66 citations · 375 across the 33 of their papers we have counts for
8 papers · 1 filter
Deep Nonparametric Estimation of Intrinsic Data Structures by Chart Autoencoders: Generalization Error and Robustness
Hao Liu, Alex Havrilla, Rongjie Lai +1
Autoencoders have demonstrated remarkable success in learning low-dimensional latent features of high-dimensional data across various applications. Assuming that data are sampled n…
On Deep Generative Models for Approximation and Estimation of Distributions on Manifolds
Biraj Dahal, Alex Havrilla, Minshuo Chen +2
Generative networks have experienced great empirical successes in distribution learning. Many existing experiments have demonstrated that generative networks can generate high-dime…
Benefits of Overparameterized Convolutional Residual Networks: Function Approximation under Smoothness Constraint
Hao Liu, Minshuo Chen, Siawpeng Er +3
Overparameterized neural networks enjoy great representation power on complex data, and more importantly yield sufficiently smooth output, which is crucial to their generalization…
A Manifold Two-Sample Test Study: Integral Probability Metric with Neural Networks
Jie Wang, Minshuo Chen, Tuo Zhao +2
Two-sample tests are important areas aiming to determine whether two collections of observations follow the same distribution or not. We propose two-sample tests based on integral…
Deep Nonparametric Estimation of Operators between Infinite Dimensional Spaces
Hao Liu, Haizhao Yang, Minshuo Chen +2
Learning operators between infinitely dimensional spaces is an important learning task arising in wide applications in machine learning, imaging science, mathematical modeling and…
Besov Function Approximation and Binary Classification on Low-Dimensional Manifolds Using Convolutional Residual Networks
Hao Liu, Minshuo Chen, Tuo Zhao +1
Most of existing statistical theories on deep neural networks have sample complexities cursed by the data dimension and therefore cannot well explain the empirical success of deep…
Multiscale regression on unknown manifolds
Wenjing Liao, Mauro Maggioni, Stefano Vigogna
We consider the regression problem of estimating functions on but supported on a -dimensional manifold with . Draw…
Adaptive Geometric Multiscale Approximations for Intrinsically Low-dimensional Data
Wenjing Liao, Mauro Maggioni
We consider the problem of efficiently approximating and encoding high-dimensional data sampled from a probability distribution in , that is nearly supported on a…