Statistical Inference Via Convex Optimization

Anatoli Juditsky and Arkadi Nemirovski explore how high-dimensional statistics and optimization relate to each other. Using the latest research, they show how convex optimization theory can be used to design statistical inference procedures and to analyze how close to optimal those procedures are. The book approaches the fundamental problems of hypothesis testing and signal recovery in an accessible way.

It is described as the first systematic treatment of the statistical techniques that have grown out of advances in optimization theory. The authors concentrate on four familiar statistical problems: sparse recovery, hypothesis testing, and recovery from indirect observations of both signals and functions of signals. They show that each can be solved more efficiently when posed as a convex optimization problem. Throughout, the aim is the best possible statistical performance.

A distinctive feature is that inference routines are built, and their statistical performance is quantified, by efficient computation rather than by the analytical derivations typical of conventional statistics. Besides being friendly to computation, the methods let practitioners deal with many situations too hard for closed-form analysis, such as composite hypothesis testing and signal recovery in inverse problems.

The book is meant for optimization specialists who are new to statistics and its applications, and for data scientists who want to strengthen their optimization methods. It includes exercises with solutions and extensive appendixes, which make it suitable as a graduate text.