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CW, AROW, and SCW

CW, AROW, and SCW

Confidence-weighted Algorithm (CW), Adaptive Regularization of Weight Vectors (AROW), and Exact Soft Confidence-Weighted Learning (SCW).

Sorami Hisamoto

May 27, 2014
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  1. Sorami Hisamoto 27 May, 2014 $8 "308 BOE4$8

  2. 7BSJPVTPOMJOFMFBSOJOHBMHPSJUINT ‣ 1FSDFQUSPO<3PTFOCMBUU> ‣ \.BSHJO 7PUFE "WFSBHFE 4FDPOEPSEFS 4USVDUVSFE ʜ^1FSDFQUSPO

    ‣ .*3"1".BSHJO*OGVTFE3FMBYFE"MHPSJUIN1BTTJWF"HHSFTTJWF<$SBNNFS > ‣ $8$POpEFODF8FJHIUFE"MHPSJUIN<%SFE[F > ‣ *&--*1*NQSPWFE&MMJQTPJE.FUIPE<:BOH > ‣ "308"EBQUJWF3FHVMBSJ[BUJPOPG8FJHIU7FDUPST<$SBNNFS > ‣ /"308/FX"EBQUJWF"MHPSJUINTGPS0OMJOF$MBTTJpDBUJPO<0SBCPOB$SBNNFS> ‣ /)&3%/PSNBM)FSE<$SBNNFS > ‣ "EB(SBE"EBQUJWF4VC(SBEJFOU.FUIPET<%VDIJ > ‣ 4$8&YBDU4PGU$POpEFODF8FJHIUFE-FBSOJOH<8BOH > ‣ ʜ 2
  3. 1"1BTTJWF"HHSFTTJWFBMHPSJUIN<$SBNNFS > 3 ‣ *GSFTVMUDPSSFDU EPOPUIJOH QBTTJWF  ‣ *GSFTVMUXSPOH

    NJOJNBMMZVQEBUFXFJHIUTUPDMBTTJGZDPSSFDUMZ BHHSFTTJWF 
  4. 1"1BTTJWF"HHSFTTJWFBMHPSJUIN<$SBNNFS > 3 minimally update ‣ *GSFTVMUDPSSFDU EPOPUIJOH QBTTJWF 

    ‣ *GSFTVMUXSPOH NJOJNBMMZVQEBUFXFJHIUTUPDMBTTJGZDPSSFDUMZ BHHSFTTJWF 
  5. 1"1BTTJWF"HHSFTTJWFBMHPSJUIN<$SBNNFS > 3 minimally update ‣ *GSFTVMUDPSSFDU EPOPUIJOH QBTTJWF 

    ‣ *GSFTVMUXSPOH NJOJNBMMZVQEBUFXFJHIUTUPDMBTTJGZDPSSFDUMZ BHHSFTTJWF  correctly classify
  6. 1"1BTTJWF"HHSFTTJWFBMHPSJUIN<$SBNNFS > ‣ )BTDMPTFEGPSNTPMVUJPO 3 minimally update ‣ *GSFTVMUDPSSFDU EPOPUIJOH

    QBTTJWF  ‣ *GSFTVMUXSPOH NJOJNBMMZVQEBUFXFJHIUTUPDMBTTJGZDPSSFDUMZ BHHSFTTJWF  correctly classify
  7. 1"JMMVTUSBUFE 4 Figure from http://kazoo04.hatenablog.com/entry/2012/12/20/000000

  8. 1"JMMVTUSBUFE 4 Figure from http://kazoo04.hatenablog.com/entry/2012/12/20/000000 Do nothing.

  9. 1"JMMVTUSBUFE 4 Figure from http://kazoo04.hatenablog.com/entry/2012/12/20/000000 Minimally update to correctly classify.

