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Abstract:
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In applications such as financial markets, social networks, and gene expression data, the variables often interact in complex ways. Yet accurately characterizing pairwise variable interactions can be a difficult task, let alone efficiently characterizing complex higher-order interactions, which is an unsolved problem. This difficulty is exacerbated when variable interactions change across the data. For example, gene interactions in single-cell RNA-sequencing (scRNA-seq) data will typically differ from one cell type to another.
To solve these problems, we propose a new method called Local Correlation Explanation (CorEx). Local CorEx captures higher-order variable interactions at a local scale by first clustering data points based on their proximity on the data manifold. We then use a multivariate version of mutual information, called the total correlation, to construct a latent factor representation of the data within each cluster to learn the local variable interactions. We compare Local CorEx with other methods and show that it performs favorably on both synthetic and real data including images and scRNA-seq data.
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