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On the Estimation of alpha-Divergences

Published on May 06, 20113290 Views

We propose new nonparametric, consistent Renyi-alpha and Tsallis-alpha divergence estimators for continuous distributions. Given two independent and identically distributed samples, a ``naive'' app

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On the Estimation of alpha-Divergences00:00
http://www.cs.cmu.edu/~bapoczos/tmp/aistats2011pres_pdf.pdf00:22
Outline00:34
Divergences (pseudo-distances)01:00
Tsallis & Rényi divergence01:44
Applications02:12
Applications (continued)02:46
The Goal04:50
How should we estimate divergences?05:16
kNN density estimation06:27
The Estimator08:02
“There is nothing more practical than a good theory” [Lewin]09:19
Main Theorems09:25
Distribution of “normalized” k-NN distances10:40
Erlang distribution11:52
Asymptotically unbiased (1)12:23
Asymptotically unbiased (2)13:23
A little problem…14:10
Numerical Experiments15:11
Results for divergence estimation - 2D Normal15:14
5D beta distributions15:46
Mutual Information Estimation15:57
Results for MI estimation16:30
Low-dim embedding17:02
Take me home!18:36