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The mathematics of data / Michael W. Mahoney, John C. Duchi, Anna C. Gilbert, editors

Contributor(s): Resource type: Ressourcentyp: Buch (Online)Book (Online)Language: English Series: IAS/Park City mathematics series ; volume 25Publisher: [Providence, Rhode Island] : American Mathematical Society, [2018]Description: 1 Online-RessourceISBN:
  • 9781470449902
Subject(s): Genre/Form: Additional physical formats: 1470435756 | 9781470435752 | 1470449900. | Erscheint auch als: The mathematics of data. Druck-Ausgabe [Providence] : American Mathematical Society, 2018. xii, 325 Seiten | Erscheint auch als: No title Druck-AusgabeDDC classification:
  • 510
MSC: MSC: *68-06 | 62-06 | 65-06 | 90-06 | 55U99 | 62-07 | 65F30 | 68T05 | 68W20 | 90C15 | 00B25RVK: RVK: SD 2016Online resources: Summary: Cover; Title page; Preface; Introduction; Lectures on Randomized Numerical Linear Algebra; Introduction; Linear Algebra; Basics.; Norms.; Vector norms.; Induced matrix norms.; The Frobenius norm.; The Singular Value Decomposition.; SVD and Fundamental Matrix Spaces.; Matrix Schatten norms.; The Moore-Penrose pseudoinverse.; References.; Discrete Probability; Random experiments: basics.; Properties of events.; The union bound.; Disjoint events and independent events.; Conditional probability.; Random variables.; Probability mass function and cumulative distribution functionSummary: Nesterov's Accelerated Gradient: Weakly Convex CaseNesterov's Accelerated Gradient: Strongly Convex Case; Lower Bounds on Rates; Newton Methods; Basic Newton's Method; Newton's Method for Convex Functions; Newton Methods for Nonconvex Functions; A Cubic Regularization Approach; Conclusions; Introductory Lectures on Stochastic Optimization; Introduction; Scope, limitations, and other references; Notation; Basic Convex Analysis; Introduction and Definitions; Properties of Convex Sets; Continuity and Local Differentiability of Convex Functions; Subgradients and Optimality ConditionsSummary: The running time of the R\scriptsize ANDL\scriptsize EASTS\scriptsize QUARES algorithm.References.; A RandNLA Algorithm for Low-rank Matrix Approximation; The main algorithm and main theorem.; An alternative expression for the error.; A structural inequality.; Completing the proof of Theorem 6.1.1.; Running time.; References.; \replace{Optimization Algorithms for Data Analysis}; Introduction; Omissions; Notation; Optimization Formulations of Data Analysis Problems; Setup; Least Squares; Matrix Completion; Nonnegative Matrix Factorization; Sparse Inverse Covariance EstimationSummary: Data science is a highly interdisciplinary field, incorporating ideas from applied mathematics, statistics, probability, and computer science, as well as many other areas. This book gives an introduction to the mathematical methods that form the foundations of machine learning and data science, presented by leading experts in computer science, statistics, and applied mathematics. Although the chapters can be read independently, they are designed to be read together as they lay out algorithmic, statistical, and numerical approaches in diverse but complementary ways. This book can be used both aPPN: PPN: 104548427XPackage identifier: Produktsigel: ZDB-4-NLEBK
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