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05/29/2023
Statistically Optimal K-means Clustering via Nonnegative Low-rank Semidefinite Programming
K-means clustering is a widely used machine learning method for identify...
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05/26/2023
Fast and Minimax Optimal Estimation of Low-Rank Matrices via Non-Convex Gradient Descent
We study the problem of estimating a low-rank matrix from noisy measurem...
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11/30/2022
Overcoming the Convex Relaxation Barrier for Neural Network Verification via Nonconvex Low-Rank Semidefinite Relaxations
To rigorously certify the robustness of neural networks to adversarial p...
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10/23/2022
Simple Alternating Minimization Provably Solves Complete Dictionary Learning
This paper focuses on complete dictionary learning problem, where the go...
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08/24/2022
Accelerating SGD for Highly Ill-Conditioned Huge-Scale Online Matrix Completion
The matrix completion problem seeks to recover a d× d ground truth matri...
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07/05/2022
Improved Global Guarantees for the Nonconvex Burer–Monteiro Factorization via Rank Overparameterization
We consider minimizing a twice-differentiable, L-smooth, and μ-strongly ...
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06/07/2022
Preconditioned Gradient Descent for Overparameterized Nonconvex Burer–Monteiro Factorization with Global Optimality Certification
We consider using gradient descent to minimize the nonconvex function f(...
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04/21/2021
Sharp Global Guarantees for Nonconvex Low-Rank Matrix Recovery in the Overparameterized Regime
We prove that it is possible for nonconvex low-rank matrix recovery to c...
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06/11/2020
On the Tightness of Semidefinite Relaxations for Certifying Robustness to Adversarial Examples
The robustness of a neural network to adversarial examples can be provab...
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01/07/2019
Sharp Restricted Isometry Bounds for the Inexistence of Spurious Local Minima in Nonconvex Matrix Recovery
Nonconvex matrix recovery is known to contain no spurious local minima u...
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05/25/2018
How Much Restricted Isometry is Needed In Nonconvex Matrix Recovery?
When the linear measurements of an instance of low-rank matrix recovery ...
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02/14/2018
Large-Scale Sparse Inverse Covariance Estimation via Thresholding and Max-Det Matrix Completion
The sparse inverse covariance estimation problem is commonly solved usin...
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02/14/2018
Linear-Time Algorithm for Learning Large-Scale Sparse Graphical Models
The sparse inverse covariance estimation problem is commonly solved usin...
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11/24/2017