Discovering Structure in High-Dimensional Data Through Correlation Explanation

We introduce a method to learn a hierarchy of successively more abstract representations ofcomplex data based on optimizing an information-theoretic objective. Intuitively, the optimization searches for a set of latent factors that best explain thecorrelations 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) automatically discoversmeaningful structure for data from diverse sources including personality tests, DNA, and human language.