@article{pdg-aaai,
  title={Probabilistic Dependency Graphs},
  author={Oliver E Richardson and Joseph Y Halpern},
  journal={AAAI '21},
  year={2021},
  eprint={2012.10800},
  archivePrefix={arXiv},
  primaryClass={cs.AI}
}
% journal={AAAI},
@book{mackay2003information,
  title={Information Theory, Inference and Learning Algorithms},
author={MacKay, David J. C.},
  year={2003},
  publisher={Cambridge University Press}
}
@book{halpern2017reasoning,
	title={Reasoning About Uncertainty},
	author={Halpern, Joseph Y},
	year={2017},
	publisher={MIT press}
}
@article{jaynes1957information,
  title={Information Theory and Statistical Mechanics},
  author={Jaynes, Edwin T},
  journal={Physical review},
  volume={106},
  number={4},
  pages={620},
  year={1957},
  publisher={APS}
}
@article{chu1965shortest,
  title={On the Shortest Arborescence of a Directed Graph},
  author={Chu, Yoeng-Jin},
  journal={Scientia Sinica},
  volume={14},
  pages={1396--1400},
  year={1965}
}
@article{one-true-loss,
  title={Loss as the Inconsistency of a Probabilistic Dependency Graph: Choose Your Model, Not Your Loss Function},
  author={Oliver E Richardson},
  journal={AISTATS '22},
  year={2022},
  eprint={2202.11862},
  archivePrefix={arXiv},
  primaryClass={cs.AI},
  series = {Proceedings of Machine Learning Research},
  volume = {151},
  publisher = {PMLR},
}
  %
  % pages = {2706-2735},
%   booktitle = {International Conference on Artificial Intelligence and Statistics, AISTATS 2022, 28-30 March 2022, Virtual Event},
%   editor = {Gustau Camps-Valls and Francisco J. R. Ruiz and Isabel Valera},
%  journal={AISTATS},
%  inproceedings{one-true-loss,
%   title = {Loss as the Inconsistency of a Probabilistic Dependency Graph: Choose Your Model, Not Your Loss Function},
%   author = {Oliver E Richardson},
%   journal={AISTATS '22},
%   year = {2022},
%   url = {https://proceedings.mlr.press/v151/richardson22b.html},
%   pages = {2706-2735},
%   booktitle = {International Conference on Artificial Intelligence and Statistics, AISTATS 2022, 28-30 March 2022, Virtual Event},
%   editor = {Gustau Camps-Valls and Francisco J. R. Ruiz and Isabel Valera},
%   series = {Proceedings of Machine Learning Research},
%   volume = {151},
%   publisher = {PMLR},
% }
@article{dahl2022primal,
  title={A Primal-Dual Interior-Point Algorithm For Nonsymmetric Exponential-Cone Optimization},
  author={Dahl, Joachim and Andersen, Erling D},
  journal={Mathematical Programming},
  volume={194},
  number={1},
  pages={341--370},
  year={2022},
  publisher={Springer}
}
@article{yuille2003concave,
  title={The Concave-Convex Procedure},
  author={Yuille, Alan L and Rangarajan, Anand},
  journal={Neural computation},
  volume={15},
  number={4},
  pages={915--936},
  year={2003},
  publisher={MIT Press}
}
@article{badenbroek2021algorithm,
  title={An Algorithm for Nonsymmetric Conic Optimization Inspired by Mosek},
  author={Badenbroek, Riley and Dahl, Joachim},
  journal={Optimization Methods and Software},
  pages={1--38},
  year={2021},
  publisher={Taylor \& Francis}
}
@article{chandrasekaran2012complexity,
  title={Complexity of Inference in Graphical Models},
  author={Chandrasekaran, Venkat and Srebro, Nathan and Harsha, Prahladh},
  journal={arXiv preprint arXiv:1206.3240},
  year={2012}
}
Portions of this work were done while the first and third authors were at the Toyota Technological Institute in
Chicago. A preliminary version of this paper appeared in Proc. 24th Conference on Uncertainty in Artificial Intelligence (UAI), 2008 (Chandrasekaran et al., 2008)
@InProceedings{networkx,
  author =       {Aric A. Hagberg and Daniel A. Schult and Pieter J. Swart},
  title =        {Exploring Network Structure, Dynamics, and Function using NetworkX},
  booktitle =   {Proceedings of the 7th Python in Science Conference},
  pages =     {11 - 15},
  address = {Pasadena, CA USA},
  year =      {2008},
  editor =    {Ga\"el Varoquaux and Travis Vaught and Jarrod Millman},
}
@book{koller2009probabilistic,
	title={Probabilistic Graphical Models: Principles and Techniques},
	author={Koller, Daphne and Friedman, Nir},
	year={2009},
	publisher={MIT press}