    Do nothing.
  10. &YUFOTJPOT1"*1"** ‣ 0SJHJOBM1"UPPlBHHSFTTJWFzJOTPNFTJUVBUJPOT DPOTUSBJOUBMXBZTDMBTTJGZDPSSFDUMZ  ‣ 8FBLUPMBCFMOPJTF ‎ HFOUMFSVQEBUFTUSBUFHJFT TPGUNBSHJO

     5 PA-I PA-II
  11. &YUFOTJPOT1"*1"** ‣ 0SJHJOBM1"UPPlBHHSFTTJWFzJOTPNFTJUVBUJPOT DPOTUSBJOUBMXBZTDMBTTJGZDPSSFDUMZ  ‣ 8FBLUPMBCFMOPJTF ‎ HFOUMFSVQEBUFTUSBUFHJFT TPGUNBSHJO

     5 PA-I PA-II
  12. &YUFOTJPOT1"*1"** ‣ 0SJHJOBM1"UPPlBHHSFTTJWFzJOTPNFTJUVBUJPOT DPOTUSBJOUBMXBZTDMBTTJGZDPSSFDUMZ  ‣ 8FBLUPMBCFMOPJTF ‎ HFOUMFSVQEBUFTUSBUFHJFT TPGUNBSHJO

     5 PA-I PA-II
  13. 1"QTFVEPDPEF 6 Algorithm from [Crammer+ 2006] “Online Passive-Aggressive Algorithms”

  14. $8$POpEFODF8FJHIUFEBMHPSJUIN<%SFE[F > ‣ *EFBXFJHIUTGPSGSFRVFOUGFBUVSFTNPSFlDPOpEFOUzUIBOSBSFPOFT ‎ $POTJEFS(BVTTJBOEJTUSJCVUJPOGPSXFJHIUTVQEBUFNFBOWBSJBODF 7 Figure from http://kazoo04.hatenablog.com/entry/2012/12/20/000000

    Previous: CW:
  15. $8$POpEFODF8FJHIUFEBMHPSJUIN<%SFE[F > ‣ *EFBXFJHIUTGPSGSFRVFOUGFBUVSFTNPSFlDPOpEFOUzUIBOSBSFPOFT ‎ $POTJEFS(BVTTJBOEJTUSJCVUJPOGPSXFJHIUTVQEBUFNFBOWBSJBODF 7 No memory. Figure

    from http://kazoo04.hatenablog.com/entry/2012/12/20/000000 Previous: CW:
  16. $8$POpEFODF8FJHIUFEBMHPSJUIN<%SFE[F > ‣ *EFBXFJHIUTGPSGSFRVFOUGFBUVSFTNPSFlDPOpEFOUzUIBOSBSFPOFT ‎ $POTJEFS(BVTTJBOEJTUSJCVUJPOGPSXFJHIUTVQEBUFNFBOWBSJBODF 7 No memory. Figure

    from http://kazoo04.hatenablog.com/entry/2012/12/20/000000 Previous: CW:
  17. $8$POpEFODF8FJHIUFEBMHPSJUIN<%SFE[F > ‣ *EFBXFJHIUTGPSGSFRVFOUGFBUVSFTNPSFlDPOpEFOUzUIBOSBSFPOFT ‎ $POTJEFS(BVTTJBOEJTUSJCVUJPOGPSXFJHIUTVQEBUFNFBOWBSJBODF 7 No memory. Figure

    from http://kazoo04.hatenablog.com/entry/2012/12/20/000000 Previous: CW: More “confident”.
  18. *OTJEF$8 ‣ *OTUFBEPGXFJHIUX VTFЖ NFBOWFDUPS BOEЄ DPWBSJBODFNBUSJY  8 It

    has closed form solution (c.f. [Dredze+ 2008]). Often use diag only instead of Σ" to make it simpler (not much performance change).
  19. *OTJEF$8 ‣ *OTUFBEPGXFJHIUX VTFЖ NFBOWFDUPS BOEЄ DPWBSJBODFNBUSJY  8 Minimally

    update It has closed form solution (c.f. [Dredze+ 2008]). Often use diag only instead of Σ" to make it simpler (not much performance change).
  20. *OTJEF$8 ‣ *OTUFBEPGXFJHIUX VTFЖ NFBOWFDUPS BOEЄ DPWBSJBODFNBUSJY  8 Minimally

    update Correctly classify with 
 prob >= η It has closed form solution (c.f. [Dredze+ 2008]). Often use diag only instead of Σ" to make it simpler (not much performance change).
  21. $81TFVEPDPEF 9

