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Statistical Inference via Convex Optimization

Anatoli Juditsky, Arkadi Nemirovski

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Princeton University Press img Link Publisher

Naturwissenschaften, Medizin, Informatik, Technik / Mathematik

Beschreibung

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.

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Schlagwörter

Bias of an estimator, Monte Carlo method, Preference (economics), Convex function, Probability space, Convex set, Error function, Covariance matrix, Convex optimization, Linear regression, Sampling (statistics), Error analysis (mathematics), Multivariate normal distribution, Invertible matrix, Convergence of random variables, Convex hull, Linear matrix inequality, Moment (mathematics), Duality (optimization), Observational error, Binary search algorithm, Logistic regression, Statistical hypothesis testing, Gaussian noise, Parameter, Variational inequality, Nonparametric regression, Optimization problem, Moment-generating function, Mathematical optimization, Rectangle, Measurement, Statistical inference, Nonparametric statistics, Compressed sensing, Upper and lower bounds, Convex cone, Probability theory, Random variable, Rate of convergence, Inference, Norm (mathematics), Accuracy and precision, Linear inequality, Likelihood function, Stochastic matrix, Function (mathematics), Proportionality (mathematics), Random matrix, Conditional probability distribution, Joint probability distribution, Computational complexity theory, Probability, Estimation, Estimation theory, Stochastic approximation, Characteristic function (probability theory), Stochastic optimization, Poisson distribution, Variable (mathematics), Bayesian, Bounded set (topological vector space), Empirical probability, Sparse matrix, Discrete cosine transform, Probability distribution, Uniform distribution (discrete), Statistics, P versus NP problem, Statistical significance