}
@incollection{dcp-article,
  title={Disciplined Convex Programming},
  author={Grant, Michael and Boyd, Stephen and Ye, Yinyu},
  booktitle={Global optimization},
  pages={155--210},
  year={2006},
  publisher={Springer},
  url={\url{https://web.stanford.edu/~boyd/papers/pdf/mcg\_thesis.pdf}}
}
@phdthesis{dcp-thesis,
  author  = {Michael Charles Grant},
  title   = {Disciplined Convex Programming},
  school  = {Stanfor University},
  year    = {2004},
  month   = {December},
  url  = {https://web.stanford.edu/~boyd/papers/pdf/mcg_thesis.pdf}
}
@inproceedings{bodlaender1993linear,
  title={A Linear Time Algorithm for Finding Tree-Decompositions of Small Treewidth},
  author={Bodlaender, Hans L},
  booktitle={Proceedings of the twenty-fifth annual ACM symposium on Theory of computing},
  pages={226--234},
  year={1993}
}
@article{wainwright2008graphical,
  title={Graphical Models, Exponential Families, and Variational Inference},
  author={Wainwright, Martin J and Jordan, Michael I and others},
  journal={Foundations and Trends{} in Machine Learning},
  volume={1},
  number={1--2},
  pages={1--305},
  year={2008},
  publisher={Now Publishers, Inc.}
}
@article{diamond2016cvxpy,
  author  = {Steven Diamond and Stephen Boyd},
  title   = {{CVXPY}: {A} {P}ython-Embedded Modeling Language for Convex Optimization},
  journal = {Journal of Machine Learning Research},
  year    = {2016},
  volume  = {17},
  number  = {83},
  pages   = {1--5},
}
@article{agrawal2018rewriting,
  author  = {Agrawal, Akshay and Verschueren, Robin and Diamond, Steven and Boyd, Stephen},
  title   = {A Rewriting System for Convex Optimization Problems},
  journal = {Journal of Control and Decision},
  year    = {2018},
  volume  = {5},
  number  = {1},
  pages   = {42--60},
}
@manual{mosek,
   author = "MOSEK ApS",
   title = "MOSEK Optimizer API for Python 10.0.25",
   year = 2022,
   url = "https://docs.mosek.com/10.0/pythonapi/index.html"
 }
 @book{lee2013smooth,
   title={Smooth Manifolds},
   author={Lee, John M},
   booktitle={Introduction to Smooth Manifolds},
   pages={50--55},
   year={2013},
   publisher={Springer}
 }

@InProceedings{lubin,
author="Lubin, Miles
and Yamangil, Emre
and Bent, Russell
and Vielma, Juan Pablo",
editor="Louveaux, Quentin
and Skutella, Martin",
title="Extended Formulations in Mixed-Integer Convex Programming",
booktitle="Integer Programming and Combinatorial Optimization",
year="2016",
publisher="Springer International Publishing",
address="Cham",
pages="102--113",
abstract="We present a unifying framework for generating extended formulations for the polyhedral outer approximations used in algorithms for mixed-integer convex programming (MICP). Extended formulations lead to fewer iterations of outer approximation algorithms and generally faster solution times. First, we observe that all MICP instances from the MINLPLIB2 benchmark library are conic representable with standard symmetric and nonsymmetric cones. Conic reformulations are shown to be effective extended formulations themselves because they encode separability structure. For mixed-integer conic-representable problems, we provide the first outer approximation algorithm with finite-time convergence guarantees, opening a path for the use of conic solvers for continuous relaxations. We then connect the popular modeling framework of disciplined convex programming (DCP) to the existence of extended formulations independent of conic representability. We present evidence that our approach can yield significant gains in practice, with the solution of a number of open instances from the MINLPLIB2 benchmark library.",
isbn="978-3-319-33461-5"
}
@article{skajaa2015homogeneous,
  title={A Homogeneous Interior-Point Algorithm for Nonsymmetric Convex Conic Optimization},
  author={Skajaa, Anders and Ye, Yinyu},
  journal={Mathematical Programming},
  volume={150},
  number={2},
  pages={391--422},
  year={2015},
  publisher={Springer}
}
@article{duan2022faster,
  title={Faster Matrix Multiplication via Asymmetric Hashing},
  author={Duan, Ran and Wu, Hongxun and Zhou, Renfei},
  journal={arXiv preprint},
  doi = {10.48550/ARXIV.2210.10173},
