Exploiting Structure In Large Scale Optimization For Machine Learning
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Exploiting Structure in Large-scale Optimization for Machine Learning
With an immense growth of data, there is a great need for solving large-scale machine learning problems. Classical optimization algorithms usually cannot scale up due to huge amount of data and/or model parameters. In this thesis, we will show that the scalability issues can often be resolved by exploiting three types of structure in machine learning problems: problem structure, model structure, and data distribution. This central idea can be applied to many machine learning problems. In this thesis, we will describe in detail how to exploit structure for kernel classification and regression, matrix factorization for recommender systems, and structure learning for graphical models. We further provide comprehensive theoretical analysis for the proposed algorithms to show both local and global convergent rate for a family of in-exact first-order and second-order optimization methods.
Optimization for Machine Learning
An up-to-date account of the interplay between optimization and machine learning, accessible to students and researchers in both communities. The interplay between optimization and machine learning is one of the most important developments in modern computational science. Optimization formulations and methods are proving to be vital in designing algorithms to extract essential knowledge from huge volumes of data. Machine learning, however, is not simply a consumer of optimization technology but a rapidly evolving field that is itself generating new optimization ideas. This book captures the state of the art of the interaction between optimization and machine learning in a way that is accessible to researchers in both fields. Optimization approaches have enjoyed prominence in machine learning because of their wide applicability and attractive theoretical properties. The increasing complexity, size, and variety of today's machine learning models call for the reassessment of existing assumptions. This book starts the process of reassessment. It describes the resurgence in novel contexts of established frameworks such as first-order methods, stochastic approximations, convex relaxations, interior-point methods, and proximal methods. It also devotes attention to newer themes such as regularized optimization, robust optimization, gradient and subgradient methods, splitting techniques, and second-order methods. Many of these techniques draw inspiration from other fields, including operations research, theoretical computer science, and subfields of optimization. The book will enrich the ongoing cross-fertilization between the machine learning community and these other fields, and within the broader optimization community.
Tractability
Author: Lucas Bordeaux
language: en
Publisher: Cambridge University Press
Release Date: 2014-02-06
Classical computer science textbooks tell us that some problems are 'hard'. Yet many areas, from machine learning and computer vision to theorem proving and software verification, have defined their own set of tools for effectively solving complex problems. Tractability provides an overview of these different techniques, and of the fundamental concepts and properties used to tame intractability. This book will help you understand what to do when facing a hard computational problem. Can the problem be modelled by convex, or submodular functions? Will the instances arising in practice be of low treewidth, or exhibit another specific graph structure that makes them easy? Is it acceptable to use scalable, but approximate algorithms? A wide range of approaches is presented through self-contained chapters written by authoritative researchers on each topic. As a reference on a core problem in computer science, this book will appeal to theoreticians and practitioners alike.