Bayesian estimation and classification with incomplete data using mixture models

Reasoning from data in practical problems is frequently hampered by missing observations. Mixture models provide a powerful general semi-parametric method for modelling densities and have close links to radial basis function neural networks (RBFs). We extend the Data Augmentation (DA) technique for multiple imputation to Gaussian mixture models to permit fully Bayesian inference of model parameters and estimation of the missing values. The method is compared to imputation using a single normal density on synthetic and real-world data. In addition to a lower mean squared error than can be achieved by simple imputation methods, mixture models provide valuable information on the potentially multi-modal nature of imputed values. The DA formalism is extended to a classifier closely related to RBF networks permitting Bayesian classification with incomplete data; the technique is illustrated on synthetic and real datasets.