MI2AMI: Missing Data Imputation Using Mixed Deep Gaussian Mixture Models

Abstract

Imputing missing data is still a challenge for mixed datasets containing variables of different nature such as continuous, count, ordinal, categorical, and binary variables. The recently introduced Mixed Deep Gaussian Mixture Models (MDGMM) explicitly handle such different variable types. MDGMMs learn continuous and low dimensional representations of mixed datasets that capture the inter-variable dependence structure. We propose a model inversion that uses the learned latent representation and maps it with the observed parts of the signal. Latent areas of interest are identified for each missing value using an optimization method and synthetic imputation values are drawn. This new procedure is called MI2AMI (Missing data Imputation using MIxed deep GAussian MIxture models). The approach is tested against state-of-the-art mixed data imputation algorithms based on chained equations, Random Forests, k-Nearest Neighbours, and Generative Adversarial Networks. Two missing values designs were tested, namely the Missing Completly at Random (MCAR) and Missing at Random (MAR) designs, with missing value rates ranging from 10% to 30%.