Discovering Structure in High-Dimensional Data Through Correlation Explanation

We introduce a method to learn a hierarchy of successively more abstract represen-tations of complex data based on optimizing an information-theoretic objective. Intuitively, the optimization searches for the simplest set of factors that can ex-plain the correlations in the data as measured by multivariate mutual information. The method is unsupervised, requires no model assumptions, and scales linearly with the number of variables which makes it an attractive approach for very high dimensional systems. We demonstrate that Correlation Explanation (CorEx) auto-matically discovers meaningful structure for data from diverse sources including personality tests, DNA, and human language.