Direct Estimation of the Derivative of Quadratic Mutual Information with Application in Sufficient Dimension Reduction

摘要

An accurate estimator of a function does not necessary mean that its derivative is an accurate estimator of the derivative of the function. Motivated by this fact, we propose a method to directly estimate the derivative of quadratic mutual information (QMI) without estimating QMI itself. QMI is a robust and stable variant of ordinary MI and is useful in various statistical datatanalysis tasks. We apply the proposed direct QMI derivative estimator to sufficient dimension reduction, and develop a natural gradient algorithm over the Grassmann manifold to find the most informative features. Finally, the usefulness of the proposed method is demonstrated through experiments.