24 citations · 28 across the 9 of their papers we have counts for
6 papers · 1 filter
Absence of spurious solutions far from ground truth: A low-rank analysis with high-order losses
Ziye Ma, Ying Chen, Javad Lavaei +1
Matrix sensing problems exhibit pervasive non-convexity, plaguing optimization with a proliferation of suboptimal spurious solutions. Avoiding convergence to these critical points…
Algorithmic Regularization in Tensor Optimization: Towards a Lifted Approach in Matrix Sensing
Ziye Ma, Javad Lavaei, Somayeh Sojoudi
Gradient descent (GD) is crucial for generalization in machine learning models, as it induces implicit regularization, promoting compact representations. In this work, we examine t…
Over-parametrization via Lifting for Low-rank Matrix Sensing: Conversion of Spurious Solutions to Strict Saddle Points
Ziye Ma, Igor Molybog, Javad Lavaei +1
This paper studies the role of over-parametrization in solving non-convex optimization problems. The focus is on the important class of low-rank matrix sensing, where we propose an…
Semidefinite Programming versus Burer-Monteiro Factorization for Matrix Sensing
Baturalp Yalcin, Ziye Ma, Javad Lavaei +1
Many fundamental low-rank optimization problems, such as matrix completion, phase synchronization/retrieval, power system state estimation, and robust PCA, can be formulated as the…
Noisy Low-rank Matrix Optimization: Geometry of Local Minima and Convergence Rate
Ziye Ma, Somayeh Sojoudi
This paper is concerned with low-rank matrix optimization, which has found a wide range of applications in machine learning. This problem in the special case of matrix sensing has…
Sharp Restricted Isometry Property Bounds for Low-rank Matrix Recovery Problems with Corrupted Measurements
Ziye Ma, Yingjie Bi, Javad Lavaei +1
In this paper, we study a general low-rank matrix recovery problem with linear measurements corrupted by some noise. The objective is to understand under what conditions on the res…