Intro and Foundations of Data Science I
summary
A compact course first promotes a finite-moment method that replaces exponential moment proofs with Rth moments and an R! bound to get Gaussian-like moment tails up to the Sth moment then uses that to prove a Gaussian annulus theorem and a clean Johnson-Lindenstrauss via Gaussians result. It then contrasts JL failure on two equal spherical Gaussians separated by O(1) in ambient dimension D with the success of SVD = best-fit subspace and randomized linear-algebra routines and sketches where PCA finds the separation while oblivious projection loses the signal.
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chapters (14)
- 0:00Intro
- 0:19A Brief Description
- 1:07Bootcamp Overview
- 8:37Sums of independent random variables
- 10:24Distributions in Data Science
- 14:58The Theorem
- 22:50Corollaries
- 25:00Exponential, Power Law Distributions
- 26:22Dimension Reduction-two methods
- 31:13Length Preserving Projection
- 33:25Projection with Gaussian Vectors
- 35:10Random Projection Theorem
- 40:13Means Separated by O(1) Standard Deviations
- 45:18Singular Value Decomposition
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