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Machine Learning on Distributions
Published on Jan 16, 20134500 Views
Low-dimensional embedding, manifold learning, clustering, classification, and anomaly detection are among the most important problems in machine learning. The existing methods usually consider the
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Chapter list
Machine Learning on Distributions00:00
Joint work with…00:02
GOAL: Machine Learning on Distributions00:08
Outline02:26
Divergence estimation03:03
The Estimator05:17
Does it make sense?06:52
Asymptotically Unbiased07:52
A little problem…10:49
Be careful, some mistakes are easy to make…12:40
2nd Contribution ML on distributions13:37
Machine Learning on Distributions13:44
Distribution Classification14:17
Support Distribution Machine15:15
Kernel Estimation16:33
3rd Contribution Applications19:53
Image Representation with Distributions20:07
Detecting Anomalous Images (1)21:57
Detecting Anomalous Images (2)22:50
GMM-5 Density Approximation23:14
Noisy USPS Dataset Classification24:00
Multidimensional Scaling of USPS Data25:36
Local Linear Embedding of Distributions26:18
Object Classification (1)27:32
Object Classification (2)28:34
Outdoor Scenes Classification29:00
Sport Events Classification29:35
Finding Unusual Galaxy Clusters30:32
Understanding Turbulences32:49
Turbulence Data Classification33:36
Finding Vortices34:58
Find Interesting Phenomena in Turbulence Data35:21
4th Contribution Theory35:59
So far, we got good experimental results in applications36:05
Standard, finite dimensional regression Nadaraya-Watson, 196436:27
Distribution Regression Problem Definition38:02
The kernel-kernel estimator39:22
Assumptions42:56
Bounding the risk45:14
Doubling Measure47:54
Examples for finite doubling dimension48:44
Rates50:32
Proofs50:52
Why small ball probabilities?51:55
Proof continued…52:04
Distribution Regression52:17
Take Me Home!52:58