Mutual information based dimensionality reduction with application to non-linear regression

In this paper we introduce a supervised linear dimensionality reduction algorithm which is based on finding a projected input space that maximizes mutual information between input and output values. The algorithm utilizes the recently introduced MeanNN estimator for differential entropy. We show that the estimator is an appropriate tool for the dimensionality reduction task. Next we provide a nonlinear regression algorithm based on the proposed dimensionality reduction approach. The regression algorithm achieves comparable to state-of-the-art performance on the standard datasets being three orders of magnitude faster. In addition we demonstrate an application of the proposed dimensionality reduction algorithm to reduced-complexity classification.