66 citations · 375 across the 33 of their papers we have counts for
33 papers
Fourier Features for Identifying Differential Equations (FourierIdent)
Mengyi Tang, Hao Liu, Wenjing Liao +1
We investigate the benefits and challenges of utilizing the frequency information in differential equation identification. Solving differential equations and Fourier analysis are c…
Effective Minkowski Dimension of Deep Nonparametric Regression: Function Approximation and Statistical Theories
Zixuan Zhang, Minshuo Chen, Mengdi Wang +2
Existing theories on deep nonparametric regression have shown that when the input data lie on a low-dimensional manifold, deep neural networks can adapt to the intrinsic data struc…
Group projected Subspace Pursuit for Identification of variable coefficient differential equations (GP-IDENT)
Yuchen He, Sung-Ha Kang, Wenjing Liao +2
We propose an effective and robust algorithm for identifying partial differential equations (PDEs) with space-time varying coefficients from a single trajectory of noisy observatio…
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…
High Dimensional Binary Classification under Label Shift: Phase Transition and Regularization
Jiahui Cheng, Minshuo Chen, Hao Liu +2
Label Shift has been widely believed to be harmful to the generalization performance of machine learning models. Researchers have proposed many approaches to mitigate the impact of…
WeakIdent: Weak formulation for Identifying Differential Equations using Narrow-fit and Trimming
Mengyi Tang, Wenjing Liao, Rachel Kuske +1
Data-driven identification of differential equations is an interesting but challenging problem, especially when the given data are corrupted by noise. When the governing differenti…
Numerical Identification of Nonlocal Potential in Aggregation
Yuchen He, Sung Ha Kang, Wenjing Liao +2
Aggregation equations are broadly used to model population dynamics with nonlocal interactions, characterized by a potential in the equation. This paper considers the inverse probl…
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…
Stability and Super-resolution of MUSIC and ESPRIT for Multi-snapshot Spectral Estimation
Weilin Li, Zengying Zhu, Weiguo Gao +1
This paper studies the spectral estimation problem of estimating the locations of a fixed number of point sources given multiple snapshots of Fourier measurements collected by a un…
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…
Doubly Robust Off-Policy Learning on Low-Dimensional Manifolds by Deep Neural Networks
Minshuo Chen, Hao Liu, Wenjing Liao +1
Causal inference explores the causation between actions and the consequent rewards on a covariate set. Recently deep learning has achieved a remarkable performance in causal infere…
Robust Identification of Differential Equations by Numerical Techniques from a Single Set of Noisy Observation
Yuchen He, Sung Ha Kang, Wenjing Liao +2
We propose robust methods to identify underlying Partial Differential Equation (PDE) from a given set of noisy time dependent data. We assume that the governing equation is a linea…
Distribution Approximation and Statistical Estimation Guarantees of Generative Adversarial Networks
Minshuo Chen, Wenjing Liao, Hongyuan Zha +1
Generative Adversarial Networks (GANs) have achieved a great success in unsupervised learning. Despite its remarkable empirical performance, there are limited theoretical studies o…
An auto-parameter denoising method for nuclear magnetic resonance spectroscopy based on low-rank Hankel matrix
Tianyu Qiu, Wenjing Liao, Di Guo +4
Nuclear Magnetic Resonance (NMR) spectroscopy, which is modeled as the sum of damped exponential signals, has become an indispensable tool in various scenarios, such as the structu…
Learning functions varying along a central subspace
Hao Liu, Wenjing Liao
Many functions of interest are in a high-dimensional space but exhibit low-dimensional structures. This paper studies regression of a -Hölder function in whic…
Nonparametric Regression on Low-Dimensional Manifolds using Deep ReLU Networks : Function Approximation and Statistical Recovery
Minshuo Chen, Haoming Jiang, Wenjing Liao +1
Real world data often exhibit low-dimensional geometric structures, and can be viewed as samples near a low-dimensional manifold. This paper studies nonparametric regression of Höl…
Conditioning of restricted Fourier matrices and super-resolution of MUSIC
Weilin Li, Wenjing Liao
This paper studies stable recovery of a collection of point sources from its noisy low-frequency Fourier coefficients. We focus on the super-resolution regime where the minim…
Super-resolution limit of the ESPRIT algorithm
Weilin Li, Wenjing Liao, Albert Fannjiang
The problem of imaging point objects can be formulated as estimation of an unknown atomic measure from its consecutive noisy Fourier coefficients. The standard resolution of…
IDENT: Identifying Differential Equations with Numerical Time evolution
Sung Ha Kang, Wenjing Liao, Yingjie Liu
Identifying unknown differential equations from a given set of discrete time dependent data is a challenging problem. A small amount of noise can make the recovery unstable, and no…
Stable super-resolution limit and smallest singular value of restricted Fourier matrices
Weilin Li, Wenjing Liao
We consider the inverse problem of recovering the locations and amplitudes of a collection of point sources represented as a discrete measure, given of its noisy low-frequenc…