Random matrix methods for machine learning [E-Book] / Romain Couillet, Zhenyu Liao
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...
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| Personal Name(s): | Couillet, Romain, author |
| Liao, Zhenyu, author | |
| Imprint: |
Cambridge :
Cambridge University Press,
2022
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| Physical Description: |
1 online resource (vi, 402 pages) |
| Note: |
englisch |
| ISBN: |
9781009128490 |
| Subject (LOC): |
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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. |