Dr. Koichi Tojo

Exponential families play an important role in the field of information geometry, statistics and machine learning. By definition, there are infinitely many exponential families. However, only a small part of them is widely used. We want to give a framework to deal with these “good” families systematically. In light of the observation that the sample spaces of most of them are homogeneous spaces of certain Lie groups, we proposed a method to construct exponential families on homogeneous spaces by taking advantage of representation theory in [1]. This method generates widely used exponential families such as normal, gamma, Bernoulli, categorical, Wishart, von Mises-Fisher, and hyperboloid distributions. In this talk, we will explain the method and its properties. [1] K. Tojo, T. Yoshino, A method to construct exponential families by representation theory, arXiv:1811.01394

Koichi Tojo is a postdoctoral researcher in RIKEN AIP at Mathematical Science Team. He received Ph.D. (Mathematical Science) under Prof. Taro Yoshino from the University of Tokyo in 2018. His research interests include representation theory, Lie group theory, information geometry and machine learning.