@inproceedings{langley00,
 author    = {P. Langley},
 title     = {Crafting Papers on Machine Learning},
 year      = {2000},
 pages     = {1207--1216},
 editor    = {Pat Langley},
 booktitle     = {Proceedings of the 17th International Conference
              on Machine Learning (ICML 2000)},
 address   = {Stanford, CA},
 publisher = {Morgan Kaufmann}
}

@TechReport{mitchell80,
  author = 	 "T. M. Mitchell",
  title = 	 "The Need for Biases in Learning Generalizations",
  institution =  "Computer Science Department, Rutgers University",
  year = 	 "1980",
  address =	 "New Brunswick, MA",
}

@phdthesis{kearns89,
  author = {M. J. Kearns},
  title =  {Computational Complexity of Machine Learning},
  school = {Department of Computer Science, Harvard University},
  year =   {1989}
}

@Book{MachineLearningI,
  editor = 	 "R. S. Michalski and J. G. Carbonell and T.
		  M. Mitchell",
  title = 	 "Machine Learning: An Artificial Intelligence
		  Approach, Vol. I",
  publisher = 	 "Tioga",
  year = 	 "1983",
  address =	 "Palo Alto, CA"
}

@Book{DudaHart2nd,
  author =       "R. O. Duda and P. E. Hart and D. G. Stork",
  title =        "Pattern Classification",
  publisher =    "John Wiley and Sons",
  edition =      "2nd",
  year =         "2000"
}

@misc{anonymous,
  title= {Suppressed for Anonymity},
  author= {Author, N. N.},
  year= {2021}
}

@InCollection{Newell81,
  author =       "A. Newell and P. S. Rosenbloom",
  title =        "Mechanisms of Skill Acquisition and the Law of
                  Practice", 
  booktitle =    "Cognitive Skills and Their Acquisition",
  pages =        "1--51",
  publisher =    "Lawrence Erlbaum Associates, Inc.",
  year =         "1981",
  editor =       "J. R. Anderson",
  chapter =      "1",
  address =      "Hillsdale, NJ"
}


@Article{Samuel59,
  author = 	 "A. L. Samuel",
  title = 	 "Some Studies in Machine Learning Using the Game of
		  Checkers",
  journal =	 "IBM Journal of Research and Development",
  year =	 "1959",
  volume =	 "3",
  number =	 "3",
  pages =	 "211--229"
}



@article{kolmogorov,
author="A. Kolmogorov",
title="Sulla determinazione empirica di una legge di distribuzione",
journal="G. Ist. Ital. Attuari",
year="1933",
volume="4",
pages="83-91",
}

@article{smirnov,
author = {N. Smirnov},
title = {{Table for Estimating the Goodness of Fit of Empirical Distributions}},
volume = {19},
journal = {The Annals of Mathematical Statistics},
number = {2},
pages = {279 -- 281},
year = {1948},
}

@article{ktst,
author = {Gretton, Arthur and Borgwardt, Karsten M. and Rasch, Malte J. and Sch\"{o}lkopf, Bernhard and Smola, Alexander},
title = {A Kernel Two-Sample Test},
year = {2012},
issue_date = {3/1/2012},
publisher = {JMLR.org},
volume = {13},
number = {null},
issn = {1532-4435},
abstract = {We propose a framework for analyzing and comparing distributions, which we use to construct statistical tests to determine if two samples are drawn from different distributions. Our test statistic is the largest difference in expectations over functions in the unit ball of a reproducing kernel Hilbert space (RKHS), and is called the maximum mean discrepancy (MMD).We present two distribution free tests based on large deviation bounds for the MMD, and a third test based on the asymptotic distribution of this statistic. The MMD can be computed in quadratic time, although efficient linear time approximations are available. Our statistic is an instance of an integral probability metric, and various classical metrics on distributions are obtained when alternative function classes are used in place of an RKHS. We apply our two-sample tests to a variety of problems, including attribute matching for databases using the Hungarian marriage method, where they perform strongly. Excellent performance is also obtained when comparing distributions over graphs, for which these are the first such tests.},
journal = {J. Mach. Learn. Res.},
month = {mar},
pages = {723–773},
numpages = {51},
keywords = {two-sample test, kernel methods, schema matching, integral probability metric, hypothesis testing, uniform convergence bounds}
}


@inproceedings{liu2021learning,
      title={Learning Deep Kernels for Non-Parametric Two-Sample Tests}, 
      author={Feng Liu and Wenkai Xu and Jie Lu and Guangquan Zhang and Arthur Gretton and Danica J. Sutherland},
      year={2020},
      booktitle = {ICML}
}


@InProceedings{Kirchler2020two,
  title = 	 {Two-sample Testing Using Deep Learning},
  author = {Kirchler, Matthias and Khorasani, Shahryar and Kloft, Marius and Lippert, Christoph},
  booktitle = 	 {AISTATS},
  year = 	 {2020},
}


@book{lehmann2005testing,
  added-at = {2010-03-21T00:26:58.000+0100},
  author = {Lehmann, E. L. and Romano, Joseph P.},
  interhash = {9517319578e44006dcf98ae19f983394},
  intrahash = {8201f448d2af0d4fd287181787c0d128},
  keywords = {book reference statistics},
  mrclass = {62-02 (62C05 62F03 62H15)},
  mrnumber = {MR2135927 (2006m:62005)},
  pages = {xiv+784},
  publisher = {Springer},
  series = {Springer Texts in Statistics},
  timestamp = {2010-03-21T00:26:59.000+0100},
  title = {Testing statistical hypotheses},
  year = 2005
}

@article{valiant1984pac,
author = {Valiant, L. G.},
title = {A Theory of the Learnable},
year = {1984},
issue_date = {Nov. 1984},
publisher = {Association for Computing Machinery},
address = {New York, NY, USA},
volume = {27},
number = {11},
issn = {0001-0782},
url = {https://doi.org/10.1145/1968.1972},
doi = {10.1145/1968.1972},
journal = {Commun. ACM},
month = {nov},
pages = {1134–1142},
numpages = {9},
keywords = {inductive inference, probabilistic models of learning, propositional expressions}
}

