(Ebook) Random Matrix Methods for Machine Learning. by Romain Couillet, Zhenyu Liao.

(Ebook) Random Matrix Methods for Machine Learning. by Romain Couillet, Zhenyu Liao.

Numerous and large dimensional data is now a default setting in modern ma-chine learning (ML). Standard ML algorithms, starting with kernel methodssuch as support vector machines and graph-based methods like the PageRankalgorithm, were however initially designed out of small-dimensional intuitionsand tend to misbehave, if not completely collapse, when dealing with real-worldlarge datasets. Random matrix theory has recently developed a broad spec-trum of tools to help understand this new "curse of dimensionality," to helprepair or completely recreate the suboptimal algorithms, and most importantlyto provide new intuitions to deal with modern data mining.This book primarily aims to deliver these intuitions, by providing a digest ofthe recent theoretical and applied breakthroughs of random matrix theory intoML. Targeting a broad audience, spanning from undergraduate students inter-ested in statistical learning to artificial intelligence engineers and researchersalike, the mathematical prerequisites to the book are minimal (basics of prob-ability theory, linear algebra, and real and complex analyses are sufficient): Asopposed to introductory books in the mathematical literature of random matrixtheory and large-dimensional statistics, the theoretical focus here is restrictedto the essential requirements to ML applications. These applications rangefrom detection, statistical inference, and estimation, to graph- and kernel-basedsupervised, semisupervised and unsupervised classification, as well as neuralnetworks: For these, a precise theoretical prediction of the algorithm perfor-mance (often inaccessible when not resorting to a random matrix analysis),large dimensional insights, methods of improvement, along with a fundamen-tal justification of the wide-scope applicability of the methods to real data, areprovided.Most methods, algorithms, and figure proposed in the book are coded inMATLAB and Python