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Stephen Boyd

Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers

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Surveys the theory and history of the alternating direction method of multipliers, and discusses its applications to a wide variety of statistical and machine learning problems of recent interest, including the lasso, sparse logistic regression, basis pursuit, covariance selection, support vector machines, and many others.

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Surveys the theory and history of the alternating direction method of multipliers, and discusses its applications to a wide variety of statistical and machine learning problems of recent interest, including the lasso, sparse logistic regression, basis pursuit, covariance selection, support vector machines, and many others.Many problems of recent interest in statistics and machine learning can be posed in the framework of convex optimization. Due to the explosion in size and complexity of modern datasets, it is increasingly important to be able to solve problems with a very large number of features or training examples. As a result, both the decentralized collection or storage of these datasets as well as accompanying distributed solution methods are either necessary or at least highly desirable. Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers argues that the alternating direction method of multipliers is well suited to distributed convex optimization, and in particular to large-scale problems arising in statistics, machine learning, and related areas. The method was developed in the 1970s, with roots in the 1950s, and is equivalent or closely related to many other algorithms, such as dual decomposition, the method of multipliers, Douglas-Rachford splitting, Spingarn's method of partial inverses, Dykstra's alternating projections, Bregman iterative algorithms for ?1 problems, proximal methods, and others. After briefly surveying the theory and history of the algorithm, it discusses applications to a wide variety of statistical and machine learning problems of recent interest, including the lasso, sparse logistic regression, basis pursuit, covariance selection, support vector machines, and many others. It also discusses general distributed optimization, extensions to the nonconvex setting, and efficient implementation, including some details on distributed MPI and Hadoop MapReduce implementations.

Specifications

Series Title
Foundations and Trends(r) in Machine Learning
Publisher
Now Publishers
Book Format
Paperback
Original Languages
ENG
Number of Pages
140
Author
Stephen Boyd
Title
Distributed Optimization and Statistical Learning Via the Alternating Direction Method of Multipliers
ISBN-13
9781601984609
Publication Date
June, 2011
Assembled Product Dimensions (L x W x H)
9.21 x 6.14 x 0.30 Inches
ISBN-10
160198460X

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