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机器学习的数学理论与应用-Mathematical Theories of Machine Learning - Theory and Applications文件编号:1405

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标题(title):Mathematical Theories of Machine Learning - Theory and Applications
机器学习的数学理论与应用
作者(author):Bin Shi, S. S. Iyengar
出版社(publisher):Springer International Publishing
大小(size):3 MB (3101985 bytes)
格式(extension):pdf
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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.


Table of contents :
Front Matter ....Pages i-xxi
Front Matter ....Pages 1-1
Introduction (Bin Shi, S. S. Iyengar)....Pages 3-11
General Framework of Mathematics (Bin Shi, S. S. Iyengar)....Pages 13-16
Optimization Formulation (Bin Shi, S. S. Iyengar)....Pages 17-28
Development of Novel Techniques of CoCoSSC Method (Bin Shi, S. S. Iyengar)....Pages 29-33
Necessary Notations of the Proposed Method (Bin Shi, S. S. Iyengar)....Pages 35-37
Related Work on Geometry of Non-Convex Programs (Bin Shi, S. S. Iyengar)....Pages 39-44
Front Matter ....Pages 45-45
Gradient Descent Converges to Minimizers: Optimal and Adaptive Step-Size Rules (Bin Shi, S. S. Iyengar)....Pages 47-62
A Conservation Law Method Based on Optimization (Bin Shi, S. S. Iyengar)....Pages 63-85
Front Matter ....Pages 87-87
Improved Sample Complexity in Sparse Subspace Clustering with Noisy and Missing Observations (Bin Shi, S. S. Iyengar)....Pages 89-101
Online Discovery for Stable and Grouping Causalities in Multivariate Time Series (Bin Shi, S. S. Iyengar)....Pages 103-119
Conclusion (Bin Shi, S. S. Iyengar)....Pages 121-121
Back Matter ....Pages 123-133

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