Bayesian ART for incomplete datasets

Abstract

Adaptive Resonance Theory (ART) models allow for categorizing data in a fast and incremental manner. In particular, the Bayesian ART leverages Bayesian methodology to capture complex relationships between categories. While Bayesian methods are well-known for handling uncertainty, Bayesian ART models are at the mercy of a recurring foe: missing data. When data is missing, practitioners must rely on off-the-shelf solutions to impute the data before using Bayesian ART, effectively truncating the uncertainty quantification. To overcome such limitation, we (I) estimate the distribution of missing data entries using a Gaussian mixture model and (II) modify the three steps of Bayesian ART (category choice, matching, and update) to propagate the uncertainty around the missing entries. Experiments in a variety of tabular datasets show that, in general, our novel methodology leads to better results than using off-the-shelf imputation solutions. The performance gap becomes especially noticeable as the number of missing data entries increases.