ICA and Kernel Distribution Testing00:00
Overview00:52
Some notation and conventions02:10
ICA<br>... where to be careful when doing it02:54
ICA (Population version)03:00
ICA (empirical version)03:52
A toy example (1)04:04
A toy example (2)04:26
Things that are impossible for ICA (1)04:45
Things that are impossible for ICA (1) 0105:17
Things that are impossible for ICA (2)05:37
Things that are impossible for ICA (3)06:10
Things that are impossible for ICA (4)06:42
ICA Step 1 - <br>Decorrelation07:15
First step in ICA: decorrelate07:20
Example: what does decorrelation achieve?07:34
Decorrelation: a drawback08:03
What is left: rotation08:48
Rotation (continued)09:00
ICA: maximum likelihood09:19
Maximum likelihood: example10:48
Maximum likelihood: where it fails11:21
ICA Step 2(b) <br>Rotation: contrast functions12:21
What is a copy?12:30
Contrast functions13:03
Contrast functions and maximum likelihood14:08
Contrast functions and mutual information (1)15:05
Contrast functions and mutual information (2)15:44
Contrast functions (3): Some famous cases16:52
Kurtosis: an important concept17:32
Contrast functions: Example (1)18:20
Contrast functions: Example (2)18:40
Disclaimer!19:37
ICA for non-i.i.d. signals (1)20:14
ICA for non-i.i.d. signals (2)22:10
Advanced (kernel!) - <br>independence measures23:21
Kernel dependence measures23:25
Outline24:50
Dependence detection26:05
A second order method26:35
Take nonlinear features27:20
The kernel trick (1)29:30
The kernel trick (2)30:12
An empirical estimate30:46
COCO measures independence31:02
Why universal?31:33
Background: statistical tests (1)33:10
Background: statistical tests (2)35:28
When is dependence hard to detect?37:23
Hard-to-detect dependence (2)39:48
Hard-to-detect dependence (3)41:27
Hard-to-detect dependence (4)42:38
A test of independence43:12
Choosing kernel size (1)45:48
Choosing kernel size (2)47:51
Application to ICA49:02
Positive, Negative, and Zero kurtosis50:34
Outlier resistance51:46
The Two-Sample Problem52:25
The two-sample problem52:31
The MMD (1)53:41
The MMD (2)54:31
The MMD (2) 0156:05
Empirical estimate57:15
