Constrained Low-rank Matrix Estimation: Phase Transitions, Approximate Message Passing and Applications

Understand

This article is an extended version of previous work of the authors [40, 41] on low-rank matrix estimation in the presence of constraints on the factors into which the matrix is factorized.

• Low-rank matrix factorization is one of the basic methods used in data analysis for unsupervised learning of relevant features and other types of dimensionality reduction.
• We present a framework to study the constrained low-rank matrix estimation for a general prior on the factors, and a general output channel through which the matrix is observed.
• We draw a paralel with the study of vector-spin glass models - presenting a unifying way to study a number of problems considered previously in separate statistical physics works.