# RMT4ML
This repository contains [`MATLAB`](https://www.mathworks.com/products/matlab.html) and [`Python`](https://www.python.org/) codes for visualizing random matrix theory results and their applications to machine learning, in [Random Matrix Theory for Machine Learning](https://zhenyu-liao.github.io/pdf/RMT4ML.pdf).
In each subfolder (named after the corresponding section) there are:
* a `.html` file containing the [`MATLAB`](https://www.mathworks.com/products/matlab.html) or [IPython Notebook](https://ipython.org/notebook.html) demos
* a `.m` or `.ipynb` source file
* Chapter 1 Introduction
* Chapter 2 Random Matrix Theory
* Section 2.1 Fundamental objects
* Section 2.2 Foundational random matrix results
* Section 2.2.1 Key lemma and identities: [Matlab code](https://htmlpreview.github.io/?https://github.com/Zhenyu-LIAO/RMT4ML/blob/master/2.2/html/lemma_plots.html) and [Python code](https://nbviewer.jupyter.org/github/Zhenyu-LIAO/RMT4ML/blob/master/2.2/lemma_plots.ipynb)
* Section 2.2.2 The Marcenko-Pastur and semicircle laws: [Matlab code](https://htmlpreview.github.io/?https://github.com/Zhenyu-LIAO/RMT4ML/blob/master/2.2/html/MP_and_SC.html) and [Python code](https://nbviewer.jupyter.org/github/Zhenyu-LIAO/RMT4ML/blob/master/2.2/MP_and_SC.ipynb)
* Section 2.2.3 Large sample covariance matrices and generalized semicircles: [Matlab code](https://htmlpreview.github.io/?https://github.com/Zhenyu-LIAO/RMT4ML/blob/master/2.2/html/SCM_and_DSC.html) and [Python code](https://nbviewer.jupyter.org/github/Zhenyu-LIAO/RMT4ML/blob/master/2.2/SCM_and_DSC.ipynb)
* Section 2.3 Advanced spectrum considerations for sample covariances: [Matlab code](https://htmlpreview.github.io/?https://github.com/Zhenyu-LIAO/RMT4ML/blob/master/2.3/html/advanced_spectrum.html) and [Python code](https://nbviewer.jupyter.org/github/Zhenyu-LIAO/RMT4ML/blob/master/2.3/advanced_spectrum.ipynb)
* Section 2.4 Preliminaries on statistical inference
* Section 2.4.1 Linear eigenvalue statistics: [Matlab code](https://htmlpreview.github.io/?https://github.com/Zhenyu-LIAO/RMT4ML/blob/master/2.4/html/linear_eig_stats.html) and [Python code](https://nbviewer.jupyter.org/github/Zhenyu-LIAO/RMT4ML/blob/master/2.4/linear_eig_stats.ipynb)
* Section 2.4.2 Eigenvector projections and subspace methods: [Matlab code](https://htmlpreview.github.io/?https://github.com/Zhenyu-LIAO/RMT4ML/blob/master/2.4/html/eigenvec_proj.html) and [Python code](https://nbviewer.jupyter.org/github/Zhenyu-LIAO/RMT4ML/blob/master/2.4/eigenvec_proj.ipynb)
* Section 2.5 Spiked model: [Matlab code](https://htmlpreview.github.io/?https://github.com/Zhenyu-LIAO/RMT4ML/blob/master/2.5/html/spiked_models.html) and [Python code](https://nbviewer.jupyter.org/github/Zhenyu-LIAO/RMT4ML/blob/master/2.5/spiked_models.ipynb)
* Section 2.6 Information-plus-noise, deformed Wigner, and other models
* Section 2.7 Beyond vectors of independent entries: concentration of measure in RMT
* Section 2.8 Concluding remarks
* Section 2.9 Exercises
* Chapter 3 Statistical Inference in Linear Models
* Section 3.1 Detection and estimation in information-plus-noise models
* Section 3.1.1 GLRT asymptotics: [Matlab code](https://htmlpreview.github.io/?https://github.com/Zhenyu-LIAO/RMT4ML/blob/master/3.1/html/GLRT.html) and [Python code](https://nbviewer.jupyter.org/github/Zhenyu-LIAO/RMT4ML/blob/master/3.1/GLRT.ipynb)
* Section 3.1.2 Linear and Quadratic Discriminant Analysis: [Matlab code](https://htmlpreview.github.io/?https://github.com/Zhenyu-LIAO/RMT4ML/blob/master/3.1/html/LDA.html) and [Python code](https://nbviewer.jupyter.org/github/Zhenyu-LIAO/RMT4ML/blob/master/3.1/LDA.ipynb)