  url = {https://arxiv.org/abs/2210.10173},
  year={2022}
}
@techreport{nesterov1996infeasible,
  title={Infeasible-Start Primal-Dual Methods and Infeasibility Detectors for Nonlinear Programming Problems},
  author={Nesterov, Yu E and Todd, Michael J and Ye, Yinyu},
  year={1999},
  journal={Mathematical Programming},
  volume={84},
  pages={227--267},
  doi={https://doi.org/10.1007/s10107980009a}
}
% institution={Cornell University Operations Research and Industrial Engineering}
@book{nesterov1994book,
  title={Interior-Point Polynomial Algorithms in Convex Programming},
  author={Nesterov, Yurii and Nemirovskii, Arkadii},
  year={1994},
  publisher={SIAM}
}
@article{treewidth-bertele&brioschi,
    author={Bertel{\`e}, Umberto; Brioschi, Francesco},
    year={1972},
    journnal={Nonserial Dynamic Programming},
    publisher={Academic Press},
    pages={37--38},
    isbn={978-0-12-093450-8}
}
@article{patil1986structure,
  title={On the structure of k-trees},
  author={Patil, HP},
  journal={Journal of Combinatorics, Information and System Sciences},
  volume={11},
  number={2-4},
  pages={57--64},
  year={1986}
}
@inproceedings{karmarkar1984new,
  title={A New Polynomial-Time Algorithm for Linear Programming},
  author={Karmarkar, Narendra},
  booktitle={Proceedings of the Sixteenth Annual ACM Symposium on Theory of Computing},
  pages={302--311},
  year={1984}
}
@article{courcelle1990,
title = {The Monadic Second-order Logic of Graphs. I. Recognizable Sets of Finite Graphs},
journal = {Information and Computation},
volume = {85},
number = {1},
pages = {12-75},
year = {1990},
issn = {0890-5401},
doi = {https://doi.org/10.1016/0890-5401(90)90043-H},
url = {https://www.sciencedirect.com/science/article/pii/089054019090043H},
author = {Bruno Courcelle},
abstract = {The notion of a recognizable set of finite graphs is introduced. Every set of finite graphs, that is definable in monadic second-order logic is recognizable, but not vice versa. The monadic second-order theory of a context-free set of graphs is decidable.}
}
@book{fletcher2013practical,
  title={Practical methods of optimization},
  author={Fletcher, Roger},
  year={2013},
  publisher={John Wiley \& Sons}
}
@article{kingma2014adam,
  title={Adam: A Method for Stochastic Optimization},
  author={Kingma, Diederik P and Ba, Jimmy},
  journal={arXiv preprint arXiv:1412.6980},
  year={2014}
}

@misc{pytorch,
  doi = {10.48550/ARXIV.1912.01703}, 
  url = {https://arxiv.org/abs/1912.01703},
  author = {Paszke, Adam and Gross, Sam and Massa, Francisco and Lerer, Adam and Bradbury, James and Chanan, Gregory and Killeen, Trevor and Lin, Zeming and Gimelshein, Natalia and Antiga, Luca and Desmaison, Alban and Köpf, Andreas and Yang, Edward and DeVito, Zach and Raison, Martin and Tejani, Alykhan and Chilamkurthy, Sasank and Steiner, Benoit and Fang, Lu and Bai, Junjie and Chintala, Soumith},
  keywords = {Machine Learning (cs.LG), Mathematical Software (cs.MS), Machine Learning (stat.ML), FOS: Computer and information sciences, FOS: Computer and information sciences},
  title = {PyTorch: An Imperative Style, High-Performance Deep Learning Library},
  publisher = {arXiv},
  year = {2019},
  copyright = {arXiv.org perpetual, non-exclusive license}
}

@article{kschischang2001sumproduct,
    author={F. R. {Kschischang} and B. J. {Frey} and H. -. {Loeliger}},
    journal={IEEE Transactions on Information Theory},
    title={Factor Graphs and the Sum-product Algorithm},
    year={2001},
    volume={47},
    number={2},
    pages={498-519},
}
@article{kingma2013autoencoding,
    title={Auto-Encoding Variational Bayes},
    author={Diederik P Kingma and Max Welling},
    journal={Proceedings of the International Conference on Learning Representations (ICLR)},
    year={2014},
    eprint={1312.6114},
    archivePrefix={arXiv},
    primaryClass={stat.ML}
}
@INPROCEEDINGS{ECOS,
  author={Domahidi, Alexander and Chu, Eric and Boyd, Stephen},
  booktitle={2013 European Control Conference (ECC)}, 
  title={ECOS: An SOCP solver for embedded systems}, 
  year={2013},
  volume={},
  number={},
  pages={3071-3076},
  doi={10.23919/ECC.2013.6669541}}
