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Foundations of Data Science - Cornell University

Foundations of data Science Avrim Blum, John Hopcroft, and Ravindran KannanThursday 4thJanuary, 2018 Copyright 2015. All rights reserved1 Contents1 Introduction92 High-Dimensional Introduction .. The Law of Large Numbers .. The Geometry of High Dimensions .. Properties of the Unit Ball .. of the Unit Ball .. Near the Equator .. Generating Points Uniformly at Random from a Ball .. Gaussians in High Dimension .. Random Projection and Johnson-Lindenstrauss Lemma .. Separating Gaussians .. Fitting a Spherical Gaussian to data .. Bibliographic Notes .. Exercises .. 323 Best-Fit Subspaces and Singular Value Decomposition (SVD) Introduction.

elds calls for a change in our understanding of data and how to handle it in the modern setting. The emergence of the web and social networks as central aspects of daily life presents both opportunities and challenges for theory. While traditional areas of computer science remain highly important, increasingly re-

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