Factor Analysis via Modern Optimization Lens

• Activity Number: 137
• Type: Contributed
• Date/Time: Monday, August 4, 2014 : 8:30 AM to 10:20 AM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Rahul Mazumder*+ and Dimitris Bertsimas
• Companies: and MIT
• Keywords: factor analysis ; Mathematical Optimization ; rank minimization ; Semidefinite Optimization

Abstract

Factor Analysis (FA) is a technique of fundamental importance that is widely used in classical and modern multivariate statistics. In this talk, we will revisit the classical rank-constrained FA problem, which seeks to approximate an observed covariance matrix under PSD constraints. In this work, we propose a flexible family of rank-constrained, nonlinear Semidefinite Optimization based formulations for this task, of which popular FA estimation formulations can be viewed as special cases. We introduce a novel reformulation of the general rank-constrained FA estimation problem, as a smooth optimization problem with convex compact constraints. Furthermore, we propose a unified algorithmic framework, utilizing state of the art techniques in nonlinear optimization and first order methods in convex optimization to obtain high-quality solutions for our proposed formulation. This, in particular, advances the state of the art of algorithms for existing formulations. Our approach aids statistical interpretability, provides computational scalability and significantly improved accuracy when compared to current, publicly available popular methods for rank-constrained FA.