@book{vapnik1999nature,
  title={The nature of statistical learning theory},
  author={Vapnik, Vladimir},
  year={1999},
  publisher={Springer science \& business media}
}

@book{cormen2022introduction,
  title={Introduction to algorithms},
  author={Cormen, Thomas H and Leiserson, Charles E and Rivest, Ronald L and Stein, Clifford},
  year={2022},
  publisher={MIT press}
}

@book{serfling2009approximation,
  title={Approximation theorems of mathematical statistics},
  author={Serfling, Robert J},
  year={2009},
  publisher={John Wiley \& Sons}
}

@inproceedings{kingma2014semi,
  title={Semi-supervised learning with deep generative models},
  author={Kingma, Durk P and Mohamed, Shakir and Jimenez Rezende, Danilo and Welling, Max},
  booktitle={NeurIPS},
  year={2014}
}

@inproceedings{higgins2016beta,
  title={beta-vae: Learning basic visual concepts with a constrained variational framework},
  author={Higgins, Irina and Matthey, Loic and Pal, Arka and Burgess, Christopher and Glorot, Xavier and Botvinick, Matthew and Mohamed, Shakir and Lerchner, Alexander},
  booktitle={ICLR},
  year={2016}
}

@article{baldi2014searching,
  title={Searching for exotic particles in high-energy physics with deep learning},
  author={Baldi, Pierre and Sadowski, Peter and Whiteson, Daniel},
  journal={Nature communications},
  volume={5},
  number={1},
  pages={4308},
  year={2014},
  publisher={Nature Publishing Group UK London}
}



@article{cheng2020classificationlogittwosampletesting,
  title={Classification logit two-sample testing by neural networks for differentiating near manifold densities},
  author={Cheng, Xiuyuan and Cloninger, Alexander},
  journal={IEEE Transactions on Information Theory},
  volume={68},
  number={10},
  pages={6631--6662},
  year={2022},
  publisher={IEEE}
}

@article{ehm_binomial_1991,
	title = {Binomial approximation to the {Poisson} binomial distribution},
	volume = {11},
	number = {1},
	urldate = {2024-01-19},
	journal = {Statistics \& Probability Letters},
	author = {Ehm, Werner},
	year = {1991},
	pages = {7--16},
}

@article{valiant_theory_1984,
	title = {A theory of the learnable},
	volume = {27},
	issn = {0001-0782},
	url = {https://dl.acm.org/doi/10.1145/1968.1972},
	doi = {10.1145/1968.1972},
	number = {11},
	urldate = {2024-01-15},
	journal = {Communications of the ACM},
	author = {Valiant, L. G.},
	month = nov,
	year = {1984},
	keywords = {inductive inference, probabilistic models of learning, propositional expressions},
	pages = {1134--1142},
}

@book{noauthor_testing_2005,
	address = {New York, NY},
	series = {Springer {Texts} in {Statistics}},
	title = {Testing {Statistical} {Hypotheses}},
	url = {http://link.springer.com/10.1007/0-387-27605-X},
	language = {en},
	urldate = {2024-01-03},
	publisher = {Springer},
	year = {2005},
	doi = {10.1007/0-387-27605-X},
	note = {ISSN: 1431-875X},
	keywords = {Excel, Resampling, Statistical Hypotheses, Statistical Theory, best fit},
}


@misc{dong_diversity-enhancing_2023,
	title = {Diversity-enhancing {Generative} {Network} for {Few}-shot {Hypothesis} {Adaptation}},
	url = {http://arxiv.org/abs/2307.05948},
	doi = {10.48550/arXiv.2307.05948},
	abstract = {Generating unlabeled data has been recently shown to help address the few-shot hypothesis adaptation (FHA) problem, where we aim to train a classifier for the target domain with a few labeled target-domain data and a well-trained source-domain classifier (i.e., a source hypothesis), for the additional information of the highly-compatible unlabeled data. However, the generated data of the existing methods are extremely similar or even the same. The strong dependency among the generated data will lead the learning to fail. In this paper, we propose a diversity-enhancing generative network (DEG-Net) for the FHA problem, which can generate diverse unlabeled data with the help of a kernel independence measure: the Hilbert-Schmidt independence criterion (HSIC). Specifically, DEG-Net will generate data via minimizing the HSIC value (i.e., maximizing the independence) among the semantic features of the generated data. By DEG-Net, the generated unlabeled data are more diverse and more effective for addressing the FHA problem. Experimental results show that the DEG-Net outperforms existing FHA baselines and further verifies that generating diverse data plays a vital role in addressing the FHA problem},
	urldate = {2023-12-22},
	publisher = {arXiv},
	author = {Dong, Ruijiang and Liu, Feng and Chi, Haoang and Liu, Tongliang and Gong, Mingming and Niu, Gang and Sugiyama, Masashi and Han, Bo},
	month = jul,
	year = {2023},
	note = {arXiv:2307.05948 [cs]},
	keywords = {Computer Science - Machine Learning},
}

@article{balcan_discriminative_2010,
	title = {A discriminative model for semi-supervised learning},
	volume = {57},
	number = {3},
	journal = {Journal of the ACM},
	author = {Balcan, Maria-Florina and Blum, Avrim},
	year = {2010},
	pages = {19:1--19:46},
}


@inproceedings{biggs_mmd-fuse_2023,
    author = {Biggs, Felix and Schrab, Antonin and Gretton, Arthur},
    title = {{MMD}-{FUSE}: {Learning} and {Combining} {Kernels} for {Two}-{Sample} {Testing} {Without} {Data} {Splitting}},
    booktitle = {NeurIPS},
    year = 2023
}

