Approximate factor analysis model building via alternating I-divergence minimization

Abstract

Given a positive definite covariance matrix $\hat{\Sigma }$, we strive to construct an optimal \emph{approximate} factor analysis model $H{H}^{\top }+D$, with $H$ having a prescribed number of columns and $D>0$ diagonal. The optimality criterion we minimize is the I-divergence between the corresponding normal laws. Lifting the problem into a properly chosen larger space enables us to derive an alternating minimization algorithm à la Csiszár-Tusnády for the construction of the best approximation. The convergence properties of the algorithm are studied, with special attention given to the case where $D$ is singular.

References in corpus (3)

• Statistical analysis of factor models of high dimension
• Nonnegative Matrix Factorization and I-Divergence Alternating Minimization
• Approximation of Nonnegative Systems by Finite Impulse Response Convolutions