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
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0:00 Slides Efficient Mixture Modeling with RKHS Embeddings A PAC-Bayesian Analysis Outline Outline, Motivation (1) Maximum Mean Discrepancy Maximum Mean Discrepancy, Definition Maximum Mean Discrepancy, Examples Unit-ball in RHKS Unit-ball in RHKS, Proposition Unit-ball in RHKS, Corollary Outline,Motivation (2) Reproducing KMM Mixture Model Unit-ball in RHKS, Corollary Reproducing KMM Mixture Model, Corollary (KMM [Song et al., 2008]) Reproducing KMM Mixture Model, Question Outline, First Order PAC-Bayes Bound (1) U-Statistic PAC-Bayes Bound U-Statistic PAC-Bayes Bound, Corollary Proof: iid blocks Proof: iid blocks, Theorem Proof: iid blocks Proof: iid blocks, Theorem Proof: Bounded to Bernoulli Proof: Bounded to Bernoulli, Proposition Proof: iid blocks, Theorem Outline, First Order PAC-Bayes Bound (2) Is ||kQb - kDn||2 H a U-statistic? (1) Is ||kQb - kDn||2 H a U-statistic? (2) Is ||kQb - kDn||2 H a U-statistic? (3) Is ||kQb - kDn||2 H a U-statistic? (4) Is ||kQb - kDn||2 H a U-statistic? (5) Is ||kQb - kDn||2 H a U-statistic? (6) Outline, Close (1) Choosing KL Choosing KL, Example (Dirichlet) Log-Normal Projection (1) Log-Normal Projection (2) Log-Normal Projection (3) Outline, Close (2) Conclusion, Summary Conclusion, Future work Log-Normal Projection (3) Conclusion, Future work Questions

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