What question did this study set out to answer?

To develop a scalable second-order optimization framework that reliably completes low-rank matrices from minimal sample sizes, even when matrices are severely ill-conditioned.

June 3, 2021Open Access

A Scalable Second Order Method for Ill-Conditioned Matrix Completion from Few Samples

View Full Paper

Ask AI

Bookmark

Authors

CKChristian KümmerleUniversity of North Carolina at Charlotte CVClaudio Mayrink VerdunHarvard University

Discussion

Member takes

Implication

Computational study demonstrates quadratic convergence in ill-conditioned matrix completion from few samples, indicating superior scalability over existing methods.

Key Points

To develop a scalable second-order optimization framework that reliably completes low-rank matrices from minimal sample sizes, even when matrices are severely ill-conditioned.
Designed an iterative optimization method unifying iteratively reweighted least squares, a saddle-escaping smoothing Newton scheme, and a variable metric proximal gradient method on a non-convex rank surrogate.
Conducted theoretical convergence analyses from minimal sample counts and validated performance through numerical experiments on matrices with condition numbers up to 10^10.
Established the first local quadratic convergence guarantee for this algorithm class given a minimal number of samples.
Maintained well-conditioned linear subproblems throughout iterations, successfully reconstructing matrices with condition numbers reaching 10^10 while accelerating scalability by several orders of magnitude over prior IRLS methods.

Cite This Study

Kümmerle et al. (2021) studied this question.

synapsesocial.com/papers/6a6fcca38031ec7bb1dbf4b1 https://doi.org/10.48550/arxiv.2106.02119

View Full Paper

Ask AI

Bookmark

Implication

Computational study demonstrates quadratic convergence in ill-conditioned matrix completion from few samples, indicating superior scalability over existing methods.

A Scalable Second Order Method for Ill-Conditioned Matrix Completion from Few Samples

Discussion

Member takes

Implication

Key Points

Cite This Study

A Scalable Second Order Method for Ill-Conditioned Matrix Completion from Few Samples

Discussion

Member takes

Implication

Key Points

Cite This Study

Also Consider

Also Consider