Past Event: Oden Institute Seminar

Closed-Form Information-Theoretic Roughness Measures for Mixture Densities

Uwe Hanebeck, Karlsruhe University

Abstract

In estimation, control, and machine learning under uncertainties, latent variables are usually described by a probability density function (pdf). The optimal reconstruction of a continuous pdf from given samples or moments is an important and ubiquitous task. Unfortunately, it typically results in an underdetermined optimization problem, as the pdf is not fully constrained by the given samples or moments. As a regularizer, I propose to use the (little-known) “Fisher Information Number (FIN)”. Minimizing the FIN ensures that as little information as possible is added to the given constraints. For the important class of mixture densities, FIN can only be computed numerically. In this talk, I will derive a closed-form solution by transforming the problem to the space of root mixture densities. This results in a tandem processing scheme simultaneously working in the original mixture space and the corresponding root mixture space: The density parameters are optimized in root mixture space based on the closed-form FIN. The desired constraints are evaluated in the original mixture space. Several examples will demonstrate the principles of the proposed method and show its usefulness and efficiency.

Biography

Uwe D. Hanebeck is a chaired professor of Computer Science at the Karlsruhe Institute of Technology (KIT) in Germany and director of the Intelligent Sensor-Actuator-Systems Laboratory (ISAS). He obtained his Ph.D. degree in 1997 and his habilitation degree in 2003, both in Electrical Engineering from the Technical University in Munich, Germany. His research interests are in the areas of information fusion, nonlinear state estimation, stochastic modeling, system identification, and control with a strong emphasis on theory-driven approaches based on stochastic system theory and uncertainty models. He is author and coauthor of about 600 publications in various high-ranking journals and conferences, an IEEE Fellow, and currently president of the International Society of Information Fusion (ISIF).