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06/26/2023
Effective Minkowski Dimension of Deep Nonparametric Regression: Function Approximation and Statistical Theories
Existing theories on deep nonparametric regression have shown that when ...
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04/12/2023
Group projected Subspace Pursuit for Identification of variable coefficient differential equations (GP-IDENT)
We propose an effective and robust algorithm for identifying partial dif...
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03/17/2023
Deep Nonparametric Estimation of Intrinsic Data Structures by Chart Autoencoders: Generalization Error and Robustness
Autoencoders have demonstrated remarkable success in learning low-dimens...
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02/25/2023
On Deep Generative Models for Approximation and Estimation of Distributions on Manifolds
Generative networks have experienced great empirical successes in distri...
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12/01/2022
High Dimensional Binary Classification under Label Shift: Phase Transition and Regularization
Label Shift has been widely believed to be harmful to the generalization...
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11/06/2022
WeakIdent: Weak formulation for Identifying Differential Equations using Narrow-fit and Trimming
Data-driven identification of differential equations is an interesting b...
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07/07/2022
Numerical Identification of Nonlocal Potential in Aggregation
Aggregation equations are broadly used to model population dynamics with...
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05/04/2022
A Manifold Two-Sample Test Study: Integral Probability Metric with Neural Networks
Two-sample tests are important areas aiming to determine whether two col...
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01/01/2022
Deep Nonparametric Estimation of Operators between Infinite Dimensional Spaces
Learning operators between infinitely dimensional spaces is an important...
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09/07/2021
Besov Function Approximation and Binary Classification on Low-Dimensional Manifolds Using Convolutional Residual Networks
Most of existing statistical theories on deep neural networks have sampl...
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05/29/2021
Stability and Super-resolution of MUSIC and ESPRIT for Multi-snapshot Spectral Estimation
This paper studies the spectral estimation problem of estimating the loc...
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01/13/2021
Multiscale regression on unknown manifolds
We consider the regression problem of estimating functions on ℝ^D but su...
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11/03/2020
Doubly Robust Off-Policy Learning on Low-Dimensional Manifolds by Deep Neural Networks
Causal inference explores the causation between actions and the conseque...
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06/11/2020
Robust PDE Identification from Noisy Data
We propose robust methods to identify underlying Partial Differential Eq...
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02/10/2020
Statistical Guarantees of Generative Adversarial Networks for Distribution Estimation
Generative Adversarial Networks (GANs) have achieved great success in un...
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01/30/2020
Gaussian noise removal with exponential functions and spectral norm of weighted Hankel matrices
Exponential functions are powerful tools to model signals in various sce...
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01/22/2020
Learning functions varying along an active subspace
Many functions of interest are in a high-dimensional space but exhibit l...
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08/05/2019
Efficient Approximation of Deep ReLU Networks for Functions on Low Dimensional Manifolds
Deep neural networks have revolutionized many real world applications, d...
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05/03/2019
Super-resolution limit of the ESPRIT algorithm
The problem of imaging point objects can be formulated as estimation of ...
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05/02/2019
Conditioning of restricted Fourier matrices and super-resolution of MUSIC
This paper studies stable recovery of a collection of point sources from...
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11/03/2016