Learning Joint Intensity in a Multivariate Poisson Process on Statistical Manifolds

Simon Luo, Feng Zhou, Lamiae Azizi, Mahito Sugiyama

Keywords: Poisson Process, Log-Linear Model, Energy-Based Model, Generalized Additive Models, Information Geometry

TL;DR: We show the connection between Generalized Additive Models, Poisson Process and the log-linear model.

Abstract: We show that generalized additive models (GAMs) can be treated via the log-linear model on a structured sample space, which has a well established information geometric background. Connecting GAMs with multivariate stochastic processes, we present the additive Poisson process (APP), a novel framework that can model the higher-order interaction effects of the intensity functions in stochastic processes using lower dimensional projections. Learning of the model is achieved via convex optimization, thanks to the dually flat statistical manifold generated by the log-linear model.