Learning Local Higher-Order Interactions with Total Correlation

In domains such as ecological systems, collaborations, and the human brain the variables can interact in complex ways. Yet accurately characterizing higher-order variable interactions (HOIs) is a difficult problem that is further exacerbated when the HOIs vary locally. To solve this problem we propose a new method called Local Correlation Explanation (CorEx) to learn HOIs at a local scale by first clustering data points based on their proximity on the data manifold. We then use a multivariate version of the mutual information called the total correlation, to construct a latent factor representation of the data within each cluster to learn the local HOIs. We show that Local CorEx matches or outperforms global methods in effectively learning HOIs in synthetic data and demonstrate its suitability to explore and interpret the inner workings of trained neural networks.