Modelling in Classification and Statistical Learning Workshop

Nonparametric Tests between Distributions

author: Alexander J. Smola, Australian National University - ANU

Description

Reproducing Kernel Hilbert Spaces have been mainly used for estimation. Distributional tests in this area were mainly concerned with tests for independence of random variables. We give concentration of measure bounds for the latter using an easy to compute criterion between spaces of observations. In addition, we show that a similar criterion can be used easily for the purpose of testing the identity between two distributions. In both cases, we prove necessary and sufficient conditions for the tests.

Categories

Top: Mathematics: Statistics

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*Slides*
0:15	Nonparametric Distribution Testing
0:33	Outline
2:48	Tests for distributions
4:42	Why?
6:27	Key Strategy
7:58	Q1: Disjoint Support
9:41	Linear separability
9:46	Nonlinear separability?
10:09	Nonlinear separability?
10:18	Q1: Disjoint Support
11:45	Q2: Independence
13:57	Independent random variables
14:32	Dependent random variables
14:51	Or are we just unlucky?
15:08	Covariance operators
18:00	Hilbert Space representation
19:32	Computing
22:19	Estimating
24:38	Uniform convergence bounds for
28:20	ICA Experiments
31:52	Automatic Regularization
33:20	Outlier Robustness
34:47	Q3: Identity
34:50	Automatic Regularization
35:55	Q3: Identity
38:28	Identical distributions
39:28	Different distributions
39:52	Or are we just unlucky?
39:58	Maximum mean discrepancy
40:53	Empirical estimates and Banach spaces
49:16	Computing it
53:01	Concentration of measure
53:42	Value of norm discrepancy
56:21	Consequences
57:06	Summary
57:58	Shameless Plugs

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