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Nonparametric Tests between Distributions
Published on Feb 25, 20077391 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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Chapter list
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
Nonlinear separability?10:09
Q1: Disjoint Support10:18
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
Automatic Regularization34:50
Q3: Identity35:55
Identical distributions38:28
Different distributions39:28
Or are we just unlucky?39:52
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