005,
	journal      = {Science},
	volume       = 308
}
@inproceedings{salimans2017pixelcnn,
	title        = {{PixelCNN++: A PixelCNN Implementation with Discretized Logistic Mixture Likelihood and Other Modifications}},
	author       = {Tim Salimans and Andrej Karpathy and Xi Chen and Diederik P. Kingma},
	year         = 2017,
	booktitle    = {ICLR}
}
@inproceedings{schoelkopf2012on,
	title        = {{On causal and anticausal learning}},
	author       = {Bernhard Sch{\"{o}}lkopf and Dominik Janzing and Jonas Peters and Eleni Sgouritsa and Kun Zhang and Joris M. Mooij},
	year         = 2012,
	booktitle    = {Proceedings of the 29th International Conference on Machine Learning, {ICML} 2012, Edinburgh, Scotland, UK, June 26 - July 1, 2012},
	publisher    = {icml.cc / Omnipress}
}
@article{schoelkopf2021towards,
	title        = {{Toward causal representation learning}},
	author       = {Sch{\"o}lkopf, Bernhard and Locatello, Francesco and Bauer, Stefan and Ke, Nan Rosemary and Kalchbrenner, Nal and Goyal, Anirudh and Bengio, Yoshua},
	year         = 2021,
	journal      = {Proceedings of the IEEE},
	publisher    = {IEEE},
	volume       = 109,
	number       = 5
}
@article{scutari2010learning,
	title        = {{Learning Bayesian Networks with the bnlearn R Package}},
	author       = {Marco Scutari},
	year         = 2010,
	journal      = {Journal of Statistical Software},
	volume       = 35,
	number       = 3
}
@article{seitzer2021causal,
	title        = {{Causal influence detection for improving efficiency in reinforcement learning}},
	author       = {Seitzer, Maximilian and Sch{\"o}lkopf, Bernhard and Martius, Georg},
	year         = 2021,
	journal      = {Advances in Neural Information Processing Systems},
	volume       = 34
}
@article{shanmugam2015learning,
	title        = {{Learning Causal Graphs with Small Interventions}},
	author       = {Shanmugam, Karthikeyan and Kocaoglu, Murat and Dimakis, Alexandros G and Vishwanath, Sriram},
	year         = 2015,
	journal      = {Advances in Neural Information Processing Systems},
	volume       = 28
}
@article{shimizu2006linear,
	title        = {{A Linear Non-Gaussian Acyclic Model for Causal Discovery}},
	author       = {Shimizu, Shohei and Hoyer, Patrik O. and Hyv\"{a}rinen, Aapo and Kerminen, Antti},
	year         = 2006,
	month        = {dec},
	journal      = {J. Mach. Learn. Res.},
	publisher    = {JMLR.org},
	volume       = 7,
	abstract     = {In recent years, several methods have been proposed for the discovery of causal structure from non-experimental data. Such methods make various assumptions on the data generating process to facilitate its identification from purely observational data. Continuing this line of research, we show how to discover the complete causal structure of continuous-valued data, under the assumptions that (a) the data generating process is linear, (b) there are no unobserved confounders, and (c) disturbance variables have non-Gaussian distributions of non-zero variances. The solution relies on the use of the statistical method known as independent component analysis, and does not require any pre-specified time-ordering of the variables. We provide a complete Matlab package for performing this LiNGAM analysis (short for Linear Non-Gaussian Acyclic Model), and demonstrate the effectiveness of the method using artificially generated data and real-world data.},
	numpages     = 28
}
@inproceedings{shoshan2021GANControl,
	title        = {{GAN-Control: Explicitly Controllable GANs}},
	author       = {Shoshan, Alon and Bhonker, Nadav and Kviatkovsky, Igor and Medioni, G\'erard},
	year         = 2021,
	month        = {October},
	booktitle    = {Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV)}
}
@inproceedings{sorrenson2020disentanglement,
	title        = {{Disentanglement by Nonlinear ICA with General Incompressible-flow Networks (GIN)}},
	author       = {Peter Sorrenson and Carsten Rother and Ullrich Köthe},
	year         = 2020,
	booktitle    = {International Conference on Learning Representations}
}
@article{spearman1904proof,
