Shun-ichi Amari, RIKEN Brain Science Institute, Japan Title: Divergence, Optimization and Geometry

Abstract: Divergence measures are used in many engineering problems such as statistics, mathematical programming, computational vision, and neural networks. The Kullback-Leibler divergence is its typical example which is defined between two probability distributions. This is generalized to a class of Csiszar f-divergences, which are invariant in the sense of information reduction. The Bregman divergence is another type of divergences, which are used often in optimization and signal processing. This is a class of divergences having dually flat geometrical structure. A divergence function provides a geometrical structure to the underlying manifold of engineering problems. We search for its differential geometrical background and show that the class of f-divergences is unique, giving invariant divergences in the manifold of probability distributions and positive measures. We survey applications of these divergences in statistical inference, information theory, machine learning, computational vision, convex programming, neural networks and others.

Bio Sketch: Shun-ichi Amari was born in Tokyo, Japan, on January 3, 1936. He graduated from the Graduate School of the University of Tokyo in 1963 majoring in mathematical engineering and received the Dr. Eng. Degree.
    He worked as an Associate Professor at Kyushu University and the University of Tokyo, and then a Full professor at the University of Tokyo, and is now Professor-Emeritus. He served as Director of RIKEN Brain Science Institute for five years, and is now its senior advisor. He has been engaged in research in wide areas of mathematical engineering, in particular, mathematical foundations of neural networks, including statistical neurodynamics, dynamical theory of neural fields, associative memory, self-organization, and general learning theory. Another main subject of his research is information geometry initiated by himself, which provides a new powerful method to information sciences and neural networks.
    Dr. Amari founded Asia Pacific Neural Network Assembly (APNNA) in 1993, after IJCNN'93 Nagoya. Furthermore, he served as President of Institute of Electronics, Information and Communication Engineers, Japan and President of International Neural Networks Society. He received the Emanuel A. Piore Award and the Neural Networks Pioneer Award from IEEE, the Japan Academy Award, C&C award, among many others.