Statistical Inference via Convex Optimization

This authoritative book draws on the latest research to explore the interplay of high-dimensional statistics with optimization. Through an accessible analysis of fundamental problems of hypothesis testing and signal recovery, Anatoli Juditsky and Arkadi Nemirovski show how convex optimization theory can be used to devise and analyze near-optimal statistical inferences.

Statistical Inference via Convex Optimization is an essential resource for optimization specialists who are new to statistics and its applications, and for data scientists who want to improve their optimization methods. Juditsky and Nemirovski provide the first systematic treatment of the statistical techniques that have arisen from advances in the theory of optimization. They focus on four well-known statistical problems—sparse recovery, hypothesis testing, and recovery from indirect observations of both signals and functions of signals—demonstrating how they can be solved more efficiently as convex optimization problems. The emphasis throughout is on achieving the best possible statistical performance. The construction of inference routines and the quantification of their statistical performance are given by efficient computation rather than by analytical derivation typical of more conventional statistical approaches. In addition to being computation-friendly, the methods described in this book enable practitioners to handle numerous situations too difficult for closed analytical form analysis, such as composite hypothesis testing and signal recovery in inverse problems.

Statistical Inference via Convex Optimization features exercises with solutions along with extensive appendixes, making it ideal for use as a graduate text.

"Comprehensive and highly significant. In recent years, optimization and statistics have moved closer together, with top researchers becoming versatile in both. This monumental work proposes much deeper connections between the two fields, and its approach will be taught in PhD courses for years to come."—Alexander Rakhlin, Massachusetts Institute of Technology

"Juditsky and Nemirovski's use of tools and concepts from convex optimization to solve statistical problems is very promising and will have a lasting impact in both statistics and data science more broadly. The book's format consists of extended lecture notes with examples, numerical experiments, and exercises, which is particularly suitable for presenting this material."—Arnak Dalalyan, ENSAE ParisTech