ABSTRACT

In the talk, I will present a VAE-like generative model for Doubly Stochastic Point Processes. A central question in VAEs is: does the space of approximate posteriors contain the true posterior? In this specific setting, the questions are whether or not the posterior intensity process has a nice SDE representation if the prior intensity can be described via an SDE. Using tools of initial enlargement of filtrations, we were able to show that the posterior does indeed have a SDE representation with a modified drift term. We compute explicitly the drift correction term when the process is a CIR process and when there’s only one observation interval. Further work in progress.

BIOGRAPHY

Xinlong Du is an incoming first-year PhD student in the Industrial Engineering department, working with Professor Harsha Honnappa. He previously earned a master’s degree in Statistics and Computer Science from Purdue University.