概率論是研究隨機性或不確定性等現象的數學

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穀歌研究員Kevin Patrick Murphy撰寫的經典機器學習圖書,由MIT出版社出版,《Machine Learning: a Probabilistic Perspective》,自2012年發行以來就奉為經典機器學習書目。本書內容完整,講解詳細,便於閱讀,方便工程使用。最近作者在Github上發布了關於本書的Python代碼,更加方便使用!本文附帶1098頁pdf下載。

Python配套代碼

Github:https://github.com/probml/pyprobml

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We apply local laws of random matrices and free probability theory to study the spectral properties of two kernel-based sensor fusion algorithms, nonparametric canonical correlation analysis (NCCA) and alternating diffusion (AD), for two simultaneously recorded high dimensional datasets under the null hypothesis. The matrix of interest is the product of the kernel matrices associated with the databsets, which may not be diagonalizable in general. We prove that in the regime where dimensions of both random vectors are comparable to the sample size, if NCCA and AD are conducted using a smooth kernel function, then the first few nontrivial eigenvalues will converge to real deterministic values provided the datasets are independent Gaussian random vectors. Toward the claimed result, we also provide a convergence rate of eigenvalues of a kernel affinity matrix.

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