	title        = {{The Proof and Measurement of Association Between Two Things}},
	author       = {Spearman, C.},
	year         = 1904,
	journal      = {American Journal of Psychology},
	volume       = 15,
	added-at     = {2010-10-21T15:57:00.000+0200},
	interhash    = {ccfadff2f334e8f053dbb2e1473a9137},
	intrahash    = {41bbb05b2436805efcd2bae6499be0e3},
	keywords     = {imported}
}
@article{spiegelhalter1992learning,
	title        = {{Learning in probabilistic expert systems}},
	author       = {Spiegelhalter, D. J.  and Cowell, R. G.},
	year         = 1992,
	journal      = {Bayesian Statistics},
	volume       = 4
}
@book{Spirtes_2000,
	title        = {{Causation, Prediction, and Search}},
	author       = {Spirtes, Peter and Glymour, Clark and Scheines, Richard},
	year         = 2000,
	publisher    = {MIT Press},
	address      = {Cambridge MA},
	added-at     = {2016-11-26T13:19:29.000+0100},
	date-added   = {2008-05-16 16:46:46 -0700},
	date-modified = {2008-05-16 16:48:00 -0700},
	edition      = {2nd},
	interhash    = {559e17fcd12a76214629ba6c4efe3f9a},
	intrahash    = {e2b107e8fd3469c8b0e944ca37a559f3},
	keywords     = {imported ml}
}
@book{spirtes2000causation,
	title        = {{Causation, Prediction, and Search, Second Edition}},
	author       = {Peter Spirtes and Clark Glymour and Richard Scheines},
	year         = 2000,
	publisher    = {{MIT} Press},
	series       = {Adaptive computation and machine learning},
	isbn         = {978-0-262-19440-2}
}
@article{squires2020active,
	title        = {{Active structure learning of causal DAGs via directed clique trees}},
	author       = {Squires, Chandler and Magliacane, Sara and Greenewald, Kristjan and Katz, Dmitriy and Kocaoglu, Murat and Shanmugam, Karthikeyan},
	year         = 2020,
	journal      = {Adv. Neural Inf. Process. Syst.},
	volume       = 33,
	keywords     = {Intervention Design}
}
@inproceedings{squires2020permutation,
	title        = {{Permutation-based causal structure learning with unknown intervention targets}},
	author       = {Squires, Chandler and Wang, Yuhao and Uhler, Caroline},
	year         = 2020,
	booktitle    = {Conference on Uncertainty in Artificial Intelligence},
	organization = {PMLR}
}
@misc{stanford2021stanford,
	title        = {{The Stanford 3D Scanning Repository}},
	author       = {Stanford Computer Graphics Laboratory},
	year         = 2021,
	howpublished = {\url{http://graphics.stanford.edu/data/3Dscanrep/}}
}
@inproceedings{sun2007a,
	title        = {{A kernel-based causal learning algorithm}},
	author       = {Xiaohai Sun and Dominik Janzing and Bernhard Sch{\"{o}}lkopf and Kenji Fukumizu},
	year         = 2007,
	booktitle    = {Machine Learning, Proceedings of the Twenty-Fourth International Conference {(ICML} 2007), Corvallis, Oregon, USA, June 20-24, 2007},
	publisher    = {{ACM}},
	series       = {{ACM} International Conference Proceeding Series},
	volume       = 227
}
@inproceedings{szot2021habitat,
	title        = {{Habitat 2.0: Training Home Assistants to Rearrange their Habitat}},
	author       = {Szot, Andrew and Clegg, Alexander and Undersander, Eric and Wijmans, Erik and Zhao, Yili and Turner, John and Maestre, Noah and Mukadam, Mustafa and Chaplot, Devendra Singh and Maksymets, Oleksandr and Gokaslan, Aaron and Vondru\v{s}, Vladim\'{\i}r and Dharur, Sameer and Meier, Franziska and Galuba, Wojciech and Chang, Angel and Kira, Zsolt and Koltun, Vladlen and Malik, Jitendra and Savva, Manolis and Batra, Dhruv},
	year         = 2021,
	booktitle    = {Advances in Neural Information Processing Systems},
	publisher    = {Curran Associates, Inc.},
	volume       = 34
}
@inproceedings{traeuble2021disentangled,
	title        = {{On Disentangled Representations Learned from Correlated Data}},
	author       = {Tr{\"a}uble, Frederik and Creager, Elliot and Kilbertus, Niki and Locatello, Francesco and Dittadi, Andrea and Goyal, Anirudh and Sch{\"o}lkopf, Bernhard and Bauer, Stefan},
	year         = 2021,
	month        = {18--24 Jul},
	booktitle    = {Proceedings of the 38th International Conference on Machine Learning},
	publisher    = {PMLR},
