Search Results for author: Jianhao Ma

Found 8 papers, 2 papers with code

Convergence of Gradient Descent with Small Initialization for Unregularized Matrix Completion

no code implementations9 Feb 2024 Jianhao Ma, Salar Fattahi

In the over-parameterized regime where $r'\geq r$, we show that, with $\widetilde\Omega(dr^9)$ observations, GD with an initial point $\|\rm{U}_0\| \leq \epsilon$ converges near-linearly to an $\epsilon$-neighborhood of $\rm{X}^\star$.

Matrix Completion

Robust Sparse Mean Estimation via Incremental Learning

1 code implementation24 May 2023 Jianhao Ma, Rui Ray Chen, Yinghui He, Salar Fattahi, Wei Hu

This paper presents a simple mean estimator that overcomes both challenges under moderate conditions: it runs in near-linear time and memory (both with respect to the ambient dimension) while requiring only $\tilde O(k)$ samples to recover the true mean.

Incremental Learning

Can Learning Be Explained By Local Optimality In Low-rank Matrix Recovery?

no code implementations21 Feb 2023 Jianhao Ma, Salar Fattahi

In matrix completion, even with slight rank overestimation and mild noise, true solutions either emerge as non-critical or strict saddle points.

Matrix Completion

Behind the Scenes of Gradient Descent: A Trajectory Analysis via Basis Function Decomposition

1 code implementation1 Oct 2022 Jianhao Ma, Lingjun Guo, Salar Fattahi

This work analyzes the solution trajectory of gradient-based algorithms via a novel basis function decomposition.

Tensor Decomposition

Blessing of Nonconvexity in Deep Linear Models: Depth Flattens the Optimization Landscape Around the True Solution

no code implementations15 Jul 2022 Jianhao Ma, Salar Fattahi

This work characterizes the effect of depth on the optimization landscape of linear regression, showing that, despite their nonconvexity, deeper models have more desirable optimization landscape.

Global Convergence of Sub-gradient Method for Robust Matrix Recovery: Small Initialization, Noisy Measurements, and Over-parameterization

no code implementations17 Feb 2022 Jianhao Ma, Salar Fattahi

We prove that a simple SubGM with small initialization is agnostic to both over-parameterization and noise in the measurements.

Sign-RIP: A Robust Restricted Isometry Property for Low-rank Matrix Recovery

no code implementations5 Feb 2021 Jianhao Ma, Salar Fattahi

Restricted isometry property (RIP), essentially stating that the linear measurements are approximately norm-preserving, plays a crucial role in studying low-rank matrix recovery problem.

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