  22. 8IBU`TXSPOHXJUI$8 ‣ 6QEBUFJTUPPlBHHSFTTJWFz ‣ "MXBZTDMBTTJGZXJUIQSPCБ ‎ 8FBLUPMBCFMOPJTF FBTJMZPWFSpU ‣ $8BTTVNFTMJOFBSMZTFQBSBCMFEBUB

    ‣ %J⒏DVMUUPTPGUFODPOTUSBJOUGSPNJUTPSJHJOBMGPSN 10
  23. "308"EBQUJWF3FHVMBSJ[BUJPOPG8FJHIU7FDUPST<$SBNNFS > ‣ -BSHFNBSHJOUSBJOJOH ‣ $POpEFODFXFJHIUJOH ‣ )BOEMJOHOPOTFQBSBCMFEBUB 11

  24. *OTJEF"308 12 Values of hyper-parameter λ’s not so important (e.g.

    0.1). It has closed form solution (c.f. [Crammer+ 2009]).
  25. *OTJEF"308 12 Minimally update Values of hyper-parameter λ’s not so

    important (e.g. 0.1). It has closed form solution (c.f. [Crammer+ 2009]).
  26. *OTJEF"308 12 Minimally update Minimize loss Values of hyper-parameter λ’s

    not so important (e.g. 0.1). It has closed form solution (c.f. [Crammer+ 2009]).
  27. *OTJEF"308 12 Minimally update Minimize loss More data, 
 more

    confident Values of hyper-parameter λ’s not so important (e.g. 0.1). It has closed form solution (c.f. [Crammer+ 2009]).
  28. "3081TFVEPDPEF 13

  29. 4$84PGU$POpEFODF8FJHIUFEMFBSOJOH<8BOH > ‣ -BSHFNBSHJOUSBJOJOH ‣ $POpEFODFXFJHIUJOH ‣ )BOEMJOHOPOTFQBSBCMFEBUB ‣ "EBQUJWFNBSHJO

    14 Can see it as PA-I/PA-II equivalent of CW.
  30. *OTJEF4$8 15 They have closed form solutions (c.f. [Wang+ 2012]).

    Formulas from d.hatena.ne.jp/kisa12012/20120625/
  31. *OTJEF4$8 15 They have closed form solutions (c.f. [Wang+ 2012]).

    Formulas from d.hatena.ne.jp/kisa12012/20120625/
  32. 4$81TFVEPDPEF 16

  33. 0OMJOFBMHPSJUINTDPNQBSFE 17 Table from [Wang+ 2012] “Exact Soft Confidence-Weighted Learning”

  34. &WBMVBUJPO 18 ‣ .BSHJOCBTFEVTVBMMZPVUQFSGPSNTOPONBSHJOCBTFE ‎ -BSHFNBSHJO ‣ 4FDPOEPSEFSVTVBMMZPVUQFSGPSNTpSTUPSEFS ‎ $POpEFODFXFJHIUJOH

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  35. 4VNNBSZ ‣ $8DPOTJEFSDPOpEFODFPGXFJHIUT5PPBHHSFTTJWF XFBLUPOPJTF ‣ "308 4$8TPGUFOUIFDPOTUSBJOUPG$8 ‣ "3084$8DPNQBSBCMFQFSGPSNBODF ‣

    4$8JGZPVEPO`UNJOEpOEJOHPQUJNBMIZQFSQBSBNFUFSTʜ  ‣ "308PUIFSXJTFʜ 19 … but it all depends on the data sets!
  36. References

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