	series       = {Proceedings of Machine Learning Research},
	volume       = 139,
	abstract     = {The focus of disentanglement approaches has been on identifying independent factors of variation in data. However, the causal variables underlying real-world observations are often not statistically independent. In this work, we bridge the gap to real-world scenarios by analyzing the behavior of the most prominent disentanglement approaches on correlated data in a large-scale empirical study (including 4260 models). We show and quantify that systematically induced correlations in the dataset are being learned and reflected in the latent representations, which has implications for downstream applications of disentanglement such as fairness. We also demonstrate how to resolve these latent correlations, either using weak supervision during training or by post-hoc correcting a pre-trained model with a small number of labels.}
}
@inproceedings{traeuble2022the,
	title        = {{The Role of Pretrained Representations for the OOD Generalization of RL Agents}},
	author       = {Frederik Tr{\"a}uble and Andrea Dittadi and Manuel Wuthrich and Felix Widmaier and Peter Vincent Gehler and Ole Winther and Francesco Locatello and Olivier Bachem and Bernhard Sch{\"o}lkopf and Stefan Bauer},
	year         = 2022,
	booktitle    = {International Conference on Learning Representations}
}
@article{transientAndObligateProteins2005,
	title        = {{Structure, function, and evolution of transient and obligate protein–protein interactions}},
	author       = {Julian Mintseris  and Zhiping Weng},
	year         = 2005,
	journal      = {Proceedings of the National Academy of Sciences},
	volume       = 102,
	number       = 31,
	abstract     = {Recent analyses of high-throughput protein interaction data coupled with large-scale investigations of evolutionary properties of interaction networks have left some unanswered questions. To what extent do protein interactions act as constraints during evolution of the protein sequence? How does the type of interaction, specifically transient or obligate, play into these constraints? Are the mutations in the binding site of an interacting protein correlated with mutations in the binding site of its partner? We address these and other questions by relying on a carefully curated dataset of protein complex structures. Results point to the importance of distinguishing between transient and obligate interactions. We conclude that residues in the interfaces of obligate complexes tend to evolve at a relatively slower rate, allowing them to coevolve with their interacting partners. In contrast, the plasticity inherent in transient interactions leads to an increased rate of substitution for the interface residues and leaves little or no evidence of correlated mutations across the interface.}
}
@article{transientProteins2011,
	title        = {{Transient protein–protein interactions}},
	author       = {Acuner Ozbabacan, Saliha Ece and Engin, Hatice Billur and Gursoy, Attila and Keskin, Ozlem},
	year         = 2011,
	month        = {06},
	journal      = {Protein Engineering, Design and Selection},
	volume       = 24,
	number       = 9,
	abstract     = {{Transient complexes are crucial for diverse biological processes such as biochemical pathways and signaling cascades in the cell. Here, we give an overview of the transient interactions; the importance of transient interactions as drug targets; and the structural characterization of transient protein–protein complexes based on the geometrical and physicochemical features of the transient complexes’ interfaces. To better understand and eventually design transient protein–protein interactions (TPPIs), a molecular perspective of the protein–protein interfaces is necessary. Obtaining high-quality structures of protein–protein interactions could be one way of achieving this goal. After introducing the association kinetics of TPPIs, we elaborate on the experimental techniques detecting TPPIs in combination with the computational methods which classify transient and/or non-obligate complexes. In this review, currently available databases and servers that can be used to identify and predict TPPIs are also compiled.}}