* Section 3.1.1 Subspace methods: the G-MUSIC algorithm: [Matlab code](https://htmlpreview.github.io/?https://github.com/Zhenyu-LIAO/RMT4ML/blob/master/3.1/html/GMUSIC.html) and [Python code](https://nbviewer.jupyter.org/github/Zhenyu-LIAO/RMT4ML/blob/master/3.1/GMUSIC.ipynb)
* Section 3.2 Covariance matrix distance estimation: [Matlab code](https://htmlpreview.github.io/?https://github.com/Zhenyu-LIAO/RMT4ML/blob/master/3.2/html/cov_distance_estimation.html) and [Python code](https://nbviewer.jupyter.org/github/Zhenyu-LIAO/RMT4ML/blob/master/3.2/cov_distance_estimation.ipynb)
* Section 3.3 M-estimator of scatter: [Matlab code](https://htmlpreview.github.io/?https://github.com/Zhenyu-LIAO/RMT4ML/blob/master/3.3/html/M_estim_of_scatter.html) and [Python code](https://nbviewer.jupyter.org/github/Zhenyu-LIAO/RMT4ML/blob/master/3.3/M_estim_of_scatter.ipynb)
* Section 3.4 Concluding remarks
* Section 3.5 Practical course material:
* The Wasserstein distance estimation: [Matlab code](https://htmlpreview.github.io/?https://github.com/Zhenyu-LIAO/RMT4ML/blob/master/3.5/html/Wasserstein_dist.html) and [Python code](https://nbviewer.jupyter.org/github/Zhenyu-LIAO/RMT4ML/blob/master/3.5/Wasserstein_dist.ipynb)
* Robust portfolio optimization via Tyler estimator: [Matlab code](https://htmlpreview.github.io/?https://github.com/Zhenyu-LIAO/RMT4ML/blob/master/3.5/html/robust_portfolio.html) and [Python code](https://nbviewer.jupyter.org/github/Zhenyu-LIAO/RMT4ML/blob/master/3.5/robust_portfolio.ipynb)
* Chapter 4 Kernel Methods
* Section 4.1 Basic setting
* Section 4.2 Distance and inner-product random kernel matrices
* Section 4.2.1 Main intuitions
* Section 4.2.2 Main results: distance random kernel matrices: [Matlab code](https://htmlpreview.github.io/?https://github.com/Zhenyu-LIAO/RMT4ML/blob/master/4.2/html/dist_kernel.html) and [Python code](https://nbviewer.jupyter.org/github/Zhenyu-LIAO/RMT4ML/blob/master/4.2/dist_kernel.ipynb)
* Section 4.2.3 Motivations: alpha-beta random kernel matrices
* Section 4.2.4 Main results: alpha-beta random kernel matrices: [Matlab code](https://htmlpreview.github.io/?https://github.com/Zhenyu-LIAO/RMT4ML/blob/master/4.2/html/alpha_beta_kernel.html) and [Python code](https://nbviewer.jupyter.org/github/Zhenyu-LIAO/RMT4ML/blob/master/4.2/alpha_beta_kernel.ipynb)
* Section 4.3 Properly scaling kernel model: [Matlab code](https://htmlpreview.github.io/?https://github.com/Zhenyu-LIAO/RMT4ML/blob/master/4.3/html/proper_scale_kernel.html) and [Python code](https://nbviewer.jupyter.org/github/Zhenyu-LIAO/RMT4ML/blob/master/4.3/proper_scale_kernel.ipynb)
* Section 4.4 Implications to kernel methods
* Section 4.4.1 Application to kernel spectral clustering: [Matlab code](https://htmlpreview.github.io/?https://github.com/Zhenyu-LIAO/RMT4ML/blob/master/4.4/html/kernel_spectral_clustering.html) and [Python code](https://nbviewer.jupyter.org/github/Zhenyu-LIAO/RMT4ML/blob/master/4.4/kernel_spectral_clustering.ipynb)
* Section 4.4.2 Application to semi-supervised kernel learning: [Matlab code](https://htmlpreview.github.io/?https://github.com/Zhenyu-LIAO/RMT4ML/blob/master/4.4/html/semi_supervised_kernel.html) and [Python code](https://nbviewer.jupyter.org/github/Zhenyu-LIAO/RMT4ML/blob/master/4.4/semi_supervised_kernel.ipynb)
* Section 4.4.3 Application to kernel ridge regression: [Matlab code](https://htmlpreview.github.io/?https://github.com/Zhenyu-LIAO/RMT4ML/blob/master/4.4/html/kernel_ridge.html) and [Python code](https://nbviewer.jupyter.org/github/Zhenyu-LIAO/RMT4ML/blob/master/4.4/kernel_ridge.ipynb)
* Section 4.4.4 Summary of Section 4.4
