Intrinsically Interpretable Gaussian Mixture Model

Abstract

Understanding the reasoning behind a predictive model’s decision is an important and longstanding problem driven by ethical and legal considerations. Most recent research has focused on the interpretability of supervised models, whereas unsupervised learning has received less attention. However, the majority of the focus was on interpreting the whole model in a manner that undermined accuracy or model assumptions, while local interpretation received much less attention. Therefore, we propose an intrinsic interpretation for the Gaussian mixture model that provides both global insight and local interpretations. We employed the Bhattacharyya coefficient to measure the overlap and divergence across clusters to provide a global interpretation in terms of the differences and similarities between the clusters. By analyzing the GMM exponent with the Garthwaite–Kock corr-max transformation, the local interpretation is provided in terms of the relative contribution of each feature to the overall distance. Experimental results obtained on three datasets show that the proposed interpretation method outperforms the post hoc model-agnostic LIME in determining the feature contribution to the cluster assignment.