@misc{wang_disentangled_2023,
	title = {Disentangled {Representation} {Learning}},
	url = {http://arxiv.org/abs/2211.11695},
	abstract = {Disentangled Representation Learning (DRL) aims to learn a model capable of identifying and disentangling the underlying factors hidden in the observable data in representation form. The process of separating underlying factors of variation into variables with semantic meaning benefits in learning explainable representations of data, which imitates the meaningful understanding process of humans when observing an object or relation. As a general learning strategy, DRL has demonstrated its power in improving the model explainability, controlability, robustness, as well as generalization capacity in a wide range of scenarios such as computer vision, natural language processing, data mining etc. In this article, we comprehensively review DRL from various aspects including motivations, definitions, methodologies, evaluations, applications and model designs. We discuss works on DRL based on two well-recognized definitions, i.e., Intuitive Definition and Group Theory Definition. We further categorize the methodologies for DRL into four groups, i.e., Traditional Statistical Approaches, Variational Auto-encoder Based Approaches, Generative Adversarial Networks Based Approaches, Hierarchical Approaches and Other Approaches. We also analyze principles to design different DRL models that may benefit different tasks in practical applications. Finally, we point out challenges in DRL as well as potential research directions deserving future investigations. We believe this work may provide insights for promoting the DRL research in the community.},
	urldate = {2023-12-05},
	publisher = {arXiv},
	author = {Wang, Xin and Chen, Hong and Tang, Si'ao and Wu, Zihao and Zhu, Wenwu},
	month = aug,
	year = {2023},
	note = {arXiv:2211.11695 [cs]},
	keywords = {Computer Science - Artificial Intelligence, Computer Science - Machine Learning},
}

@misc{doersch_tutorial_2021,
	title = {Tutorial on {Variational} {Autoencoders}},
	url = {http://arxiv.org/abs/1606.05908},
	abstract = {In just three years, Variational Autoencoders (VAEs) have emerged as one of the most popular approaches to unsupervised learning of complicated distributions. VAEs are appealing because they are built on top of standard function approximators (neural networks), and can be trained with stochastic gradient descent. VAEs have already shown promise in generating many kinds of complicated data, including handwritten digits, faces, house numbers, CIFAR images, physical models of scenes, segmentation, and predicting the future from static images. This tutorial introduces the intuitions behind VAEs, explains the mathematics behind them, and describes some empirical behavior. No prior knowledge of variational Bayesian methods is assumed.},
	urldate = {2023-12-04},
	publisher = {arXiv},
	author = {Doersch, Carl},
	month = jan,
	year = {2021},
	note = {arXiv:1606.05908 [cs, stat]},
	keywords = {Computer Science - Machine Learning, Statistics - Machine Learning},
}

@misc{bengio_representation_2014,
	title = {Representation {Learning}: {A} {Review} and {New} {Perspectives}},
	shorttitle = {Representation {Learning}},
	url = {http://arxiv.org/abs/1206.5538},
	doi = {10.48550/arXiv.1206.5538},
	abstract = {The success of machine learning algorithms generally depends on data representation, and we hypothesize that this is because different representations can entangle and hide more or less the different explanatory factors of variation behind the data. Although specific domain knowledge can be used to help design representations, learning with generic priors can also be used, and the quest for AI is motivating the design of more powerful representation-learning algorithms implementing such priors. This paper reviews recent work in the area of unsupervised feature learning and deep learning, covering advances in probabilistic models, auto-encoders, manifold learning, and deep networks. This motivates longer-term unanswered questions about the appropriate objectives for learning good representations, for computing representations (i.e., inference), and the geometrical connections between representation learning, density estimation and manifold learning.},
	urldate = {2023-12-01},
	publisher = {arXiv},
	author = {Bengio, Yoshua and Courville, Aaron and Vincent, Pascal},
	month = apr,
	year = {2014},
	note = {arXiv:1206.5538 [cs]},
	keywords = {Computer Science - Machine Learning},
}

@inproceedings{tschannen_recent_2018,
	title = {Recent {Advances} in {Autoencoder}-{Based} {Representation} {Learning}},
	author = {Tschannen, Michael and Bachem, Olivier and Lucic, Mario},
        booktitle = {NeurIPS 2018 Workshop on Bayesian Deep Learning},
	year = {2018},
}

@inproceedings{kirchler_two-sample_2020,
	title = {Two-sample {Testing} {Using} {Deep} {Learning}},
	url = {https://proceedings.mlr.press/v108/kirchler20a.html},
	abstract = {We propose a two-sample testing procedure based on learned deep neural network representations. To this end, we define two test statistics that perform an asymptotic location test on data samples mapped onto a hidden layer. The tests are consistent and asymptotically control the type-1 error rate. Their test statistics can be evaluated in linear time (in the sample size). Suitable data representations are obtained in a data-driven way, by solving a supervised or unsupervised transfer-learning task on an auxiliary (potentially distinct) data set. If no auxiliary data is available, we split the data into two chunks: one for learning representations and one for computing the test statistic. In experiments on audio samples, natural images and three-dimensional neuroimaging data our tests yield significant decreases in type-2 error rate (up to 35 percentage points) compared to state-of-the-art two-sample tests such as kernel-methods and classifier two-sample tests.},
	language = {en},
	urldate = {2023-11-27},
	booktitle = {Proceedings of the {Twenty} {Third} {International} {Conference} on {Artificial} {Intelligence} and {Statistics}},
	publisher = {PMLR},
	author = {Kirchler, Matthias and Khorasani, Shahryar and Kloft, Marius and Lippert, Christoph},
	month = jun,
	year = {2020},
	note = {ISSN: 2640-3498},
	pages = {1387--1398},
}

@inproceedings{jonas2022awit,
    author = {Kübler, Jonas M. and Jitkrittum, Wittawat and Schölkopf, Bernhard and Muandet, Krikamol},
    title = {A {Witness} {Two}-{Sample} {Test}},
    booktitle = {AISTATS},
    year = {2022}
}

@article{shekhar_permutation-free_2022,
	title = {A permutation-free kernel two-sample test},
	volume = {35},
	url = {https://proceedings.neurips.cc//paper_files/paper/2022/hash/731b952bdc833485eb72f458cdd5c489-Abstract-Conference.html},
	language = {en},
	urldate = {2023-11-23},
	journal = {Advances in Neural Information Processing Systems},
	author = {Shekhar, Shubhanshu and Kim, Ilmun and Ramdas, Aaditya},
	month = dec,
	year = {2022},
	pages = {18168--18180},
}

