CANCELLED
Title: Variational Inference in Data-Driven Stochastic Modeling
Abstract: How should optimal design and performance prediction of queueing systems be conducted in data-driven settings? The standard stochastic modeling workflow is to posit a queueing model (say a Markovian queue), compute performance metrics as functions of the model variables (by solving the Kolmogorov Backward Equation, for instance) and, finally, plugging-in estimated model variables (such as the arrival and service intensities) to obtain estimated performance metrics. This talk will focus on two issues: first, how to address the complicated input uncertainty quantification problem that is concomitant to this workflow, where the random effects of parameter estimation can be hard to distinguish from the inherent, or aleatoric, stochasticity of the model? Second, how can the statistical estimation problem be placed at the heart of the workflow, rather than the end, thereby ameliorating the uncertainty quantification problem to an extent? First, Bayesian statistical methods are a natural vehicle for addressing the uncertainty quantification problem. However, in the queueing system setting, posterior computation is intractable, necessitating approximate inference. In the first part of the talk, I will present our approximate inference framework for performance prediction and system design in data-driven settings. Specifically, we adapt the variational inference (VI) methodology developed in the machine learning community towards our objectives. I will demonstrate the application of our framework to performance prediction and system design problems, and present our theoretical analyses establishing the large sample frequentist consistency of our methodology. Second, I will present our recent methodological work extending variational autoencoders (VAEs) to learning structured nonstationary stochastic models. VAEs (and generative models, in general) allow us to move the statistical estimation problem to the heart of the stochastic modeling workflow. In their standard form VAEs are deep generative models, marrying variational inference with deep neural networks. Data-driven performance prediction in the context of nonstationary stochastic models is a complicated, infinite dimensional statistical estimation problem. Extant approaches use explicit time discretization, and point estimation within each time period, to estimate performance metrics. Our work, on the other hand, avoids this explicit discretization by developing VAEs over path space by exploiting the recently developed neural ordinary/stochastic differential equation methodology in approximate inference. We demonstrate the superiority of our method through extensive experimentation.
Bio: Harsha Honnappa is an Assistant Professor in the School of Industrial Engineering at Purdue University. His research interests are at the intersection of applied probability, simulation and statistics. Specifically, his work in applied probability focuses on performance analysis, optimization and control of nonstationary stochastic models. His interest in simulation and statistics primarily focuses on approximate inference and simulation optimization. His research is supported by the National Science Foundation and the Purdue Research Foundation, and he is the recipient of the biennial Lajos Takacs Award for his thesis work on Transitory Queueing Theory.