}
@article{triantafillou2015constraint,
	title        = {{Constraint-based Causal Discovery from Multiple Interventions over Overlapping Variable Sets}},
	author       = {Sofia Triantafillou and Ioannis Tsamardinos},
	year         = 2015,
	journal      = {Journal of Machine Learning Research},
	volume       = 16,
	number       = 66
}
@article{tsamardinos2006the,
	title        = {{The Max-Min Hill-Climbing Bayesian Network Structure Learning Algorithm}},
	author       = {Tsamardinos, Ioannis and Brown, Laura E. and Aliferis, Constantin F.},
	year         = 2006,
	journal      = {Machine Learning},
	publisher    = {Kluwer Academic Publishers},
	address      = {USA},
	volume       = 65,
	number       = 1,
	issn         = {0885-6125},
	abstract     = {We present a new algorithm for Bayesian network structure learning, called Max-Min Hill-Climbing ( MMHC ). The algorithm combines ideas from local learning, constraint-based, and search-and-score techniques in a principled and effective way. It first reconstructs the skeleton of a Bayesian network and then performs a Bayesian-scoring greedy hill-climbing search to orient the edges. In our extensive empirical evaluation MMHC outperforms on average and in terms of various metrics several prototypical and state-of-the-art algorithms, namely the PC , Sparse Candidate, Three Phase Dependency Analysis, Optimal Reinsertion, Greedy Equivalence Search, and Greedy Search. These are the first empirical results simultaneously comparing most of the major Bayesian network algorithms against each other. MMHC offers certain theoretical advantages, specifically over the Sparse Candidate algorithm, corroborated by our experiments. MMHC and detailed results of our study are publicly available at http://www.dsl-lab.org/supplements/mmhc_paper/mmhc_index.html.},
	issue_date   = {October 2006},
	keywords     = {Structure learning, Bayesian networks, Graphical models},
	numpages     = 48
}
@inproceedings{turk1994zippered,
	title        = {{Zippered Polygon Meshes from Range Images}},
	author       = {Turk, Greg and Levoy, Marc},
	year         = 1994,
	booktitle    = {Proceedings of the 21st Annual Conference on Computer Graphics and Interactive Techniques},
	publisher    = {Association for Computing Machinery},
	address      = {New York, NY, USA},
	series       = {SIGGRAPH '94},
	isbn         = {0897916670},
	abstract     = {Range imaging offers an inexpensive and accurate means for digitizing the shape of three-dimensional objects. Because most objects self occlude, no single range image suffices to describe the entire object. We present a method for combining a collection of range images into a single polygonal mesh that completely describes an object to the extent that it is visible from the outside.The steps in our method are: 1) align the meshes with each other using a modified iterated closest-point algorithm, 2) zipper together adjacent meshes to form a continuous surface that correctly captures the topology of the object, and 3) compute local weighted averages of surface positions on all meshes to form a consensus surface geometry.Our system differs from previous approaches in that it is incremental; scans are acquired and combined one at a time. This approach allows us to acquire and combine large numbers of scans with minimal storage overhead. Our largest models contain up to 360,000 triangles. All the steps needed to digitize an object that requires up to 10 range scans can be performed using our system with five minutes of user interaction and a few hours of compute time. We show two models created using our method with range data from a commercial rangefinder that employs laser stripe technology.},
	numpages     = 8,
	keywords     = {polygon mesh, surface fitting, structured light range scanner, surface reconstruction, range images}
}
@inproceedings{vahdat2020nvae,
	title        = {{NVAE: A Deep Hierarchical Variational Autoencoder}},