@inproceedings{liu_meta_2021,
	title = {Meta {Two}-{Sample} {Testing}: {Learning} {Kernels} for {Testing} with {Limited} {Data}},
	booktitle = {NeurIPS},
	author = {Liu, Feng and Xu, Wenkai and Lu, Jie and Sutherland, Danica J.},
	year = {2021},
}

@article{kubler_automl_2022,
	title = {{AutoML} {Two}-{Sample} {Test}},
	volume = {35},
	url = {https://proceedings.neurips.cc//paper_files/paper/2022/hash/66247b78cb1aa7259dcf856a18c9e294-Abstract-Conference.html},
	language = {en},
	urldate = {2023-11-23},
	journal = {Advances in Neural Information Processing Systems},
	author = {Kübler, Jonas M. and Stimper, Vincent and Buchholz, Simon and Muandet, Krikamol and Schölkopf, Bernhard},
	month = dec,
	year = {2022},
	pages = {15929--15941},
}

@book{noauthor_support_2008,
	address = {New York, NY},
	series = {Information {Science} and {Statistics}},
	title = {Support {Vector} {Machines}},
	url = {https://link.springer.com/10.1007/978-0-387-77242-4},
	language = {en},
	urldate = {2023-11-16},
	publisher = {Springer New York},
	year = {2008},
	doi = {10.1007/978-0-387-77242-4},
}

@article{campbell_kernel_2002,
	title = {Kernel methods: a survey of current techniques},
	volume = {48},
	issn = {09252312},
	shorttitle = {Kernel methods},
	url = {https://linkinghub.elsevier.com/retrieve/pii/S0925231201006439},
	doi = {10.1016/S0925-2312(01)00643-9},
	abstract = {Kernel methods have become an increasingly popular tool for machine learning tasks such as classiÿcation, regression or novelty detection. They exhibit good generalization performance on many real-life datasets, there are few free parameters to adjust and the architecture of the learning machine does not need to be found by experimentation. In this tutorial, we survey this subject with a principal focus on the most well-known models based on kernel substitution, namely, support vector machines. c 2002 Elsevier Science B.V. All rights reserved.},
	language = {en},
	number = {1-4},
	urldate = {2023-11-15},
	journal = {Neurocomputing},
	author = {Campbell, Colin},
	month = oct,
	year = {2002},
	pages = {63--84},
}

@article{yang_survey_2023,
	title = {A {Survey} on {Deep} {Semi}-supervised {Learning}},
	volume = {35},
	issn = {1041-4347, 1558-2191, 2326-3865},
	url = {http://arxiv.org/abs/2103.00550},
	doi = {10.1109/TKDE.2022.3220219},
	abstract = {Deep semi-supervised learning is a fast-growing field with a range of practical applications. This paper provides a comprehensive survey on both fundamentals and recent advances in deep semi-supervised learning methods from perspectives of model design and unsupervised loss functions. We first present a taxonomy for deep semi-supervised learning that categorizes existing methods, including deep generative methods, consistency regularization methods, graph-based methods, pseudo-labeling methods, and hybrid methods. Then we provide a comprehensive review of 52 representative methods and offer a detailed comparison of these methods in terms of the type of losses, contributions, and architecture differences. In addition to the progress in the past few years, we further discuss some shortcomings of existing methods and provide some tentative heuristic solutions for solving these open problems.},
	number = {9},
	urldate = {2023-11-14},
	journal = {IEEE Transactions on Knowledge and Data Engineering},
	author = {Yang, Xiangli and Song, Zixing and King, Irwin and Xu, Zenglin},
	month = sep,
	year = {2023},
	note = {arXiv:2103.00550 [cs]},
	keywords = {Computer Science - Machine Learning},
	pages = {8934--8954},
}

@article{yang_survey_2023-1,
	title = {A {Survey} on {Deep} {Semi}-supervised {Learning}},
	volume = {35},
	issn = {1041-4347, 1558-2191, 2326-3865},
	url = {http://arxiv.org/abs/2103.00550},
	doi = {10.1109/TKDE.2022.3220219},
	abstract = {Deep semi-supervised learning is a fast-growing field with a range of practical applications. This paper provides a comprehensive survey on both fundamentals and recent advances in deep semi-supervised learning methods from perspectives of model design and unsupervised loss functions. We first present a taxonomy for deep semi-supervised learning that categorizes existing methods, including deep generative methods, consistency regularization methods, graph-based methods, pseudo-labeling methods, and hybrid methods. Then we provide a comprehensive review of 52 representative methods and offer a detailed comparison of these methods in terms of the type of losses, contributions, and architecture differences. In addition to the progress in the past few years, we further discuss some shortcomings of existing methods and provide some tentative heuristic solutions for solving these open problems.},
	number = {9},
	urldate = {2023-11-14},
	journal = {IEEE Transactions on Knowledge and Data Engineering},
	author = {Yang, Xiangli and Song, Zixing and King, Irwin and Xu, Zenglin},
	month = sep,
	year = {2023},
	note = {arXiv:2103.00550 [cs]},
	keywords = {Computer Science - Machine Learning},
	pages = {8934--8954},
}

@article{van_engelen_survey_2020,
	title = {A survey on semi-supervised learning},
	volume = {109},
	issn = {1573-0565},
	url = {https://doi.org/10.1007/s10994-019-05855-6},
	doi = {10.1007/s10994-019-05855-6},
	abstract = {Semi-supervised learning is the branch of machine learning concerned with using labelled as well as unlabelled data to perform certain learning tasks. Conceptually situated between supervised and unsupervised learning, it permits harnessing the large amounts of unlabelled data available in many use cases in combination with typically smaller sets of labelled data. In recent years, research in this area has followed the general trends observed in machine learning, with much attention directed at neural network-based models and generative learning. The literature on the topic has also expanded in volume and scope, now encompassing a broad spectrum of theory, algorithms and applications. However, no recent surveys exist to collect and organize this knowledge, impeding the ability of researchers and engineers alike to utilize it. Filling this void, we present an up-to-date overview of semi-supervised learning methods, covering earlier work as well as more recent advances. We focus primarily on semi-supervised classification, where the large majority of semi-supervised learning research takes place. Our survey aims to provide researchers and practitioners new to the field as well as more advanced readers with a solid understanding of the main approaches and algorithms developed over the past two decades, with an emphasis on the most prominent and currently relevant work. Furthermore, we propose a new taxonomy of semi-supervised classification algorithms, which sheds light on the different conceptual and methodological approaches for incorporating unlabelled data into the training process. Lastly, we show how the fundamental assumptions underlying most semi-supervised learning algorithms are closely connected to each other, and how they relate to the well-known semi-supervised clustering assumption.},
	language = {en},
	number = {2},
	urldate = {2023-11-14},
	journal = {Machine Learning},
	author = {van Engelen, Jesper E. and Hoos, Holger H.},
	month = feb,
	year = {2020},
	keywords = {Classification, Machine learning, Semi-supervised learning},
	pages = {373--440},
}

