Robust Factor Analysis of Moving Average processes

This thesis addresses the problem of learning dynamic factor models generated by zero-mean Gaussian moving avarage (MA) processes. Factor models boast a long tradition and find natural application in many engineering and scientific disciplines, including, for example, psychology, econometrics, system engineering, machine learning and statistics. In general, the attention for this kind of models is motivated by their effectiveness in complex-data representation. Indeed they allow the compression of the information contained in a high dimensional data vector into a small number of common factors, based on the assumption of underlying latent non-observed variables influencing all the observations. In this thesis, we propose an extension of factor analysis to MA processes in order to extract the compressible information from them. To robustly estimate the number of factors, we construct a confidence region centered in a finite sample estimate of the underlying model which contains the true model with a prescribed probability. In this confidence region, the problem, formulated as a rank minimization of a suitable spectral density, is efficiently approximated via a trace norm convex relaxation.