Supervised learning of multivariate skew normal mixture models with missing information

We establish computationally flexible tools for the analysis of multivariate skew normal mixtures when missing values occur in data. To facilitate the computation and simplify the theoretical derivation, two auxiliary permutation matrices are incorporated into the model for the determination of observed and missing components of each observation and are manifestly effective in reducing the computational complexity. We present an analytically feasible EM algorithm for the supervised learning of parameters as well as missing observations. The proposed mixture analyzer, including the most commonly used Gaussian mixtures as a special case, allows practitioners to handle incomplete multivariate data sets in a wide range of considerations. The methodology is illustrated through a real data set with varying proportions of synthetic missing values generated by MCAR and MAR mechanisms and shown to perform well on classification tasks.