Statistical Inference via Convex Optimization

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Princeton University Press 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

Nonparametric regression, Dimension (vector space), Probability distribution, Sampling (statistics), Conditional probability distribution, Preference (economics), Linear dynamical system, Variable (mathematics), Approximation, Convex optimization, Random variable, Linear inequality, Probability theory, Error function, Parameter, Compressed sensing, Affine space, Inference, Stochastic optimization, Bounded set (topological vector space), Characteristic function (probability theory), Empirical probability, Convex cone, Linear function, Estimation theory, Independence (probability theory), Statistical hypothesis testing, Joint probability distribution, Least squares, Non-linear least squares, Computation, Bias of an estimator, Measurement, Proportionality (mathematics), Random matrix, Statistical significance, Infimum and supremum, Convex function, Uniform distribution (discrete), Linear map, Linear programming, Probability, Stochastic matrix, Measure (mathematics), Convex set, Invertible matrix, Candidate solution, Stochastic approximation, Estimator, Linear regression, Rate of convergence, Differentiable function, Observational error, Poisson distribution, Convex hull, Linear matrix inequality, Rectangle, Upper and lower bounds, Statistical inference, Function (mathematics), Variational inequality, Mathematical practice, Mathematical optimization, Nonparametric statistics, Covariance matrix, P versus NP problem, Subset, Estimation, Parametric family, Likelihood function, Lipschitz continuity, Computational complexity theory, Optimization problem, Maxima and minima, Mathematical induction, Restricted isometry property, Logistic regression, Error analysis (mathematics), Sparse matrix, Inequality (mathematics), Probability of error, Gaussian noise, Probability space, Duality (optimization), Singular value decomposition, Bayesian, Binary search algorithm, Moment (mathematics), NP-hardness, Concave function, Multivariate normal distribution, Moment-generating function, Monte Carlo method, Statistics, Convergence of random variables, Accuracy and precision, Norm (mathematics), Conditional expectation, Change detection, Discrete cosine transform