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We consider the problem of learning high dimensional polynomial transformations of Gaussians.
Approximating discrete probability distributions with dependence trees
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Tt-cross approximation for multidimensional arrays
Ivan Oseledets and Eugene Tyrtyshnikov · 2010
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Candidate one-way functions based on expander graphs
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Tensor-train decomposition
Ivan V Oseledets · 2011
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Provable ica with unknown gaussian noise, with implications for gaussian mixtures and autoencoders
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Black box approximation of tensors in hierarchical tucker format
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Learning mixtures of spherical gaussians: moment methods and spectral decompositions
Daniel Hsu and Sham M Kakade · 2013
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Auto-encoding variational bayes
Diederik P Kingma and Max Welling · 2013
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Equations for secant varieties of veronese and other varieties
Joseph M Landsberg and Giorgio Ottaviani · 2013
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Animashree Anandkumar, Rong Ge, Daniel Hsu, Sham M Kakade, and Matus Telgarsky · 2014
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Statistical inference and the sum of squares method
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Robust moment estimation and improved clustering via sum of squares
Pravesh K Kothari, Jacob Steinhardt, and David Steurer · 2018
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How well generative adversarial networks learn distributions
Tengyuan Liang · 2018
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Nonparametric density estimation under adversarial losses
Shashank Singh, Ananya Uppal, Boyue Li, Chun-Liang Li, Manzil Zaheer, and Barnabás Póczos · 2018
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High-dimensional probability: An introduction with applications in data science
Roman Vershynin · 2018
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Aditya Bhaskara, Moses Charikar, Ankur Moitra, and Aravindan Vijayaraghavan · 2014
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Generative adversarial nets
Ian Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, and Yoshua Bengio · 2014
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Alexander Novikov, Anton Rodomanov, Anton Osokin, and Dmitry Vetrov · 2014
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Dictionary learning and tensor decomposition via the sum-of-squares method
Boaz Barak, Jonathan A Kelner, and David Steurer · 2015
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Guy Bresler · 2015
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Ke Ye and Lek-Heng Lim · 2018
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Smoothed analysis in unsupervised learning via decoupling
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Negative momentum for improved game dynamics
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Mean-field approximation, convex hierarchies, and the optimality of correlation rounding: a unified perspective
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Nonparametric density estimation & convergence rates for gans under besov ipm losses
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Learning distributions generated by one-layer relu networks
Shanshan Wu, Alexandros G Dimakis, and Sujay Sanghavi · 2019
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Sparse logistic regression learns all discrete pairwise graphical models
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Multi-item mechanisms without item-independence: Learnability via robustness
Johannes Brustle, Yang Cai, and Constantinos Daskalakis · 2020
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Efficient distance approximation for structured high-dimensional distributions via learning
Arnab Bhattacharyya, Sutanu Gayen, Kuldeep S Meel, and NV Vinodchandran · 2020
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Learning a tree-structured ising model in order to make predictions
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Tensor ring decomposition: optimization landscape and one-loop convergence of alternating least squares
Ziang Chen, Yingzhou Li, and Jianfeng Lu · 2020
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Learning mixtures of linear regressions in subexponential time via fourier moments
Sitan Chen, Jerry Li, and Zhao Song · 2020
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Statistical guarantees of generative adversarial networks for distribution estimation
Minshuo Chen, Wenjing Liao, Hongyuan Zha, and Tuo Zhao · 2020
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Small covers for near-zero sets of polynomials and learning latent variable models
Ilias Diakonikolas and Daniel M Kane · 2020
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The minimax learning rates of normal and ising undirected graphical models
Luc Devroye, Abbas Mehrabian, and Tommy Reddad · 2020
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The sparse hausdorff moment problem, with application to topic models
Spencer Gordon, Bijan Mazaheri, Leonard J Schulman, and Yuval Rabani · 2020
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Learning ising and potts models with latent variables
Surbhi Goel · 2020
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Variational autoencoders and nonlinear ica: A unifying framework
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Making method of moments great again?–how can gans learn distributions
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SGD learns one-layer networks in wgans
Qi Lei, Jason Lee, Alex Dimakis, and Constantinos Daskalakis · 2020
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Zeyuan Allen-Zhu and Yuanzhi Li · 2021
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Chow-liu++: Optimal prediction-centric learning of tree ising models
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Near-optimal learning of tree-structured distributions by chow-liu
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Outlier-robust learning of ising models under dobrushin’s condition
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Sample-optimal and efficient learning of tree ising models
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A review on generative adversarial networks: Algorithms, theory, and applications
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Efficient construction of tensor ring representations from sampling
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Statistical guarantees for generative models without domination
Nicolas Schreuder, Victor-Emmanuel Brunel, and Arnak Dalalyan · 2021
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Wasserstein gans work because they fail (to approximate the wasserstein distance)
Jan Stanczuk, Christian Etmann, Lisa Maria Kreusser, and Carola-Bibiane Schönlieb · 2021
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Minimax optimality (probably) doesn’t imply distribution learning for gans
Sitan Chen, Jerry Li, Yuanzhi Li, and Raghu Meka · 2022
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