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Manifold Learning on Probabilistic Graphical Models 概率图上的流形学习

Manifold Learning on Probabilistic Graphical Models 概率图上的流形学习. 答辩人 : 邵元龙 导师 : 鲍虎军 教授 & 何晓飞 教授 浙江大学 CAD&CG 国家重点实验室 2010 年 3 月 5 日. Outline. Background & Motivation Function Learning v.s. Statistical Modeling Manifold Regularized Variational Inference Algorithm Design & Examples

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Manifold Learning on Probabilistic Graphical Models 概率图上的流形学习

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  1. Manifold Learning on Probabilistic Graphical Models概率图上的流形学习 答辩人: 邵元龙 导师: 鲍虎军 教授 &何晓飞 教授 浙江大学CAD&CG国家重点实验室 2010年3月5日

  2. Outline • Background & Motivation • Function Learning v.s. Statistical Modeling • Manifold Regularized Variational Inference • Algorithm Design & Examples • In Depth Analysis • Implementation • Experimental Results

  3. Function Learning • Given data points , and a function space , find the optimal function , such that Regularization is Important!!

  4. Statistical Modeling • All quantities, no matter given or to be estimated, are random variables. • Then we model the joint distribution.

  5. e.g. Gaussian Mixture Model

  6. Difficulties • How many components are there? • Should there be any “components” ?

  7. Difficulties (continued) • What if data reside on a non-trivial manifold

  8. Efforts towards Non-Parametric, but …

  9. What we want…

  10. Review GMM • Function Learning embedded.

  11. Problem Formulation • What to regularize? • Where to regularize?

  12. Manifold Learning

  13. Manifold Assumption • Y changes smoothly with X, and we have so should be small over manifold • Minimizing it over the manifold,

  14. Manifold Regularization

  15. Manifold Regularization Transductive Learning

  16. Problem Formulation • What to regularize? • Where to regularize?

  17. Variational Inference • For , define , a var. dist. • Approximate the true posterior with it by minimizing the KL divergence

  18. Manifold Regularized Variational Inference

  19. How to Optimize?

  20. Optimization Algorithm

  21. An Illustration

  22. Works Done • Example Distribution Types • Convergence Proof • Convexity Analysis (More TODO) • Computational Complexity • Numerical Stability • A Flexible Inference Engine

  23. YASIE (Yet Another Statistical Inference Engine) • Interface Design • Inference Scheduling • Type-Free Mixture Model • Design Issues (e.g. Balance of Memory & Comp. Time)

  24. Experiments • Data Clustering • Gaussian Mixture Model • Image Annotation • Link Mixture of Unigram

  25. Image Annotation Model • Link Mixture of Unigram

  26. Image Similarity Graph • “?” should be something like “Barcelona” ?

  27. Image Annotation Performances

  28. Image Annotation Examples

  29. Any Question? • 实验室的老师们：鲍虎军老师，何晓飞老师，蔡登老师，刘新国老师，章国锋老师，黄劲老师…… • 师兄师弟师妹们：董子龙，姜翰青，周源，张驰原，林斌斌，薛维，瞿新泉，姚冠红…… 感谢你们一直以来给我的帮助！

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