Timezone: »
Deep generative models have experienced great empirical successes in distribution learning. Many existing experiments have demonstrated that deep generative networks can efficiently generate high-dimensional complex data from a low-dimensional easy-to-sample distribution. However, this phenomenon can not be justified by existing theories. The widely held manifold hypothesis speculates that real-world data sets, such as natural images and signals, exhibit low-dimensional geometric structures. In this paper, we take such low-dimensional data structures into consideration by assuming that data distributions are supported on a low-dimensional manifold. We prove approximation and estimation theories of deep generative networks for estimating distributions on a low-dimensional manifold under the Wasserstein-1 loss. We show that the Wasserstein-1 loss converges to zero at a fast rate depending on the intrinsic dimension instead of the ambient data dimension. Our theory leverages the low-dimensional geometric structures in data sets and justifies the practical power of deep generative models. We require no smoothness assumptions on the data distribution which is desirable in practice.
Author Information
Biraj Dahal (Georgia Institute of Technology)
Alexander Havrilla (Georgia Institute of Technology)
Minshuo Chen (Princeton University)
Tuo Zhao (Georgia Tech)
Wenjing Liao (Georgia Tech)
More from the Same Authors
-
2022 : Benefits of Overparameterized Convolutional Residual Networks: Function Approximation under Smoothness Constraint »
Hao Liu · Minshuo Chen · Siawpeng Er · Wenjing Liao · Tong Zhang · Tuo Zhao -
2023 Poster: Efficient RL with Impaired Observability: Learning to Act with Delayed and Missing State Observations »
Minshuo Chen · Yu Bai · H. Vincent Poor · Mengdi Wang -
2023 Poster: Model-Based Reparameterization Policy Gradient Methods: Theory and Practical Algorithms »
Shenao Zhang · Boyi Liu · Zhaoran Wang · Tuo Zhao -
2023 Poster: Module-wise Adaptive Distillation for Multimodality Foundation Models »
Chen Liang · Jiahui Yu · Ming-Hsuan Yang · Matthew Brown · Yin Cui · Tuo Zhao · Boqing Gong · Tianyi Zhou -
2023 Poster: Robust Multi-Agent Reinforcement Learning via Adversarial Regularization: Theoretical Foundation and Stable Algorithms »
Alexander Bukharin · Yan Li · Yue Yu · Qingru Zhang · Zhehui Chen · Simiao Zuo · Chao Zhang · Songan Zhang · Tuo Zhao -
2023 Poster: Reward-Directed Conditional Diffusion: Provable Distribution Estimation and Reward Improvement »
Hui Yuan · Kaixuan Huang · Chengzhuo Ni · Minshuo Chen · Mengdi Wang -
2021 Poster: Pessimism Meets Invariance: Provably Efficient Offline Mean-Field Multi-Agent RL »
Minshuo Chen · Yan Li · Ethan Wang · Zhuoran Yang · Zhaoran Wang · Tuo Zhao -
2020 Session: Orals & Spotlights Track 34: Deep Learning »
Tuo Zhao · Jimmy Ba -
2020 Poster: Differentiable Top-k with Optimal Transport »
Yujia Xie · Hanjun Dai · Minshuo Chen · Bo Dai · Tuo Zhao · Hongyuan Zha · Wei Wei · Tomas Pfister -
2020 Poster: Why Do Deep Residual Networks Generalize Better than Deep Feedforward Networks? --- A Neural Tangent Kernel Perspective »
