5 papers
On the Absence of Identifiable Manifolds in Finite-Max Composite Optimization
Yifan Wang, Jianhao Ma, Salar Fattahi
In nonsmooth optimization, identifiable sets describe the local region eventually reached by sequences converging to a prescribed critical point. When such a set is a manifol…
Understanding the Implicit Regularization of Gradient Descent in Over-parameterized Models
Jianhao Ma, Geyu Liang, Salar Fattahi
Implicit regularization refers to the tendency of local search algorithms to converge to low-dimensional solutions, even when such structures are not explicitly enforced. Despite i…
RANSAC Revisited: An Improved Algorithm for Robust Subspace Recovery under Adversarial and Noisy Corruptions
Guixian Chen, Jianhao Ma, Salar Fattahi
In this paper, we study the problem of robust subspace recovery (RSR) in the presence of both strong adversarial corruptions and Gaussian noise. Specifically, given a limited numbe…
Convergence of Gradient Descent with Small Initialization for Unregularized Matrix Completion
Jianhao Ma, Salar Fattahi
We study the problem of symmetric matrix completion, where the goal is to reconstruct a positive semidefinite matrix of rank-, paramete…
Sparse Mean Estimation in Adversarial Settings via Incremental Learning
Jianhao Ma, Rui Ray Chen, Yinghui He +2
In this paper, we study the problem of sparse mean estimation under adversarial corruptions, where the goal is to estimate the -sparse mean of a heavy-tailed distribution from s…