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09/02/2023
Non-Asymptotic Bounds for Adversarial Excess Risk under Misspecified Models
We propose a general approach to evaluating the performance of robust es...
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06/24/2023
Current density impedance imaging with PINNs
In this paper, we introduce CDII-PINNs, a computationally efficient meth...
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05/01/2023
Differentiable Neural Networks with RePU Activation: with Applications to Score Estimation and Isotonic Regression
We study the properties of differentiable neural networks activated by r...
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04/17/2023
Deep Neural Network Approximation of Composition Functions: with application to PINNs
In this paper, we focus on approximating a natural class of functions th...
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03/28/2023
GAS: A Gaussian Mixture Distribution-Based Adaptive Sampling Method for PINNs
With recent study of the deep learning in scientific computation, the PI...
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02/05/2023
Convergence Analysis of the Deep Galerkin Method for Weak Solutions
This paper analyzes the convergence rate of a deep Galerkin method for t...
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07/21/2022
Estimation of Non-Crossing Quantile Regression Process with Deep ReQU Neural Networks
We propose a penalized nonparametric approach to estimating the quantile...
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05/19/2022
Deep Generative Survival Analysis: Nonparametric Estimation of Conditional Survival Function
We propose a deep generative approach to nonparametric estimation of con...
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04/14/2022
Efficient and practical quantum compiler towards multi-qubit systems with deep reinforcement learning
Efficient quantum compiling tactics greatly enhance the capability of qu...
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01/24/2022
Approximation bounds for norm constrained neural networks with applications to regression and GANs
This paper studies the approximation capacity of ReLU neural networks wi...
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12/19/2021
Wasserstein Generative Learning of Conditional Distribution
Conditional distribution is a fundamental quantity for describing the re...
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12/15/2021
Sample-Efficient Sparse Phase Retrieval via Stochastic Alternating Minimization
In this work we propose a nonconvex two-stage stochastic alternating min...
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11/29/2021
Just Least Squares: Binary Compressive Sampling with Low Generative Intrinsic Dimension
In this paper, we consider recovering n dimensional signals from m binar...
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11/21/2021
A Data-Driven Line Search Rule for Support Recovery in High-dimensional Data Analysis
In this work, we consider the algorithm to the (nonlinear) regression pr...
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11/03/2021
Analysis of Deep Ritz Methods for Laplace Equations with Dirichlet Boundary Conditions
Deep Ritz methods (DRM) have been proven numerically to be efficient in ...
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10/24/2021
Non-Asymptotic Error Bounds for Bidirectional GANs
We derive nearly sharp bounds for the bidirectional GAN (BiGAN) estimati...
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10/19/2021
A Deep Generative Approach to Conditional Sampling
We propose a deep generative approach to sampling from a conditional dis...
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10/06/2021
Relative Entropy Gradient Sampler for Unnormalized Distributions
We propose a relative entropy gradient sampler (REGS) for sampling from ...
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09/18/2021
Coordinate Descent for MCP/SCAD Penalized Least Squares Converges Linearly
Recovering sparse signals from observed data is an important topic in si...
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09/04/2021
Convergence Analysis for the PINNs
In recent years, physical informed neural networks (PINNs) have been sho...
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07/30/2021
Error Analysis of Deep Ritz Methods for Elliptic Equations
Using deep neural networks to solve PDEs has attracted a lot of attentio...
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07/21/2021
Robust Nonparametric Regression with Deep Neural Networks
In this paper, we study the properties of robust nonparametric estimatio...
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07/10/2021
Deep Quantile Regression: Mitigating the Curse of Dimensionality Through Composition
This paper considers the problem of nonparametric quantile regression un...
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07/10/2021
Convergence Analysis of Schrödinger-Föllmer Sampler without Convexity
Schrödinger-Föllmer sampler (SFS) is a novel and efficient approach for ...
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06/21/2021
Schrödinger-Föllmer Sampler: Sampling without Ergodicity
Sampling from probability distributions is an important problem in stati...
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06/19/2021
Deep Generative Learning via Schrödinger Bridge
We propose to learn a generative model via entropy interpolation with a ...
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05/27/2021
An error analysis of generative adversarial networks for learning distributions
This paper studies how well generative adversarial networks (GANs) learn...
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05/01/2021
Non-asymptotic Excess Risk Bounds for Classification with Deep Convolutional Neural Networks
In this paper, we consider the problem of binary classification with a c...
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04/14/2021
Deep Nonparametric Regression on Approximately Low-dimensional Manifolds
In this paper, we study the properties of nonparametric least squares re...
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03/24/2021
Convergence Rate Analysis for Deep Ritz Method
Using deep neural networks to solve PDEs has attracted a lot of attentio...
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02/28/2021
Deep Neural Networks with ReLU-Sine-Exponential Activations Break Curse of Dimensionality on Hölder Class
In this paper, we construct neural networks with ReLU, sine and 2^x as a...
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12/11/2020
Generative Learning With Euler Particle Transport
We propose an Euler particle transport (EPT) approach for generative lea...
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06/10/2020
Deep Dimension Reduction for Supervised Representation Learning
The success of deep supervised learning depends on its automatic data re...
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06/03/2020
Robust Decoding from Binary Measurements with Cardinality Constraint Least Squares
The main goal of 1-bit compressive sampling is to decode n dimensional s...
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02/09/2020
ℓ_0-Regularized High-dimensional Accelerated Failure Time Model
We develop a constructive approach for ℓ_0-penalized estimation in the s...
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02/07/2020
Learning Implicit Generative Models with Theoretical Guarantees
We propose a unified framework for implicit generative modeling (UnifiGe...
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01/27/2020
On Newton Screening
Screening and working set techniques are important approaches to reducin...
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01/16/2020
A Support Detection and Root Finding Approach for Learning High-dimensional Generalized Linear Models
Feature selection is important for modeling high-dimensional data, where...
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06/14/2019
A stochastic alternating minimizing method for sparse phase retrieval
Sparse phase retrieval plays an important role in many fields of applied...
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02/25/2019
Wasserstein-Wasserstein Auto-Encoders
To address the challenges in learning deep generative models (e.g.,the b...
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10/09/2018
SNAP: A semismooth Newton algorithm for pathwise optimization with optimal local convergence rate and oracle properties
We propose a semismooth Newton algorithm for pathwise optimization (SNAP...
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07/27/2018
VIMCO: Variational Inference for Multiple Correlated Outcomes in Genome-wide Association Studies
In Genome-Wide Association Studies (GWAS) where multiple correlated trai...
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05/03/2018
REMI: Regression with marginal information and its application in genome-wide association studies
In this study, we consider the problem of variable selection and estimat...
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02/24/2018
Semi-Smooth Newton Algorithm for Non-Convex Penalized Linear Regression
Both the smoothly clipped absolute deviation (SCAD) and the minimax conc...
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11/03/2017
Robust Decoding from 1-Bit Compressive Sampling with Least Squares
In 1-bit compressive sensing (1-bit CS) where target signal is coded int...
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03/03/2014
A Primal Dual Active Set with Continuation Algorithm for the ℓ^0-Regularized Optimization Problem
We develop a primal dual active set with continuation algorithm for solv...
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10/04/2013