PASCAL Foundations and New Trends of PAC Bayesian Learning, London 2010

Efficient Mixture Modeling with RKHS Embeddings: A PAC-Bayesian Analysis

author: Matthew Higgs, Department of Computer Science, University College London
published: April 14, 2010, recorded: March 2010, views: 107

Slides

Slides
0:00	Efficient Mixture Modeling with RKHS Embeddings A PAC-Bayesian Analysis
0:45	Outline
1:15	Outline, Motivation (1)
1:18	Maximum Mean Discrepancy
2:17	Maximum Mean Discrepancy, Definition
2:59	Maximum Mean Discrepancy, Examples
3:19	Unit-ball in RHKS
4:17	Unit-ball in RHKS, Proposition
5:00	Unit-ball in RHKS, Corollary
5:30	Outline,Motivation (2)
5:39	Reproducing KMM Mixture Model
6:14	Unit-ball in RHKS, Corollary
6:21	Reproducing KMM Mixture Model, Corollary (KMM [Song et al., 2008])
6:43	Reproducing KMM Mixture Model, Question
6:58	Outline, First Order PAC-Bayes Bound (1)
7:15	U-Statistic PAC-Bayes Bound
8:07	U-Statistic PAC-Bayes Bound, Corollary
9:03	Proof: iid blocks
9:17	Proof: iid blocks, Theorem
9:22	Proof: iid blocks
9:39	Proof: iid blocks, Theorem
10:23	Proof: Bounded to Bernoulli
10:50	Proof: Bounded to Bernoulli, Proposition
11:23	Proof: iid blocks, Theorem
11:30	Outline, First Order PAC-Bayes Bound (2)
11:32	Is \|\|kQb - kDn\|\|2 H a U-statistic? (1)
12:03	Is \|\|kQb - kDn\|\|2 H a U-statistic? (2)
12:29	Is \|\|kQb - kDn\|\|2 H a U-statistic? (3)
13:25	Is \|\|kQb - kDn\|\|2 H a U-statistic? (4)
13:29	Is \|\|kQb - kDn\|\|2 H a U-statistic? (5)
14:11	Is \|\|kQb - kDn\|\|2 H a U-statistic? (6)
14:42	Outline, Close (1)
14:51	Choosing KL
15:05	Choosing KL, Example (Dirichlet)
15:40	Log-Normal Projection (1)
15:59	Log-Normal Projection (2)
16:37	Log-Normal Projection (3)
17:12	Outline, Close (2)
17:18	Conclusion, Summary
17:37	Conclusion, Future work
17:52	Log-Normal Projection (3)
18:00	Conclusion, Future work
18:48	Questions

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