Automated learning of mixtures of factor analysis models with missing information

The mixture of factor analyzers (MFA) model has emerged as a useful tool to perform dimensionality reduction and model-based clustering for heterogeneous data. In seeking the most appropriate number of factors (q) of a MFA model with the number of components (g) fixed a priori, a two-stage procedure is commonly implemented by firstly carrying out parameter estimation over a set of prespecified numbers of factors, and then selecting the best q according to certain penalized likelihood criteria. When the dimensionality of data grows higher, such a procedure can be computationally prohibitive. To overcome this obstacle, we develop an automated learning scheme, called the automated MFA (AMFA) algorithm, to effectively merge parameter estimation and selection of q into a one-stage algorithm. The proposed AMFA procedure that allows for much lower computational cost is also extended to accommodate missing values. Moreover, we explicitly derive the score vector and the empirical information matrix for calculating standard errors associated with the estimated parameters. The potential and applicability of the proposed method are demonstrated through a number of real datasets with genuine and synthetic missing values.