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.
