research
∙
08/04/2022
Spectral Universality of Regularized Linear Regression with Nearly Deterministic Sensing Matrices
It has been observed that the performances of many high-dimensional esti...
share
research
∙
05/13/2022
Sharp Asymptotics of Kernel Ridge Regression Beyond the Linear Regime
The generalization performance of kernel ridge regression (KRR) exhibits...
research
∙
05/12/2022
An Equivalence Principle for the Spectrum of Random Inner-Product Kernel Matrices
We consider random matrices whose entries are obtained by applying a (no...
research
∙
02/16/2022
Analysis of Random Sequential Message Passing Algorithms for Approximate Inference
We analyze the dynamics of a random sequential message passing algorithm...
research
∙
02/15/2021
On the Inherent Regularization Effects of Noise Injection During Training
Randomly perturbing networks during the training process is a commonly u...
research
∙
01/19/2021
Householder Dice: A Matrix-Free Algorithm for Simulating Dynamics on Gaussian and Random Orthogonal Ensembles
This paper proposes a new algorithm, named Householder Dice (HD), for si...
research
∙
01/06/2021
Phase Transitions in Transfer Learning for High-Dimensional Perceptrons
Transfer learning seeks to improve the generalization performance of a t...
research
∙
12/08/2020
Construction of optimal spectral methods in phase retrieval
We consider the phase retrieval problem, in which the observer wishes to...
research
∙
09/16/2020
Universality Laws for High-Dimensional Learning with Random Features
We prove a universality theorem for learning with random features. Our r...
research
∙
08/27/2020
A Precise Performance Analysis of Learning with Random Features
We study the problem of learning an unknown function using random featur...
research
∙
06/15/2020
The Limiting Poisson Law of Massive MIMO Detection with Box Relaxation
Estimating a binary vector from noisy linear measurements is a prototypi...
research
∙
06/11/2020
Generalization error in high-dimensional perceptrons: Approaching Bayes error with convex optimization
We consider a commonly studied supervised classification of a synthetic ...
research
∙
02/26/2020
The role of regularization in classification of high-dimensional noisy Gaussian mixture
We consider a high-dimensional mixture of two Gaussians in the noisy reg...
research
∙
05/13/2019
Generalized Approximate Survey Propagation for High-Dimensional Estimation
In Generalized Linear Estimation (GLE) problems, we seek to estimate a s...
research
∙
03/27/2019
Asymptotics and Optimal Designs of SLOPE for Sparse Linear Regression
In sparse linear regression, the SLOPE estimator generalizes LASSO by as...
research
∙
11/11/2018
Optimal Spectral Initialization for Signal Recovery with Applications to Phase Retrieval
We present the optimal design of a spectral method widely used to initia...
research
∙
09/25/2018
Nonconvex Optimization Meets Low-Rank Matrix Factorization: An Overview
Substantial progress has been made recently on developing provably accur...
research
∙
08/06/2018
Super Resolution Phase Retrieval for Sparse Signals
In a variety of fields, in particular those involving imaging and optics...
research
∙
06/12/2018
Streaming PCA and Subspace Tracking: The Missing Data Case
For many modern applications in science and engineering, data are collec...
research
∙
05/24/2018
Phase Retrieval via Polytope Optimization: Geometry, Phase Transitions, and New Algorithms
We study algorithms for solving quadratic systems of equations based on ...
research
∙
05/22/2018
A Solvable High-Dimensional Model of GAN
Despite the remarkable successes of generative adversarial networks (GAN...
research
∙
05/17/2018
Subspace Estimation from Incomplete Observations: A High-Dimensional Analysis
We present a high-dimensional analysis of three popular algorithms, name...
research
∙
12/08/2017
Scaling Limit: Exact and Tractable Analysis of Online Learning Algorithms with Applications to Regularized Regression and PCA
We present a framework for analyzing the exact dynamics of a class of on...
research
∙
10/15/2017
The Scaling Limit of High-Dimensional Online Independent Component Analysis
We analyze the dynamics of an online algorithm for independent component...
research
∙
02/21/2017
Phase Transitions of Spectral Initialization for High-Dimensional Nonconvex Estimation
We study a spectral initialization method that serves a key role in rece...
research
∙
06/04/2016
A Tale of Two Bases: Local-Nonlocal Regularization on Image Patches with Convolution Framelets
We propose an image representation scheme combining the local and nonloc...
research
∙
01/01/2016
Understanding Symmetric Smoothing Filters: A Gaussian Mixture Model Perspective
Many patch-based image denoising algorithms can be formulated as applyin...
research
∙
12/27/2013