@article{bao_robust_2024,
	title = {Robust embedding regression for semi-supervised learning},
	volume = {145},
	issn = {0031-3203},
	url = {https://www.sciencedirect.com/science/article/pii/S0031320323005927},
	doi = {10.1016/j.patcog.2023.109894},
	abstract = {To utilize both labeled data and unlabeled data in real-world applications, semi-supervised learning is widely used as an effective technique. However, most semi-supervised methods do not perform well when there are many noises and redundant information in the original data. To address these issues, in this paper, we proposed a novel approach called robust embedding regression (RER) for semi-supervised learning by inheriting the advantages of the existing semi-supervised learning, robust linear regression, and low-rank representation techniques. Specifically, RER constructs a more robust and accurate graph by adaptively arranging the weight coefficient for each data point. Furthermore, the low-rank representation is introduced to reduce the negative influence of the redundant features and noises residing in the original data while the graph construction. More importantly, the proper norms are imposed on both the reconstruction and regularization terms to further improve the robustness and earn feature/sample selection. We designed an effective iterative algorithm to optimize the problem of RER. Comprehensive experimental results conducted on both synthetic and real-world datasets indicate that RER is superior in classification and clustering performance and robust to different types of noise compared with the existing semi-supervised methods.},
	urldate = {2023-11-14},
	journal = {Pattern Recognition},
	author = {Bao, Jiaqi and Kudo, Mineichi and Kimura, Keigo and Sun, Lu},
	month = jan,
	year = {2024},
	keywords = {Feature selection, Nuclear norm, Ridge regression, Semi-supervised learning},
	pages = {109894},
}

@article{chen_debiased_2022,
	title = {Debiased {Self}-{Training} for {Semi}-{Supervised} {Learning}},
	volume = {35},
	url = {https://papers.nips.cc/paper_files/paper/2022/hash/d10d6b28d74c4f0fcab588feeb6fe7d6-Abstract-Conference.html},
	language = {en},
	urldate = {2023-11-14},
	journal = {Advances in Neural Information Processing Systems},
	author = {Chen, Baixu and Jiang, Junguang and Wang, Ximei and Wan, Pengfei and Wang, Jianmin and Long, Mingsheng},
	month = dec,
	year = {2022},
	pages = {32424--32437},
}

@inproceedings{balcan_data_2021,
	title = {Data driven semi-supervised learning},
	volume = {34},
	url = {https://proceedings.neurips.cc/paper/2021/hash/7c93ebe873ef213123c8af4b188e7558-Abstract.html},
	abstract = {We consider a novel data driven approach for designing semi-supervised learning algorithms that can effectively learn with only a small number of labeled examples. We focus on graph-based techniques, where the unlabeled examples are connected in a graph  under the implicit assumption that similar nodes likely have similar labels. Over the past two decades, several elegant graph-based semi-supervised learning algorithms for inferring the labels of the unlabeled examples given the graph and a few labeled examples have been proposed. However, the problem of how to create the graph (which impacts the practical usefulness of these methods significantly) has been relegated to heuristics and domain-specific art, and no general principles have been proposed. In this work we present a  novel data driven approach for learning the graph and provide strong formal guarantees in both the distributional and online learning formalizations. We show how to leverage problem instances coming from an underlying problem domain to learn the graph hyperparameters for commonly used parametric families of graphs that provably perform well on new instances from the same domain. We obtain low regret and efficient algorithms in the online setting, and generalization guarantees in the distributional setting. We also show how to combine several very different similarity metrics and learn multiple  hyperparameters, our results hold for large classes of problems. We expect some of the tools and techniques we develop along the way to be of independent interest, for data driven algorithms more generally.},
	urldate = {2023-11-14},
	booktitle = {Advances in {Neural} {Information} {Processing} {Systems}},
	publisher = {Curran Associates, Inc.},
	author = {Balcan, Maria-Florina F and Sharma, Dravyansh},
	year = {2021},
	pages = {14782--14794},
}

@inproceedings{balcan_data_2021-1,
	title = {Data driven semi-supervised learning},
	volume = {34},
	url = {https://proceedings.neurips.cc/paper/2021/hash/7c93ebe873ef213123c8af4b188e7558-Abstract.html},
	abstract = {We consider a novel data driven approach for designing semi-supervised learning algorithms that can effectively learn with only a small number of labeled examples. We focus on graph-based techniques, where the unlabeled examples are connected in a graph  under the implicit assumption that similar nodes likely have similar labels. Over the past two decades, several elegant graph-based semi-supervised learning algorithms for inferring the labels of the unlabeled examples given the graph and a few labeled examples have been proposed. However, the problem of how to create the graph (which impacts the practical usefulness of these methods significantly) has been relegated to heuristics and domain-specific art, and no general principles have been proposed. In this work we present a  novel data driven approach for learning the graph and provide strong formal guarantees in both the distributional and online learning formalizations. We show how to leverage problem instances coming from an underlying problem domain to learn the graph hyperparameters for commonly used parametric families of graphs that provably perform well on new instances from the same domain. We obtain low regret and efficient algorithms in the online setting, and generalization guarantees in the distributional setting. We also show how to combine several very different similarity metrics and learn multiple  hyperparameters, our results hold for large classes of problems. We expect some of the tools and techniques we develop along the way to be of independent interest, for data driven algorithms more generally.},
	urldate = {2023-11-14},
	booktitle = {Advances in {Neural} {Information} {Processing} {Systems}},
	publisher = {Curran Associates, Inc.},
	author = {Balcan, Maria-Florina F and Sharma, Dravyansh},
	year = {2021},
	pages = {14782--14794},
}


