CW, AROW, and SCW

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

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

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

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

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

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

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

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

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

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

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

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

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

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

*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).

*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).

*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).

$81TFVEPDPEF 9

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

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

*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]).

*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]).

*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]).

*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]).

"3081TFVEPDPEF 13

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14 Can see it as PA-I/PA-II equivalent of CW.

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

4$81TFVEPDPEF 16

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

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

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

References

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CW, AROW, and SCW

CW, AROW, and SCW

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