Additive Poisson Process: Learning Intensity of Higher-Order Interaction in Poisson Processes
Abstract: We present the Additive Poisson Process (APP), a novel framework that can model the higher-order interaction effects of the intensity functions in Poisson processes using projections into lower-dimensional space. Our model combines the techniques from 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 of 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 Poisson process. Our empirical results show that our model effectively uses samples observed in lower dimensional space to estimate a higher-order intensity function with sparse observations.
Submission Length: Regular submission (no more than 12 pages of main content)
Assigned Action Editor: ~Roman_Garnett1
Submission Number: 1072
Loading