@article{gretton_optimal_nodate,
	title = {Optimal kernel choice for large-scale two-sample tests},
	abstract = {Given samples from distributions p and q, a two-sample test determines whether to reject the null hypothesis that p = q, based on the value of a test statistic measuring the distance between the samples. One choice of test statistic is the maximum mean discrepancy (MMD), which is a distance between embeddings of the probability distributions in a reproducing kernel Hilbert space. The kernel used in obtaining these embeddings is critical in ensuring the test has high power, and correctly distinguishes unlike distributions with high probability. A means of parameter selection for the two-sample test based on the MMD is proposed. For a given test level (an upper bound on the probability of making a Type I error), the kernel is chosen so as to maximize the test power, and minimize the probability of making a Type II error. The test statistic, test threshold, and optimization over the kernel parameters are obtained with cost linear in the sample size. These properties make the kernel selection and test procedures suited to data streams, where the observations cannot all be stored in memory. In experiments, the new kernel selection approach yields a more powerful test than earlier kernel selection heuristics.},
	language = {en},
	author = {Gretton, Arthur and Sejdinovic, Dino and Strathmann, Heiko and Balakrishnan, Sivaraman and Pontil, Massimiliano and Fukumizu, Kenji and Sriperumbudur, Bharath K},
}

@article{schrab2023mmd,
    author = {Schrab, Antonin and Kim, Ilmun and Albert, Melisande and Laurent, Beatrice and Guedj, Benjamin and Gretton, Arthur},
    title = {{MMD} {Aggregated} {Two}-{Sample} {Test}},
    journal = {Journal of Machine Learning Research},
    year = {2023}
}

@article{guo_robust_nodate,
	title = {Robust {Semi}-{Supervised} {Learning} when {Not} {All} {Classes} have {Labels}},
	abstract = {Semi-supervised learning (SSL) provides a powerful framework for leveraging unlabeled data. Existing SSL typically requires all classes have labels. However, in many real-world applications, there may exist some classes that are difficult to label or newly occurred classes that cannot be labeled in time, resulting in there are unseen classes in unlabeled data. Unseen classes will be misclassified as seen classes, causing poor classification performance. The performance of seen classes is also harmed by the existence of unseen classes. This limits the practical and wider application of SSL. To address this problem, this paper proposes a new SSL approach that can classify not only seen classes but also unseen classes. Our approach consists of two modules: unseen class classification and learning pace synchronization. Specifically, we first enable the SSL methods to classify unseen classes by exploiting pairwise similarity between examples and then synchronize the learning pace between seen and unseen classes by proposing an adaptive threshold with distribution alignment. Extensive empirical results show our approach achieves significant performance improvement in both seen and unseen classes compared with previous studies.},
	language = {en},
	author = {Guo, Lan-Zhe and Zhang, Yi-Ge and Wu, Zhi-Fan and Shao, Jie-Jing and Li, Yu-Feng},
}


@InProceedings{gao2021max,
  title = 	 {Maximum Mean Discrepancy Test is Aware of Adversarial Attacks},
  author =       {Gao, Ruize and Liu, Feng and Zhang, Jingfeng and Han, Bo and Liu, Tongliang and Niu, Gang and Sugiyama, Masashi},
  booktitle = 	 {ICML},
  year = 	 {2021},
}


@InProceedings{Bergamin2022model,
  title = 	 { Model-agnostic out-of-distribution detection using combined statistical tests },
  author =       {Bergamin, Federico and Mattei, Pierre-Alexandre and Drachmann Havtorn, Jakob and S\'en\'etaire, Hugo and Schmutz, Hugo and Maal{\o}e, Lars and Hauberg, Soren and Frellsen, Jes},
  booktitle = 	 {AISTATS},
  year = 	 {2022},
}

@article{GBRSS12:mmd,
author = {Gretton, Arthur and Borgwardt, Karsten M and Rasch, Malte J. and Sch{\"{o}}lkopf, Bernhard and Smola, Alexander J.},
journal = {Journal of Machine Learning Research},
pages = {723--773},
title = {A kernel two-sample test},
volume = {13},
year = {2012}
}

@inproceedings{Jitkrittum2016,
author = {Jitkrittum, Wittawat and Szabo, Zoltan and Chwialkowski, Kacper and Gretton, Arthur},
booktitle = {NeurIPS},
title = {Interpretable distribution features with maximum testing power},
year = {2016},
eprinttype = {arXiv},
eprint = {1605.06796},
}

@inproceedings{sutherland:mmd-opt,
author = {Danica J. Sutherland and Hsiao-Yu Tung and Heiko Strathmann and Soumyajit De and Aaditya Ramdas and Alex Smola and Arthur Gretton},
title = {Generative Models and Model Criticism via Optimized Maximum Mean Discrepancy},
booktitle = {ICLR},
year = {2017},
eprinttype = {arXiv},
eprint = {1611.04488},
}

@inproceedings{liu2020learning,
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  booktitle={ICML},
  year={2020},
  eprinttype = {arXiv},
  eprint = {2002.09116},
}

@incollection{Bengio+chapter2007,
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booktitle = {Large Scale Kernel Machines},
publisher = {MIT Press},
title = {Scaling Learning Algorithms Towards {AI}},
year = {2007}
}

@article{Hinton06,
author = {Hinton, Geoffrey E. and Osindero, Simon and Teh, Yee Whye},
journal = {Neural Computation},
pages = {1527--1554},
title = {A Fast Learning Algorithm for Deep Belief Nets},
volume = {18},
year = {2006}
}

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title={Deep learning},
author={Goodfellow, Ian and Bengio, Yoshua and Courville, Aaron and Bengio, Yoshua},
volume={1},
year={2016},
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  year={2012}
}

