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

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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

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

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

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

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

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1"JMMVTUSBUFE 4 Figure from http://kazoo04.hatenablog.com/entry/2012/12/20/000000

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

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1"JMMVTUSBUFE 4 Figure from http://kazoo04.hatenablog.com/entry/2012/12/20/000000 Minimally update to correctly classify. Do nothing.

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

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

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

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1"QTFVEPDPEF 6 Algorithm from [Crammer+ 2006] “Online Passive-Aggressive Algorithms”

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

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

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

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

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*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).

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*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).

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*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).

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$81TFVEPDPEF 9

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8IBU`TXSPOHXJUI$8 ‣ 6QEBUFJTUPPlBHHSFTTJWFz ‣ "MXBZTDMBTTJGZXJUIQSPCБ ‎ 8FBLUPMBCFMOPJTF FBTJMZPWFSpU ‣ $8BTTVNFTMJOFBSMZTFQBSBCMFEBUB ‣ %J⒏DVMUUPTPGUFODPOTUSBJOUGSPNJUTPSJHJOBMGPSN 10

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"308"EBQUJWF3FHVMBSJ[BUJPOPG8FJHIU7FDUPST<$SBNNFS> ‣ -BSHFNBSHJOUSBJOJOH ‣ $POpEFODFXFJHIUJOH ‣ )BOEMJOHOPOTFQBSBCMFEBUB 11

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*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]).

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*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]).

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*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]).

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*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]).

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"3081TFVEPDPEF 13

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4$84PGU$POpEFODF8FJHIUFEMFBSOJOH<8BOH> ‣ -BSHFNBSHJOUSBJOJOH ‣ $POpEFODFXFJHIUJOH ‣ )BOEMJOHOPOTFQBSBCMFEBUB ‣ "EBQUJWFNBSHJO 14 Can see it as PA-I/PA-II equivalent of CW.

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

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

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4$81TFVEPDPEF 16

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

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&WBMVBUJPO 18 ‣ .BSHJOCBTFEVTVBMMZPVUQFSGPSNTOPONBSHJOCBTFE ‎ -BSHFNBSHJO ‣ 4FDPOEPSEFSVTVBMMZPVUQFSGPSNTpSTUPSEFS ‎ $POpEFODFXFJHIUJOH ‣ $8PVUQFSGPSNTpSTUPSEFS CVUOPUXJUISFBMXPSME OPJTZ EBUB ‎ )BOEMJOHOPOTFQBSBCMFEBUB ‣ "308PVUQFSGPSNT$8XJUINBOZSFBMXPSMEEBUB CVUNPSFVQEBUFT ‎ "EBQUJWFNBSHJO Experiments on [Wang+ 2012]: various classification tasks.

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4VNNBSZ ‣ $8DPOTJEFSDPOpEFODFPGXFJHIUT5PPBHHSFTTJWF XFBLUPOPJTF ‣ "308 4$8TPGUFOUIFDPOTUSBJOUPG$8 ‣ "3084$8DPNQBSBCMFQFSGPSNBODF ‣ 4$8JGZPVEPO`UNJOEpOEJOHPQUJNBMIZQFSQBSBNFUFSTʜ ‣ "308PUIFSXJTFʜ 19 … but it all depends on the data sets!

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References

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