	author       = {Vahdat, Arash and Kautz, Jan},
	year         = 2020,
	booktitle    = {Neural Information Processing Systems (NeurIPS)}
}
@article{vandenbroucke2016causality,
	title        = {{Causality and causal inference in epidemiology: the need for a pluralistic approach}},
	author       = {Vandenbroucke, Jan P and Broadbent, Alex and Pearce, Neil},
	year         = 2016,
	journal      = {International journal of epidemiology},
	publisher    = {Oxford University Press},
	volume       = 45,
	number       = 6
}
@article{vandenoord2018representation,
	title        = {{Representation Learning with Contrastive Predictive Coding}},
	author       = {A{\"{a}}ron van den Oord and Yazhe Li and Oriol Vinyals},
	year         = 2018,
	journal      = {CoRR},
	volume       = {abs/1807.03748},
	eprinttype   = {arXiv},
	eprint       = {1807.03748}
}
@article{varando2020learning,
	title        = {{Learning DAGs without imposing acyclicity}},
	author       = {Varando, Gherardo},
	year         = 2020,
	journal      = {arXiv preprint arXiv:2006.03005}
}
@inproceedings{vonkuegelgen2021self,
	title        = {{Self-Supervised Learning with Data Augmentations Provably Isolates Content from Style}},
	author       = {von K{\"u}gelgen, Julius and Sharma, Yash and Gresele, Luigi and Brendel, Wieland and Sch{\"o}lkopf, Bernhard and Besserve, Michel and Locatello, Francesco},
	year         = 2021,
	booktitle    = {Thirty-Fifth Conference on Neural Information Processing Systems}
}
@inproceedings{wang2017permutation,
	title        = {{Permutation-based Causal Inference Algorithms with Interventions}},
	author       = {Yuhao Wang and Liam Solus and Karren D. Yang and Caroline Uhler},
	year         = 2017,
	booktitle    = {Advances in Neural Information Processing Systems 30: Annual Conference on Neural Information Processing Systems 2017, December 4-9, 2017, Long Beach, CA, {USA}}
}
@inproceedings{williams1992simple,
	title        = {{Simple statistical gradient-following algorithms for connectionist reinforcement learning}},
	author       = {Ronald J. Williams},
	year         = 1992,
	booktitle    = {Machine Learning}
}
@article{winkler2019learning,
	title        = {{Learning likelihoods with conditional normalizing flows}},
	author       = {Winkler, Christina and Worrall, Daniel and Hoogeboom, Emiel and Welling, Max},
	year         = 2019,
	journal      = {arXiv preprint arXiv:1912.00042}
}
@article{wright1921correlation,
	title        = {{Correlation and causation}},
	author       = {Wright, Sewall},
	year         = 1921,
	journal      = {Journal of agricultural research},
	publisher    = {Washington},
	volume       = 20,
	number       = 7,
	added-at     = {2017-05-10T05:54:54.000+0200},
	interhash    = {6cd977bb9d1ce8fb96b7f2498ba3e143},
	intrahash    = {63854102ba77a1f87c7283de8fca155b},
	keywords     = {causation philosophy statistics}
}
@inproceedings{yang2018characterizing,
	title        = {{Characterizing and Learning Equivalence Classes of Causal DAGs under Interventions}},
	author       = {Karren D. Yang and Abigail Katoff and Caroline Uhler},
	year         = 2018,
	booktitle    = {Proceedings of the 35th International Conference on Machine Learning, {ICML} 2018, Stockholmsm{\"{a}}ssan, Stockholm, Sweden, July 10-15, 2018},
	publisher    = {{PMLR}},
	series       = {Proceedings of Machine Learning Research},
	volume       = 80
}
@inproceedings{yang2021causalvae,
	title        = {{CausalVAE: disentangled representation learning via neural structural causal models}},
	author       = {Yang, Mengyue and Liu, Furui and Chen, Zhitang and Shen, Xinwei and Hao, Jianye and Wang, Jun},
	year         = 2021,
	booktitle    = {Proceedings of the IEEE/CVF Conference on Computer Vision and Pattern Recognition}
}
@inproceedings{yao2021learning,
	title        = {{Learning Temporally Causal Latent Processes from General Temporal Data}},
	author       = {Weiran Yao and Yuewen Sun and Alex Ho and Changyin Sun and Kun Zhang},
	year         = 2022,
	booktitle    = {International Conference on Learning Representations},
