Abstract for the talk on 17.09.2020 (17:00 h)Math Machine Learning seminar MPI MIS + UCLA
Mahito Sugiyama (National Institute of Informatics, JST, PRESTO)
Learning with Dually Flat Structure and Incidence Algebra
Statistical manifolds with dually flat structures, such as an exponential family, appear in various machine learning models. In this talk, I will introduce a close connection between dually flat manifolds and incidence algebras in order theory and present its application to machine learning. This approach allows us to flexibly design log-linear models equipped with partially ordered sample spaces, which include a number of machine learning problems such as learning of Boltzmann machines, tensor decomposition, and blind source separation. I will also talk about theoretical analysis of such models using Rissanen’s stochastic complexity and draw the connection to the double descent phenomenon via model volumes.