2018/01/17 by Koulik Khamaru, Rahul Mazumder, Khamaru, Koulik +1 · 3 citations
Computer Science · Engineering · Mathematics · #Advanced Statistical Methods and Models #Computation (stat.CO) #FOS: Computer and information sciences #FOS: Mathematics #Face and Expression Recognition #Machine Learning (stat.ML) #Optimization and Control (math.OC) #Sparse and Compressive Sensing Techniques
paper · pdf · doi:10.48550/arxiv.1801.05935
openalex publication_date 2018/01/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Factor analysis, a classical multivariate statistical technique is popularly\nused as a fundamental tool for dimensionality reduction in statistics,\neconometrics and data science. Estimation is often carried out via the Maximum\nLikelihood (ML) principle, which seeks to maximize the likelihood under the\nassumption that the positive definite covariance matrix can be decomposed as\nthe sum of a low rank positive semidefinite matrix and a diagonal matrix with\nnonnegative entries. This leads to a challenging rank constrained nonconvex\noptimization problem. We reformulate the low rank ML Factor Analysis problem as\na nonlinear nonsmooth semidefinite optimization problem, study various\nstructural properties of this reformulation and propose fast and scalable\nalgorithms based on difference of convex (DC) optimization. Our approach has\ncomputational guarantees, gracefully scales to large problems, is applicable to\nsituations where the sample covariance matrix is rank deficient and adapts to\nvariants of the ML problem with additional constraints on the problem\nparameters. Our numerical experiments demonstrate the significant usefulness of\nour approach over existing state-of-the-art approaches.\n