What is an Information Projection? An Invitation to Information Geometry
Date: Tue, February 28, 2017
Time: 2:00pm-3:00pm
Location: Holmes 389
Speaker: Prof. Frank Nielsen, Ecole Polytechnique (France)
Abstract:
In this talk, we first present two renown statistical inference methods: The Maximum Likelihood Estimator (MLE) and the Maximum Entropy Principle (MEP). We show how these estimators can be modeled as Kullback-Leibler divergence minimization problems, and therefore interpreted geometrically as information projections. We then present the basic construction of dually flat Shannon spaces and describe some useful concepts and tools (eg., space of spheres, statistical Voronoi diagrams). Finally, we touch upon the role of divergences in information theory, statistics, pattern recognition and machine learning.
Biography:
Frank Nielsen received his PhD (1996) and his habilitation (2006) on computational geometry from the University of Nice-Sophia Antipolis, France. After the French National Service, he joined Sony CSL (Japan) in 1997. He is currently a professor in the computer science department of Ecole Polytechnique (France). He co-organizes with Frederic Barbaresco (Thales) the biannual Geometric Sciences of Information (GSI, gsi2017.org) conference, and is currently co-editor of the newly launched Springer journal of Information Geometry and an associate editor of MDPI Entropy.