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Machine Learning by Sergios Theodoridis

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Chapter 8

Parameter Learning

A Convex Analytic Path

Abstract

The goal of this chapter is to present an overview of techniques for convex optimization in the context of machine learning. It starts from the definitions of convex sets, functions and the projection operator and some of its properties are derived. The fundamental theorem of POCS and its more recent online version, APSM, are presented. Then, the topic of minimizing nonsmooth convex functions is discussed and the definitions of subgradient and subdifferential are provided. The method of subgradient iterative minimization and some of its versions are presented. The regret analysis technique is discussed. The chapter closes with presenting the proximal approximation, ADMM and the ...

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