Past Event: Oden Institute Seminar

Two Vignettes on Data-driven Stochastic Modeling

Harsha Honnappa, Associate Professor, School of Industrial Engineering, Purdue University

Abstract

Data-driven stochastic modeling is a statistical approach to modeling systems or processes that involve aleatoric uncertainty or stochasticity. This involves using data collected from the stochastic system to build a model that represents the underlying stochastic relationships in the system. Data-driven stochastic modeling is often complicated by the presence of controlled dynamics and non-stationarities. Furthermore, in most settings, data collection is hard and multiple sample paths are impossible to obtain. In this talk I will present two vignettes on data-driven modeling under these conditions.

In the first vignette, I will focus on model identification/estimation in the presence of controls. I will present our recent results establishing probably approximately correct (PAC) bounds and sample complexity results for nonparametric estimators of finite controlled Markov chains, under general mixing assumptions on the control sequence generated by a logging policy. Our results highlight an important trade-off between stronger assumptions on the mixing conditions versus requiring more samples to achieve a particular PAC bound. These sample complexity bounds also immediately imply concomitant bounds for offline policy evaluation and prediction. To the best of our knowledge, this is the first result establishing the minimax optimality of a nonparametric estimator for system identification under general mixing conditions. This is joint work with Imon Banerjee and Vinayak A. Rao of the Department of Statistics at Purdue University.

In the second vignette, I will change focus to data-driven modeling in the presence of non-stationarities. Focusing specifically on a latent parameter Poisson random measure model of a non-stationary stochastic system, I will present a variational autoencoder (VAE) methodology for identifying/estimating the latent parameters. In this setting, maximum likelihood estimation (MLE) is impossible, since the MLE objective is typically in the form of an intractable integration. VAE estimates the model parameters by maximizing a surrogate objective to the MLE objective. Our simulation results highlight the apparent efficacy of the method; however I will also present our theoretical results demonstrating that, in this stochastic dynamical setting, the parameters maximizing the VAE surrogate objective will necessarily have a positive variational gap. This is joint work with Ruixin Wang, formerly of Purdue University.

 

Biography

Harsha Honnappa is an Associate Professor in the School of Industrial Engineering at Purdue University, where he runs the Stochastic Systems Lab. He is an applied probabilist with strong interests in the analysis of stochastic models, theoretical statistics, stochastic optimization and control. His research is supported by a number of grants from the National Science Foundation, including an NSF CAREER award, and the Purdue Research Foundation.