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Transcript of normalized online learning

  • 1. Normalized online learning Stephane Ross, Carnegie Mellon University Paul Mineiro, Microsoft John Langford, Microsoft Research (arXiv:1305.6646v1 [cs.LG] 28 May 2013)@shima_x

2. feature feature 3. 4. 1 5. 2 sNAG sNAG sNAG 6. Adversary Setting 7. Adversary Settingp-norm p-norm p-norm 2 S 1 2S1 p=2 1 p=2 p=21 sNAG sNAG sNAG 8. Competing against a Bounded Output Predictor C C 9. Competing against a Bounded Output Predictor q p q qpq norm q p qpS S 10. Analysis update rule weight time t t time t t 11. Analysis 1 1 Appendix Appendix Appendix 12. Analysis - Best Choice of Conditioner in Hindsight w =01 1 Aw1=0A A= 13. Analysis - Best Choice of Conditioner in Hindsight A A 1/s g s wi* 1/sigtisi wi* wi* 14. Analysis - Best Choice of Conditioner in Hindsight 2 2 S Appendix Appendix Appendix 15. Analysis - Best Choice of Conditioner in Hindsight 16. Analysis - Best Choice of Conditioner in Hindsight p= p= p= S p= p=SA A 17. Analysis - Best Choice of Conditioner in Hindsight p= p= p= 18. Analysis - Best Choice of Conditioner in Hindsight p=2 p=2 p=2 19. Analysis - Best Choice of Conditioner in Hindsight p=2 p=2 p=2 T t tT Adversary setting 1 1 20. Analysis - Transductive Case S S 2 2 S 1S 2 21. Analysis - Transductive Case t t1 1 22. Analysis - Transductive Case A lemma1, lemma3 Appendix lemma3Appendix AppendixA 2 (2)^0.5 2*(2)^0.5 23. Analysis - Streaming Case p= p= A S input data ASinput data 24. Analysis - Streaming Case 2 2 25. Analysis - Streaming Case 2AppendixHige, log loss squared loss Rmax 1 Rmax Rmax1 26. Analysis - Streaming Case i i t t 27. Experiments CT MSD CTMSD MSD 28. Experiments NAG AG NAGAG AG 29. Experiments sNAG AG sNAGAG AG sNAG NAG NAGsNAG sNAG sNAG sNAG 30. Experiments sNAG AG sNAGAG AGAG NAG NAGAG AG 31. Experiments NAG NAG