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  journal={arXiv preprint arXiv:1312.6199},
  year={2013}
}

@inproceedings{goodfellow2014explaining,
  title={Explaining and harnessing adversarial examples},
  author={Goodfellow, Ian J and Shlens, Jonathon and Szegedy, Christian},
  booktitle = {ICLR},
  year      = {2015},
}

@inproceedings{nguyen2015deep,
  title={Deep neural networks are easily fooled: High confidence predictions for unrecognizable images},
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  booktitle={Proceedings of the IEEE conference on computer vision and pattern recognition},
  pages={427--436},
  year={2015}
}

@article{grosse2017statistical,
  title={On the (statistical) detection of adversarial examples},
  author={Grosse, Kathrin and Manoharan, Praveen and Papernot, Nicolas and Backes, Michael and McDaniel, Patrick},
  journal={arXiv:1702.06280},
  year={2017}
}





@inproceedings{gao2021maximum,
  title={Maximum Mean Discrepancy is Aware of Adversarial Attacks},
  author={Gao, Ruize and Liu, Feng and Zhang, Jingfeng and Han, Bo and Liu, Tongliang and Gang, Niu and Sugiyama, Masashi},
  booktitle={ICML},
  year={2021},
  eprint = {2010.11415},
}

@book{scholkopf2002learning,
  title={Learning with kernels: support vector machines, regularization, optimization, and beyond},
  author={Sch{\"o}lkopf, Bernhard and Smola, Alexander J and Bach, Francis and others},
  year={2002},
  publisher={MIT press}
}

@book{berlinet2011reproducing,
  title={Reproducing kernel Hilbert spaces in probability and statistics},
  author={Berlinet, Alain and Thomas-Agnan, Christine},
  year={2011},
  publisher={Springer Science \& Business Media}
}

@article{muandet2016kernel,
  title={Kernel mean embedding of distributions: A review and beyond},
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  journal={arXiv preprint arXiv:1605.09522},
  year={2016}
}

@Book{BerTho04,
  author =   {A. Berlinet and C. {Thomas-Agnan}},
  title =    {Reproducing Kernel Hilbert Spaces in Probability and Statistics},
  publisher =    {Kluwer},
  year =     {2004},
}




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volume = {8},
year = {2007}
}

@inproceedings{Heller2016,
author = {Heller, Ruth and Heller, Yair},
booktitle = {NeurIPS},
title = {Multivariate tests of association based on univariate tests},
year = {2016},
eprinttype = {arXiv},
eprint = {1603.03418},
}

@article{Szekely2013,
author = {Sz{\'{e}}kely, G{\'{a}}bor J. and Rizzo, Maria L.},
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number = {8},
pages = {1249--1272},
title = {Energy statistics: A class of statistics based on distances},
volume = {143},
year = {2013}
}

@article{RamdasGarciaCuturi,
eprinttype = {arXiv},
eprint = {1509.02237},
author = {Ramdas, Aaditya and Garc{\'i}a Trillos, Nicol{\'a}s and Cuturi, Marco},
journal = {Entropy},
month = jan,
number = {2},
pages = {47},
title = {On {W}asserstein Two-Sample Testing and Related Families of Nonparametric Tests},
volume = {19},
year = {2017},
}

@article{kim2020classificationaccuracyproxysample,
author = {Ilmun Kim and Aaditya Ramdas and Aarti Singh and Larry Wasserman},
title = {Classification Accuracy as a Proxy for Two Sample Testing},
year = {2021},
journal = {Annals of Statistics},
volume = {49},
number = {1},
pages = {411 -- 434},
eprinttype = {arXiv},
eprint = {1602.02210},
}


@article{Hido2011,
author = {Hido, Shohei and Tsuboi, Yuta and Kashima, Hisashi and Sugiyama, Masashi and Kanamori, Takafumi},
journal = {Knowledge and Information Systems},
number = {2},
pages = {309--336},
title = {Statistical outlier detection using direct density ratio estimation},
volume = {26},
year = {2011}
}

@inproceedings{Smola2009,
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booktitle = {AISTATS},
pages = {536--543},
title = {{Relative novelty detection}},
year = {2009}
}

@book{Gibbons2011,
address = {New York},
author = {Gibbons, Jean Dickinson and Chakraborti, Subhabrata},
publisher = {Springer},
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year = {2011}
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@inproceedings{Blum89,
author = {Blum, Avrim and Rivest, Ronald L.},
title = {Training a 3-Node Neural Network is NP-Complete},
year = {1989},
}

@inproceedings{Blaschko2013,
author = {Zaremba, Wojciech and Gretton, Arthur and Blaschko, Matthew},
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year = {2013}
}

@article{Biau2005,
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title = {{On the asymptotic properties of a nonparametric L1-test statistic of homogeneity}},
volume = {51},
year = {2005}
}

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archivePrefix = {arXiv},
arxivId = {1106.4729},
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booktitle = {NeurIPS},
title = {{Relative density-ratio estimation for robust distribution comparison}},
pages = {596--602},
year = {2011}
}

@article{Bartlett2002,
author = {Bartlett, Peter L. and Mendelson, Shahar},
journal = {Journal of Machine Learning Research},
pages = {224--240},
title = {{Rademacher and Gaussian Complexities: Risk Bounds and Structural Results}},
volume = {3},
year = {2002}
}

@article{Maa1996,
author = {Maa, Jen Fue and Pearl, Dennis K. and Bartoszy{\'{n}}ski, Robert},
doi = {10.1214/aos/1032526956},
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@article{Bu2018,
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year = {2018}
}

@article{Schilling1986,
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title = {{Multivariate two-sample nearest tests based on nearest neighbours}},
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year = {1986}
}

@article{Lheritier2018,
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number = {5},
pages = {3361--3370},
title = {{A sequential non-parametric multivariate two-sample test}},
volume = {64},
year = {2018}
}

