Dimension reduction in regression using Gaussian Mixture Models

Linear-Nonlinear regression models play a fundamental role in characterizing nonlinear systems. In this paper, we propose a method to estimate the linear transform in such models equivalent to a subspace of a small dimension in the input space that is relevant for eliciting response. The novel aspect of this work is the formulation of the mutual information between the transformed inputs and output as a closed-form function of the parameters of their joint density in the form of Gaussian Mixture Models and we subsequently maximize this measure to find relevant dimensions. Instead of a commonly used mutual information measure based on Kullback-Leibler divergence, we use a measure called Quadratic Euclidean Mutual Information. Through experiments on both synthesized data and real MEG recordings, the effectiveness of the proposed method is demonstrated.