CAREER: Computational and Theoretical Investigations of Variational Inference

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The new era of complex and big data poses unprecedented challenges in terms of both our computational and theoretical understanding of Statistics. One of the fundamental questions in modern data science is how to efficiently process massive data sets with minimal information loss to aid scientific discovery and decision making. This has led the scientific community to adopt approximate statistical procedures that achieve the optimal trade-off between computational efficiency and statistical efficiency. On the one hand, the approximation should be tractable to gain computational benefits. On the other hand, the approximation needs to be tight, so as to not compromise much in terms of the statistical optimality of the original problem. This project aims to bridge the computational and theoretical gaps in various statistical problems under complex and nonstandard settings. The results of the proposed research will significantly impact areas known for applying computationally intensive methods on a routine basis. These include population genetics, astronomy, computer vision, political science, social science, and animal science.Recent developments in high-dimensional statistics and machine learning focus on exploring the intrinsic low-dimensional structure of the problem. This poses new challenges in terms of both statistical optimality and computational efficiency. Variational inference is a technique that addresses both challenges by seeking a variational approximation to the original problem that is not only tractable, but also tight. However, the literature lacks a systematic investigation of variational inference from both the computational and statistical perspective. The goals of the project include: (1) theoretical investigations of variational Bayesian procedures; and (2) variational optimization strategies in robust estimation. The project's success will help bridge the computational and theoretical gaps in modern data science and lead to significant theoretical and computational advances in variational inference.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.