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One-Pass AUC Optimization
A Practical Expansion of One-Pass AUC Optimization
Kazuo Kimura
Financial Technology Research Institute Inc.
Gao et al. (2016) One-Pass AUC Optimization2 AUC
AUC
NLMIXED SAS/IML
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Contents
1.
2. One-Pass AUC Optimization
3.
4.
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1.
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Gao et al.(2016)
Z, .
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AUC AR Somers’ D
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0.2
0.4
0.6
0.8
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0 0.2 0.4 0.6 0.8 1
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AUC
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0.6
0.8
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0 0.2 0.4 0.6 0.8 1
AR= ───
AR=2 AUC 1
0 66 0 10 80 8
AUC
1 0
8
AR
ARsAR
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2011
Double Summation
• Double Summation
Buffer
•
Buffer
One-Pass AUC Optimization Gao et al., 2016
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2. One-Pass AUC Optimization
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One-Pass AUC Optimization
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•
• Buffer
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Sample 1
Sample 2
Sample N
Parameter Buffer
Parameter Buffer
Parameter Buffer
Parameter Buffer
Model
Model
Model
1 One Pass
Output ←
← →Input
Input
Input
AUC
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0 1
1
L2L2
vs i.i.d.
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gradient
←
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=
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Input
Sample
Model
Buffer
Parameter
Two-Pass / Multi-Pass AUC Optimization
• One-Pass AUC Optimization 1
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• 1 2Two-Pass AUC Optimization
• 2Multi-Pass AUC Optimization
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SAS
• SAS/IMLdata step
• 3 2
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0 1
SAS
/**** ****/%macro a2;%do i = 0 %to &_r;%if &i > 0 %then %do;ELSE /* */%end; /* */IFAY[_T] = &i THEN DO;
/** **/_TS = _TS + AU[_T];/** **/BT&i = BT&i + AU[_T];/** **/AC = BC&i;BC&i = AC + (AX[_T,]-AC)/BT&i *AU[_T];/** **/AS = BS&i;BS&i = AS + t(AC)*AC - t(BC&i )*BC&i+ (t(AX[_T,])*AX[_T,] - AS - t(AC)*AC)/BT&i *AU[_T];
END;%end;%mend a2; %a2;
/****** ******/%macro a3;%do i = 0 %to &_r; /* */IFAY[_T] ^= &i THEN DO; /*← */IF BT&i > 0 THEN DO; /* */
/* *//** **/IF &i < AY[_T] THEN _SGN = 1;ELSEIF &i > AY[_T] THEN _SGN = -1;
/** **/_WW = (BT&i /(_TS - BT&i )) * AU[_T];
/** X **/CX =AX[_T,] - BC&i;
/** **/ /* ↓ */AG =AG + &_lambda * BW * _WW;AG =AG - _SGN * CX * _WW; /*→ */AG =AG + BW * (t(CX)*CX + BS&i ) * _WW;
END;END;%end;%mend a3; %a3;
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3.
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•R&I
AA+ /BB+
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5%[-1,+1]
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•
•6 R&I
2
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•
10
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Somers’ D2007 15
Somers’ D 2007-15
AR .834 .011 .816 .011
.832 .009 .818 .009
OPAUC .818 .007 .807 .009
TPAUC .821 .007 .812 .008
MPAUC U=22 .827 .007 .814 .007
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PROC FREQ DATA=…;TABLE …/MEASURES;OUTPUT SMDRC;
RUN;
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•
•.
OPAUC2007 15 10
AverageSomers’ D
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2015
1 AR
4.
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• Gao et al. (2016) One-Pass AUC Optimization
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• Two / Multi-Pass
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• Adaptive Gradient Method Ding 2015
Adaptive Online AUC Maximization AdaOAMOPAUC
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•31
[1] (2015). Weight of Evidence. 2015SAS , 211-220.
[2] (2016). . 2016SAS , 85-99.
[3] , (2009). . ,
http://www.ffr-plus.jp/material/pdf/100913/kinkoken.pdf 2017 6 21 .[4] , (2011). AR .
.[5] Ding, Y., Zhao, P., Hoi, S.C.H., Ong, Y-S. (2015). An Adaptive Gradient
Method for Online AUC Maximization. The 29th AAAI Conference on Artificial Intelligence.
[6] Gao, W., Wang, L., Jin, R., Zhu, S., and Zhou, Z.-H. (2016). One-Pass AUC Optimization. Artificial Intelligence, 236, 1-29.
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