	abstract     = {Our goal is to recover time-delayed latent causal variables and identify their relations from measured temporal data. Estimating causally-related latent variables from observations is particularly challenging as the latent variables are not uniquely recoverable in the most general case. In this work, we consider both a nonparametric, nonstationary setting and a parametric setting for the latent processes and propose two provable conditions under which temporally causal latent processes can be identified from their nonlinear mixtures. We propose LEAP, a theoretically-grounded framework that extends Variational AutoEncoders (VAEs) by enforcing our conditions through proper constraints in causal process prior. Experimental results on various datasets demonstrate that temporally causal latent processes are reliably identified from observed variables under different dependency structures and that our approach considerably outperforms baselines that do not properly leverage history or nonstationarity information. This demonstrates that using temporal information to learn latent processes from their invertible nonlinear mixtures in an unsupervised manner, for which we believe our work is one of the first, seems promising even without sparsity or minimality assumptions.}
}
@inproceedings{yao2022temporally,
	title        = {{Temporally Disentangled Representation Learning}},
	author       = {Weiran Yao and Guangyi Chen and Kun Zhang},
	year         = 2022,
	booktitle    = {Advances in Neural Information Processing Systems 35, NeurIPS}
}
@inproceedings{yoon2018gain,
	title        = {{GAIN: Missing Data Imputation using Generative Adversarial Nets}},
	author       = {Jinsung Yoon and James Jordon and Mihaela van der Schaar},
	year         = 2018,
	booktitle    = {Proceedings of the 35th International Conference on Machine Learning, {ICML} 2018, Stockholmsm{\"{a}}ssan, Stockholm, Sweden, July 10-15, 2018},
	publisher    = {{PMLR}},
	series       = {Proceedings of Machine Learning Research},
	volume       = 80
}
@inproceedings{yu2019dag,
	title        = {{DAG-GNN: DAG Structure Learning with Graph Neural Networks}},
	author       = {Yue Yu and Jie Chen and Tian Gao and Mo Yu},
	year         = 2019,
	booktitle    = {Proceedings of the 36th International Conference on Machine Learning, {ICML} 2019, 9-15 June 2019, Long Beach, California, {USA}},
	publisher    = {{PMLR}},
	series       = {Proceedings of Machine Learning Research},
	volume       = 97
}
@inproceedings{zhang2011kernel,
	title        = {{Kernel-based Conditional Independence Test and Application in Causal Discovery}},
	author       = {Kun Zhang and Jonas Peters and Dominik Janzing and Bernhard Sch{\"{o}}lkopf},
	year         = 2011,
	booktitle    = {{UAI} 2011, Proceedings of the Twenty-Seventh Conference on Uncertainty in Artificial Intelligence, Barcelona, Spain, July 14-17, 2011},
	publisher    = {{AUAI} Press}
}
@article{zhang2020causal,
	title        = {{Causal imitation learning with unobserved confounders}},
	author       = {Zhang, Junzhe and Kumor, Daniel and Bareinboim, Elias},
	year         = 2020,
	journal      = {Advances in neural information processing systems},
	volume       = 33
}
@inproceedings{zhang2020invariant,
	title        = {{Invariant Causal Prediction for Block MDPs}},
	author       = {Zhang, Amy and Lyle, Clare and Sodhani, Shagun and Filos, Angelos and Kwiatkowska, Marta and Pineau, Joelle and Gal, Yarin and Precup, Doina},
	year         = 2020,
	month        = {13--18 Jul},
	booktitle    = {Proceedings of the 37th International Conference on Machine Learning},
	publisher    = {PMLR},
	series       = {Proceedings of Machine Learning Research},
	volume       = 119,