* Section 4.5 Concluding remarks
* Section 4.6 Practical course material
* Complexity-performance trade-off in spectral clustering with sparse kernel: [Matlab code](https://htmlpreview.github.io/?https://github.com/Zhenyu-LIAO/RMT4ML/blob/master/4.6/html/sparse_clustering.html) and [Python code](https://nbviewer.jupyter.org/github/Zhenyu-LIAO/RMT4ML/blob/master/4.6/sparse_clustering.ipynb)
* Towards transfer learning with kernel regression: [Matlab code](https://htmlpreview.github.io/?https://github.com/Zhenyu-LIAO/RMT4ML/blob/master/4.6/html/transfer.html) and [Python code](https://nbviewer.jupyter.org/github/Zhenyu-LIAO/RMT4ML/blob/master/4.6/trans
Random Matrix Theory 方面的代码，
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Random Matrix Theory 方面的代码， （360个子文件） 
.gitignore 10B
semi_supervised_kernel.html 40KB kernel_spectral_clustering.html 37KB kernel_ridge.html 30KB cov_distance_estimation.html 26KB proper_scale_kernel.html 26KB LDA.html 26KB random_NN.html 25KB advanced_spectrum.html 23KB eigenvec_proj.html 23KB SCM_and_DSC.html 22KB empirical_risk_min.html 21KB grad_descent_dynamics.html 20KB DCSBM.html 19KB linear_eig_stats.html 19KB M_estim_of_scatter.html 18KB Wasserstein_dist.html 18KB RMT_universality.html 17KB spiked_models.html 17KB random_Fourier.html 16KB robust_portfolio.html 15KB alpha_beta_kernel.html 14KB dist_kernel.html 14KB random_feature_GMM.html 12KB ESN.html 11KB phase_retrieval.html 11KB sparse_clustering.html 10KB GLRT.html 10KB sparse_graph.html 10KB MP_and_SC.html 9KB GMUSIC.html 9KB SBM.html 8KB lemma_plots.html 8KB RMT_universality.ipynb 275KB RMT_universality-checkpoint.ipynb 275KB kernel_spectral_clustering-checkpoint.ipynb 262KB kernel_spectral_clustering.ipynb 262KB semi_supervised_kernel.ipynb 169KB semi_supervised_kernel-checkpoint.ipynb 169KB dist_kernel.ipynb 108KB dist_kernel-checkpoint.ipynb 108KB advanced_spectrum.ipynb 93KB advanced_spectrum-checkpoint.ipynb 93KB spiked_models-checkpoint.ipynb 90KB spiked_models.ipynb 90KB random_feature_GMM.ipynb 82KB random_feature_GMM-checkpoint.ipynb 82KB SCM_and_DSC.ipynb 79KB DCSBM.ipynb 76KB DCSBM-checkpoint.ipynb 76KB kernel_ridge.ipynb 75KB kernel_ridge-checkpoint.ipynb 75KB proper_scale_kernel.ipynb 74KB proper_scale_kernel-checkpoint.ipynb 74KB M_estim_of_scatter.ipynb 74KB M_estim_of_scatter-checkpoint.ipynb 74KB sparse_graph-checkpoint.ipynb 72KB sparse_graph.ipynb 72KB linear_eig_stats.ipynb 67KB linear_eig_stats-checkpoint.ipynb 67KB eigenvec_proj.ipynb 65KB grad_descent_dynamics.ipynb 51KB grad_descent_dynamics-checkpoint.ipynb 51KB empirical_risk_min-checkpoint.ipynb 47KB empirical_risk_min.ipynb 47KB random_NN.ipynb 45KB random_NN-checkpoint.ipynb 45KB MP_and_SC.ipynb 42KB alpha_beta_kernel.ipynb 41KB phase_retrieval.ipynb 38KB phase_retrieval-checkpoint.ipynb 38KB sparse_clustering.ipynb 37KB sparse_clustering-checkpoint.ipynb 37KB cov_distance_estimation.ipynb 37KB cov_distance_estimation-checkpoint.ipynb 37KB ESN.ipynb 34KB ESN-checkpoint.ipynb 34KB robust_portfolio.ipynb 33KB robust_portfolio-checkpoint.ipynb 33KB Wasserstein_dist.ipynb 32KB Wasserstein_dist-checkpoint.ipynb 32KB LDA.ipynb 30KB LDA-checkpoint.ipynb 30KB GMUSIC.ipynb 27KB GMUSIC-checkpoint.ipynb 27KB GLRT.ipynb 26KB GLRT-checkpoint.ipynb 26KB lemma_plots.ipynb 25KB lemma_plots-checkpoint.ipynb 25KB random_Fourier.ipynb 23KB random_Fourier-checkpoint.ipynb 23KB SBM.ipynb 22KB SBM-checkpoint.ipynb 22KB transfer.m 15KB semi_supervised_kernel.m 14KB kernel_spectral_clustering.m 12KB kernel_ridge.m 11KB LDA.m 9KB cov_distance_estimation.m 9KB random_NN.m 9KB共 360 条
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