Additive Poisson Process: Learning Intensity of Higher-Order Interaction in Stochastic Processes

TL;DR

The paper introduces the Additive Poisson Process (APP), a new framework that models higher-order interactions in stochastic processes by leveraging lower-dimensional projections and information geometry, effectively handling sparse data.

Contribution

It proposes a novel convex optimization approach to estimate higher-order intensity functions using lower-dimensional projections in stochastic processes.

Findings

Accurately estimates higher-order intensity functions from sparse samples.

Uses lower-dimensional projections to overcome curse of dimensionality.

Employs information geometry for modeling interactions.

Abstract

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. Our model combines the techniques in information geometry to model higher-order interactions on a statistical manifold and in generalized additive models to use lower-dimensional projections to overcome the effects from the curse of dimensionality. Our approach solves a convex optimization problem by minimizing the KL divergence from a sample distribution in lower dimensional projections to the distribution modeled by an intensity function in the stochastic process. Our empirical results show that our model is able to use samples observed in the lower dimensional space to estimate the higher-order intensity function with extremely sparse observations.