Random Matrix Methods for Machine Learning

Random Matrix Methods for Machine Learning

Random Matrix Methods for Machine Learning
Автор: Couillet Romain, Liao Zhenyu
Дата выхода: 2022
Издательство: Cambridge University Press
Количество страниц: 411
Размер файла: 4.0 MB
Тип файла: PDF
Добавил: codelibs
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0.0 9781009123235....1

01.0_pp_i_iv_Frontmatter....2

02.0_pp_v_vi_Contents....6

03.0_pp_vii_viii_Preface....8

04.0_pp_1_34_Introduction....10

05.0_pp_35_154_Random_Matrix_Theory....44

06.0_pp_155_206_Statistical_Inference_in_Linear_Models....164

07.0_pp_207_276_Kernel_Methods....216

08.0_pp_277_312_Large_Neural_Networks....286

09.0_pp_313_336_Large-Dimensional_Convex_Optimization....322

10.0_pp_337_363_Community_Detection_on_Graphs....346

11.0_pp_364_377_Community_Detection_on_Graphs....373

12.0_pp_378_400_Bibliography....387

13.0_pp_401_402_Index....410

This book presents a unified theory of random matrices for applications in machine learning, offering a large-dimensional data vision that exploits concentration and universality phenomena. This enables a precise understanding, and possible improvements, of the core mechanisms at play in real-world machine learning algorithms. The book opens with a thorough introduction to the theoretical basics of random matrices, which serves as a support to a wide scope of applications ranging from SVMs, through semi-supervised learning, unsupervised spectral clustering, and graph methods, to neural networks and deep learning. For each application, the authors discuss small- versus large-dimensional intuitions of the problem, followed by a systematic random matrix analysis of the resulting performance and possible improvements. All concepts, applications, and variations are illustrated numerically on synthetic as well as real-world data, with MATLAB and Python code provided on the accompanying website.


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