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We propose to learn latent graphical models when data have mixed variablesand missing values. This model could be used for further data analysis,including regression, classification, ranking etc. It also could be used forimputing missing values. We specify a latent Gaussian model for the data, wherethe categorical variables are generated by discretizing an unobserved variableand the latent variables are multivariate Gaussian. The observed data consistsof two parts: observed Gaussian variables and observed categorical variables,where the latter part is considered as partially missing Gaussian variables. Weuse the Expectation-Maximization algorithm to fit the model. To preventoverfitting we use sparse inverse covariance estimation to obtain sparseestimate of the latent covariance matrix, equivalently, the graphical model.The fitted model then could be used for problems including re- gression,classification and ranking. Such an approach is applied to a medical data setwhere our method outperforms the state-of-the-art methods. Simulation studiesand real data results suggest that our proposed model performs better thanrandom forest in terms of prediction error when the model is correctlyspecified, and is a better imputation method than hot deck imputation even ifthe model is not correctly specified.

Mixed and missing data: a unified treatment with latent graphical models