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Mathematical Theories of Machine Learning - Theory and Applications

  • Bin Shi
  • S. S. Iyengar
Book

Table of contents

  1. Front Matter
    Pages i-xxi
  2. Introduction

    1. Front Matter
      Pages 1-1
    2. Bin Shi, S. S. Iyengar
      Pages 3-11
    3. Bin Shi, S. S. Iyengar
      Pages 13-16
    4. Bin Shi, S. S. Iyengar
      Pages 17-28
    5. Bin Shi, S. S. Iyengar
      Pages 29-33
    6. Bin Shi, S. S. Iyengar
      Pages 35-37
    7. Bin Shi, S. S. Iyengar
      Pages 39-44
  3. Mathematical Framework for Machine Learning: Theoretical Part

    1. Front Matter
      Pages 45-45
    2. Bin Shi, S. S. Iyengar
      Pages 63-85
  4. Mathematical Framework for Machine Learning: Application Part

    1. Front Matter
      Pages 87-87
    2. Bin Shi, S. S. Iyengar
      Pages 121-121
  5. Back Matter
    Pages 123-133

About this book

Introduction

This book studies mathematical theories of machine learning. The first part of the book explores the optimality and adaptivity of choosing step sizes of gradient descent for escaping strict saddle points in non-convex optimization problems. In the second part, the authors propose algorithms to find local minima in nonconvex optimization and to obtain global minima in some degree from the Newton Second Law without friction. In the third part, the authors study the problem of subspace clustering with noisy and missing data, which is a problem well-motivated by practical applications data subject to stochastic Gaussian noise and/or incomplete data with uniformly missing entries. In the last part, the authors introduce an novel VAR model with Elastic-Net regularization and its equivalent Bayesian model allowing for both a stable sparsity and a group selection. 

  • Provides a thorough look into the variety of mathematical theories of machine learning
  • Presented in four parts, allowing for readers to easily navigate the complex theories 
  • Includes extensive empirical studies on both the synthetic and real application time series data

Keywords

machine learning deep learning non-convex optimization gradient decent minimizers subspace clustering multi-variate time-series

Authors and affiliations

  • Bin Shi
    • 1
  • S. S. Iyengar
    • 2
  1. 1.University of CaliforniaBerkeleyUSA
  2. 2.Florida International UniversityMiamiUSA

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-030-17076-9
  • Copyright Information Springer Nature Switzerland AG 2020
  • Publisher Name Springer, Cham
  • eBook Packages Engineering
  • Print ISBN 978-3-030-17075-2
  • Online ISBN 978-3-030-17076-9
  • Buy this book on publisher's site
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