Kernel Methods, part 1 - Arthur Gretton - MLSS 2020, Tübingen скачать в хорошем качестве

Kernel Methods, part 1 - Arthur Gretton - MLSS 2020, Tübingen

Table of Contents (powered by https://videoken.com) 0:00:00 Introduction 0:02:10 Representing and comparing probabilities with kernels: Part 1 0:02:56 A motivation: comparing two samples 0:03:34 A real-life example: two-sample tests 0:04:34 Training generative models 0:06:04 A second task: testing goodness of fit 0:07:18 A third task: testing independence 0:08:37 Outline: these slides 0:10:16 Outline: next slides 0:10:43 Reproducing Kernel Hilbert Spaces 0:10:48 Kernels and feature space (1): XOR example 0:12:30 Kernels and feature space (2): smoothing 0:13:43 Hilbert space 0:17:06 New kernels from old: sums, transformations 0:18:03 New kernels from old: products 0:22:19 Sums and products =polynomials 0:22:40 Infinite sequences 0:23:21 The reproducing property 0:24:42 Infinite sequences (proof) 0:25:15 A famous infinite feature space kernel 0:27:38 Positive definite functions 0:29:43 Kernels are positive definite 0:31:48 Sum of kernels is a kernel 0:32:34 Functions of infinitely many features 0:33:22 Functions of finitely many features 0:35:07 Functions of infinitely many features 0:35:55 Expressing the functions with kernels 0:38:42 The feature map (x) is also a function 0:41:00 The reproducing property 0:41:45 Understanding smoothness in the RKHS 0:42:30 Constructing an infinite feature space: fourier series 0:47:27 Fourier series for top hat function 0:49:37 Fourier series for kernel function 0:51:49 Fourier series for Gaussian-spectrum kernel 0:53:00 RKHS via fourier series 0:59:23 Roughness penalty explained 1:03:38 Feature map and reproducing property 1:07:29 Q&A 1:09:28 Link back to original RKHS function definition 1:12:31 Main message 1:14:33 Q&A