Kaixuan Huang · Yuqing Wang · Molei Tao · Tuo Zhao -
2020 Poster: Towards Understanding Hierarchical Learning: Benefits of Neural Representations »
Minshuo Chen · Yu Bai · Jason Lee · Tuo Zhao · Huan Wang · Caiming Xiong · Richard Socher -
2019 : Poster and Coffee Break 2 »
Karol Hausman · Kefan Dong · Ken Goldberg · Lihong Li · Lin Yang · Lingxiao Wang · Lior Shani · Liwei Wang · Loren Amdahl-Culleton · Lucas Cassano · Marc Dymetman · Marc Bellemare · Marcin Tomczak · Margarita Castro · Marius Kloft · Marius-Constantin Dinu · Markus Holzleitner · Martha White · Mengdi Wang · Michael Jordan · Mihailo Jovanovic · Ming Yu · Minshuo Chen · Moonkyung Ryu · Muhammad Zaheer · Naman Agarwal · Nan Jiang · Niao He · Nikolaus Yasui · Nikos Karampatziakis · Nino Vieillard · Ofir Nachum · Olivier Pietquin · Ozan Sener · Pan Xu · Parameswaran Kamalaruban · Paul Mineiro · Paul Rolland · Philip Amortila · Pierre-Luc Bacon · Prakash Panangaden · Qi Cai · Qiang Liu · Quanquan Gu · Raihan Seraj · Richard Sutton · Rick Valenzano · Robert Dadashi · Rodrigo Toro Icarte · Roshan Shariff · Roy Fox · Ruosong Wang · Saeed Ghadimi · Samuel Sokota · Sean Sinclair · Sepp Hochreiter · Sergey Levine · Sergio Valcarcel Macua · Sham Kakade · Shangtong Zhang · Sheila McIlraith · Shie Mannor · Shimon Whiteson · Shuai Li · Shuang Qiu · Wai Lok Li · Siddhartha Banerjee · Sitao Luan · Tamer Basar · Thinh Doan · Tianhe Yu · Tianyi Liu · Tom Zahavy · Toryn Klassen · Tuo Zhao · Vicenç Gómez · Vincent Liu · Volkan Cevher · Wesley Suttle · Xiao-Wen Chang · Xiaohan Wei · Xiaotong Liu · Xingguo Li · Xinyi Chen · Xingyou Song · Yao Liu · YiDing Jiang · Yihao Feng · Yilun Du · Yinlam Chow · Yinyu Ye · Yishay Mansour · · Yonathan Efroni · Yongxin Chen · Yuanhao Wang · Bo Dai · Chen-Yu Wei · Harsh Shrivastava · Hongyang Zhang · Qinqing Zheng · SIDDHARTHA SATPATHI · Xueqing Liu · Andreu Vall -
2019 : Poster Spotlight 2 »
Aaron Sidford · Mengdi Wang · Lin Yang · Yinyu Ye · Zuyue Fu · Zhuoran Yang · Yongxin Chen · Zhaoran Wang · Ofir Nachum · Bo Dai · Ilya Kostrikov · Dale Schuurmans · Ziyang Tang · Yihao Feng · Lihong Li · Denny Zhou · Qiang Liu · Rodrigo Toro Icarte · Ethan Waldie · Toryn Klassen · Rick Valenzano · Margarita Castro · Simon Du · Sham Kakade · Ruosong Wang · Minshuo Chen · Tianyi Liu · Xingguo Li · Zhaoran Wang · Tuo Zhao · Philip Amortila · Doina Precup · Prakash Panangaden · Marc Bellemare -
2019 Poster: Towards Understanding the Importance of Shortcut Connections in Residual Networks »
Tianyi Liu · Minshuo Chen · Mo Zhou · Simon Du · Enlu Zhou · Tuo Zhao -
2019 Poster: Efficient Approximation of Deep ReLU Networks for Functions on Low Dimensional Manifolds »
Minshuo Chen · Haoming Jiang · Wenjing Liao · Tuo Zhao -
2018 Poster: Dimensionality Reduction for Stationary Time Series via Stochastic Nonconvex Optimization »
Minshuo Chen · Lin Yang · Mengdi Wang · Tuo Zhao -
2018 Poster: Provable Gaussian Embedding with One Observation »
Ming Yu · Zhuoran Yang · Tuo Zhao · Mladen Kolar · Zhaoran Wang