Title: Estimating differential entropy in high dimensional spaces Authors:  David Weston - Birkbeck University of London (United Kingdom) [presenting]
Abstract: Entropy estimation of a continuous distribution can be achieved by first estimating the density. However, such plug-in estimators often exhibit high variance, especially in high-dimensional spaces. A well-known graph-theoretic approach to reduce the variance and increase the bias in differential entropy estimation involves constructing a minimal spanning tree from the data, where the estimator is a function of the lengths of its edges. An alternative approach is demonstrated using a measure-preserving space-filling curve to induce a Hamiltonian. The reason why this approach results in a poor estimator is explained, along with a method to enhance its performance significantly. To demonstrate the utility of the proposed method, a simple classification approach is applied to image data, which serves as an example of high-dimensional data.