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Nonparametric Tests between Distributions
Published on 2007-02-257398 Views
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 o
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Presentation
Nonparametric Distribution Testing00:15
Outline00:33
Tests for distributions02:48
Why?04:42
Key Strategy06:27
Q1: Disjoint Support07:58
Linear separability09:41
Nonlinear separability?09:46
Q2: Independence11:45
Independent random variables13:57
Dependent random variables14:32
Or are we just unlucky?14:51
Covariance operators15:08
Hilbert Space representation18:00
Computing19:32
Estimating22:19
Uniform convergence bounds for24:38
ICA Experiments28:20
Automatic Regularization31:52
Outlier Robustness33:20
Q3: Identity34:47
Identical distributions38:28
Different distributions39:28
Maximum mean discrepancy39:58
Empirical estimates and Banach spaces40:53
Computing it49:16
Concentration of measure53:01
Value of norm discrepancy53:42
Consequences56:21
Summary57:06
Shameless Plugs57:58