@article{Mondal2015,
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doi = {10.1016/j.jmva.2015.07.002},
issn = {10957243},
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publisher = {Elsevier Inc.},
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year = {2015}
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@article{Chen2017,
author = {Chen, Hao and Friedman, Jerome H.},
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number = {517},
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title = {A new graph-based two-sample test for multivariate and object data},
volume = {112},
year = {2017},
eprint = {1307.6294},
eprinttype = {arXiv},
}


@inproceedings{Gong2016,
author = {Gong, Mingming and Zhang, Kun and Liu, Tongliang and Tao, Dacheng and Glymour, Clark and Sch{\"o}lkopf, Behrnhard},
booktitle = {ICML},
title = {Domain adaptation with conditional transferable components},
year = {2016}
}

@article{Shimodaira2000,
author = {Shimodaira, Hidetoshi},
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@article{Ghifary2017,
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year = {2017}
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@book{Dudley,
author = {Dudley, Richard M.},
publisher = {Cambridge University Press},
title = {{Real Analysis and Probability}},
year = {2002}
}

@inproceedings{DosReis2016,
author = {Reis, Denis dos and Flach, Peter and Matwin, Stan and Batista, Gustavo},
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year = {2016}
}

@inproceedings{eig-mmd-null,
author = {Gretton, Arthur and Fukumizu, Kenji and Harchaoui, Za{\"i}d and Sriperumbudur, Bharath K.},
booktitle = {NeurIPS},
title = {A fast, consistent kernel two-sample test},
year = {2009}
}

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author = "Dwass, Meyer",
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pages = "181--187",
title = "Modified Randomization Tests for Nonparametric Hypotheses",
volume = "28",
year = "1957"
}



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title = {{H}ilbert space embeddings and metrics on probability measures},
volume = {11},
year = {2009}
}

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year = {1988}
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year = {2005}
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@inbook{mcdiarmid_1989,
author = {McDiarmid, Colin},
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editor = {Siemons, J.Editor},
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@inproceedings{Harchaoui2007,
author = {Harchaoui, Z. and Bach, F. and Moulines, E.},
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title = {Testing for homogeneity with kernel {F}isher discriminant analysis},
year = {2007}
}

@inproceedings{GSSSP12:kernel-choice,
author = {Gretton, Arthur and Sriperumbudur, Bharath and Sejdinovic, Dino and Strathmann, Heiko and Pontil, Massimiliano},
booktitle = {NeurIPS},
title = {Optimal kernel choice for large-scale two-sample tests},
year = {2012}
}

@inproceedings{Chwialkowski2015,
author = {Chwialkowski, Kacper and Ramdas, Aaditya and Sejdinovic, Dino and Gretton, Arthur},
booktitle = {NeurIPS},
title = {Fast two-sample testing with analytic representations of probability measures},
year = {2015},
eprinttype = {arXiv},
eprint = {1506.04725},
}

@book{Cohn2013,
address = {New York},
author = {Cohn, Donald L.},
edition = {Second},
pages = {123--125},
publisher = {Springer},
title = {Measure Theory},
year = {2013}
}



@inproceedings{Jitkrittum2017,
author = {Jitkrittum, Wittawat and Xu, Wenkai and Szabo, Zoltan and Fukumizu, Kenji and Gretton, Arthur},
booktitle = {NeurIPS},
title = {A linear-time kernel goodness-of-fit test},
year = {2017},
eprinttype = {arXiv},
eprint = {1705.07673},
}

@inproceedings{Goodfellow2014,
archivePrefix = {arXiv},
arxivId = {1406.2661},
author = {Goodfellow, Ian and Pouget-Abadie, Jean and Mirza, Mehdi and Xu, Bing and Warde-Farley, David and Ozair, Sherjil and Courville, Aaron and Bengio, Yoshua},
eprint = {1406.2661},
booktitle = {NeurIPS},
pages = {2672--2680},
title = {Generative Adversarial Nets},
year = {2014}
}


@inproceedings{Ramdas2014,
author = {Ramdas, Aaditya and Reddi, Sashank J. and Poczos, Barnabas and Singh, Aarti and Wasserman, Larry},
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title = {On the high-dimensional power of linear-time kernel two-sample testing under mean-difference alternatives},
year = {2014}
}
@inproceedings{Lloyd2015,
author = {Lloyd, James Robert and Ghahramani, Zoubin},
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title = {Statistical model criticism using kernel two sample tests},
year = {2015}
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@inproceedings{Ghoshdastidar2017,
author = {Ghoshdastidar, Debarghya and Gutzeit, Maurilio and Carpentier, Alexandra and von Luxburg, Ulrike},
booktitle = {COLT},
title = {Two-sample tests for large random graphs using network statistics},
year = {2017},
eprinttype = {arXiv},
eprint = {1705.06168},
}

@article{liu2018accumulating,
author = {Liu, Anjin and Lu, Jie and Liu, Feng and Zhang, Guangquan},
journal = {Pattern Recognition},
pages = {256--272},
title = {{Accumulating regional density dissimilarity for concept drift detection in data streams}},
volume = {76},
year = {2018}
}

@book{evans2015measure,
  title={Measure Theory and Fine Properties of Functions},
  author={Evans, Lawrence Craig and Gariepy, Ronald F},
  year={2015},
  publisher={CRC Press}
}

@article{Def_MGGD,
author    = {Fr{\'{e}}d{\'{e}}ric Pascal and
               Lionel Bombrun and
               Jean{-}Yves Tourneret and
               Yannick Berthoumieu},
title     = {Parameter Estimation For Multivariate Generalized {G}aussian Distributions},
journal   = {{IEEE} Transactions on Signal Processing},
volume    = {61},
number    = {23},
pages     = {5960--5971},
year      = {2013},
}

@inproceedings{MMD_GAN,
  author    = {Miko{\l{}}aj Bi{\'n}kowski and
               Danica J. Sutherland and
               Michael Arbel and
               Arthur Gretton},
  title     = {Demystifying {MMD} {GAN}s},
  booktitle   = {ICLR},
  year      = {2018},
  eprinttype = {arXiv},
  eprint = {1801.01401},
}

@book{Analytic_p_2002,
address = {New York},
author = {Krantz, Steven G., and Harold R. Parks},
edition = {Second},
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