Learning a Factor Model via Regularized PCA

Linear factor models have been widely used for a long time and with notable success in economics, finance, medicine, psychology, and various other natural and social sciences (Harman, 1976). In such a model, each observed variable is a linear combination of unobserved common factors plus idiosyncratic noise, and the collection of random variables is jointly Gaussian. We consider in this paper the problem of learning a factor model from a training set of vector observations. In particular, our learning problem entails simultaneously estimating the loadings of each factor and the residual variance of each variable. We seek an estimate of these parameters that best explains out-of-sample data.