	abstract     = {Generalization across environments is critical to the successful application of reinforcement learning (RL) algorithms to real-world challenges. In this work we propose a method for learning state abstractions which generalize to novel observation distributions in the multi-environment RL setting. We prove that for certain classes of environments, this approach outputs, with high probability, a state abstraction corresponding to the causal feature set with respect to the return. We give empirical evidence that analogous methods for the nonlinear setting can also attain improved generalization over single- and multi-task baselines. Lastly, we provide bounds on model generalization error in the multi-environment setting, in the process showing a connection between causal variable identification and the state abstraction framework for MDPs.}
}
@inproceedings{zheng2018dags,
	title        = {{DAGs with NO TEARS: Continuous Optimization for Structure Learning}},
	author       = {Xun Zheng and Bryon Aragam and Pradeep Ravikumar and Eric P. Xing},
	year         = 2018,
	booktitle    = {Advances in Neural Information Processing Systems 31: Annual Conference on Neural Information Processing Systems 2018, NeurIPS 2018, December 3-8, 2018, Montr{\'{e}}al, Canada}
}
@inproceedings{zheng2020learning,
	title        = {{Learning Sparse Nonparametric DAGs}},
	author       = {Xun Zheng and Chen Dan and Bryon Aragam and Pradeep Ravikumar and Eric P. Xing},
	year         = 2020,
	booktitle    = {The 23rd International Conference on Artificial Intelligence and Statistics, {AISTATS} 2020, 26-28 August 2020, Online [Palermo, Sicily, Italy]},
	publisher    = {{PMLR}},
	series       = {Proceedings of Machine Learning Research},
	volume       = 108
}
@inproceedings{zhu2020causal,
	title        = {{Causal Discovery with Reinforcement Learning}},
	author       = {Shengyu Zhu and Ignavier Ng and Zhitang Chen},
	year         = 2020,
	booktitle    = {8th International Conference on Learning Representations, {ICLR} 2020, Addis Ababa, Ethiopia, April 26-30, 2020}
}
@inproceedings{zimmermann2021contrastive,
	title        = {{Contrastive Learning Inverts the Data Generating Process}},
	author       = {Zimmermann, Roland S. and Sharma, Yash and Schneider, Steffen and Bethge, Matthias and Brendel, Wieland},
	year         = 2021,
	booktitle    = {Proceedings of the 38th International Conference on Machine Learning, {ICML}}
}
@inproceedings{peters2013causal,
 author = {Peters, Jonas and Janzing, Dominik and Sch\"{o}lkopf, Bernhard},
 booktitle = {Advances in Neural Information Processing Systems},
 editor = {C.J. Burges and L. Bottou and M. Welling and Z. Ghahramani and K.Q. Weinberger},
 pages = {},
 publisher = {Curran Associates, Inc.},
 title = {Causal Inference on Time Series using Restricted Structural Equation Models},
 volume = {26},
 year = {2013}
}
@article{assaad2022survey,
author = {Assaad, Charles K. and Devijver, Emilie and Gaussier, Eric},
title = {Survey and Evaluation of Causal Discovery Methods for Time Series},
year = {2022},
issue_date = {May 2022},
publisher = {AI Access Foundation},
address = {El Segundo, CA, USA},
volume = {73},
issn = {1076-9757},
abstract = {We introduce in this survey the major concepts, models, and algorithms proposed so far to infer causal relations from observational time series, a task usually referred to as causal discovery in time series. To do so, after a description of the underlying concepts and modelling assumptions, we present different methods according to the family of approaches they belong to: Granger causality, constraint-based approaches, noise-based approaches, score-based approaches, logic-based approaches, topology-based approaches, and difference-based approaches. We then evaluate several representative methods to illustrate the behaviour of different families of approaches. This illustration is conducted on both artificial and real datasets, with different characteristics. The main conclusions one can draw from this survey is that causal discovery in times series is an active research field in which new methods (in every family of approaches) are regularly proposed, and that no family or method stands out in all situations. Indeed, they all rely on assumptions that may or may not be appropriate for a particular dataset.},
journal = {J. Artif. Int. Res.},
month = {may},
numpages = {53},
keywords = {time series, knowledge discovery, causality}
}