1:- module(auc,[compute_areas/5,compute_areas_diagrams/5, compute_maxacc/2]).
The predicate returns
30compute_areas(LG,AUCROC,ROC,AUCPR,PR):-
31 must_be(list, LG),
32 must_be(var, AUCROC),
33 must_be(var, ROC),
34 must_be(var, AUCPR),
35 must_be(var, PR),
36 findall(E,member(_- \+(E),LG),Neg),
37 length(LG,NEx),
38 length(Neg,NNeg),
39 NPos is NEx-NNeg,
40 keysort(LG,LG1),
41 reverse(LG1,LG2),
42 catch(compute_pointsroc(LG2,+1e20,0,0,NPos,NNeg,[],ROC),
43 error(evaluation_error(zero_divisor),_),
44 ROC = []
45 ),
46 hull(ROC,0,0,0,AUCROC),
47 compute_aucpr(LG2,NPos,NNeg,AUCPR,PR).The predicate returns
*/
69compute_areas_diagrams(LG,AUCROC,ROC,AUCPR,PR):-
70 must_be(list, LG),
71 must_be(var, AUCROC),
72 must_be(var, ROC),
73 must_be(var, AUCPR),
74 must_be(var, PR),
75 compute_areas(LG,AUCROC,ROC0,AUCPR,PR0),
76 % write(ROC0),nl,write(PR0),nl,
77 ROC = c3{data:_{x:x, rows:[x-'ROC'|ROC0]},
78 axis:_{x:_{min:0.0,max:1.0,padding:0.0,
79 tick:_{values:[0.0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0]}},
80 y:_{min:0.0,max:1.0,padding:_{bottom:0.0,top:0.0},
81 tick:_{values:[0.0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0]}}}},
82 PR = c3{data:_{x:x, rows:[x-'PR'|PR0]},
83 axis:_{x:_{min:0.0,max:1.0,padding:0.0,
84 tick:_{values:[0.0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0]}},
85 y:_{min:0.0,max:1.0,padding:_{bottom:0.0,top:0.0},
86 tick:_{values:[0.0,0.1,0.2,0.3,0.4,0.5,0.6,0.7,0.8,0.9,1.0]}}}}.The predicate returns
*/
104compute_maxacc(LG, MaxAcc) :-
105 must_be(list, LG),
106 must_be(var, MaxAcc),
107 findall(E,member(_- \+(E),LG),Neg), %find all the pairs that contain a negative examples
108 length(LG,NEx),
109 length(Neg,NNeg),
110 NPos is NEx-NNeg,
111 keysort(LG,LG1), % ascending order of the pairs on probabilities
112 reverse(LG1,LG2), % discending order of the pairs on probabilities
113 compute_acc_list(LG2, 0, 0, NPos, NNeg, [], AccList),
114 max_list(AccList, MaxAcc).135compute_acc_list([], TP, FP, FN, TN, AccList0, AccList) :- 136 Acc is (TP+TN)/(TP+TN+FP+FN), 137 append(AccList0, [Acc], AccList). 138 139compute_acc_list([_P- (\+ _)|T], TP, FP, FN, TN, AccList0, AccList):-!, 140 Acc is (TP+TN)/(TP+TN+FP+FN), 141 append(AccList0, [Acc], AccListNew),% append the new accuracy (it creates a new list called AccListNew) 142 FP1 is FP+1, 143 TN1 is TN-1, 144 compute_acc_list(T, TP, FP1, FN, TN1, AccListNew, AccList). 145 146compute_acc_list([_P- _|T], TP, FP, FN, TN, AccList0, AccList):-!, 147 Acc is (TP+TN)/(TP+TN+FP+FN), 148 append(AccList0, [Acc], AccListNew), 149 TP1 is TP+1, 150 FN1 is FN-1, 151 compute_acc_list(T, TP1, FP, FN1, TN, AccListNew, AccList). 152 153 154 155 156compute_pointsroc([],_P0,_TP,_FP,_FN,_TN,P0,P1):-!, 157 append(P0,[1.0-1.0],P1). 158 159compute_pointsroc([P- (\+ _)|T],P0,TP,FP,FN,TN,Po0,Po1):-!, 160 (P<P0-> 161 FPR is FP/(FP+TN), 162 TPR is TP/(TP+FN), 163 append(Po0,[(FPR-TPR)],Po2), 164 P1=P 165 ; 166 Po2=Po0, 167 P1=P0 168 ), 169 FP1 is FP+1, 170 TN1 is TN-1, 171 compute_pointsroc(T,P1,TP,FP1,FN,TN1,Po2,Po1). 172 173compute_pointsroc([P- _|T],P0,TP,FP,FN,TN,Po0,Po1):-!, 174 (P<P0-> 175 FPR is FP/(FP+TN), 176 TPR is TP/(TP+FN), 177 append(Po0,[FPR-TPR],Po2), 178 P1=P 179 ; 180 Po2=Po0, 181 P1=P0 182 ), 183 TP1 is TP+1, 184 FN1 is FN-1, 185 compute_pointsroc(T,P1,TP1,FP,FN1,TN,Po2,Po1). 186 187 188hull([],FPR,TPR,AUC0,AUC1):- 189 AUC1 is AUC0+(1-FPR)*(1+TPR)/2. 190 191 192hull([FPR1-TPR1|T],FPR,TPR,AUC0,AUC1):- 193 AUC2 is AUC0+(FPR1-FPR)*(TPR1+TPR)/2, 194 hull(T,FPR1,TPR1,AUC2,AUC1). 195 196compute_aucpr(L,Pos,Neg,A,PR):- 197 L=[P_0-E|TL], 198 (E= (\+ _ )-> 199 FP=1, 200 TP=0, 201 FN=Pos, 202 TN is Neg -1 203 ; 204 FP=0, 205 TP=1, 206 FN is Pos -1, 207 TN=Neg 208 ), 209 compute_curve_points(TL,P_0,TP,FP,FN,TN,Points), 210 Points=[R0-P0|_TPoints], 211 (R0=:=0,P0=:=0-> 212 Flag=true 213 ; 214 Flag=false 215 ), 216 area(Points,Flag,Pos,0,0,0,A,[],PR). 217 218compute_curve_points([],_P0,TP,FP,_FN,_TN,[1.0-Prec]):-!, 219 Prec is TP/(TP+FP). 220 221compute_curve_points([P- (\+ _)|T],P0,TP,FP,FN,TN,Pr):-!, 222 (P<P0-> 223 Prec is TP/(TP+FP), 224 Rec is TP/(TP+FN), 225 Pr=[Rec-Prec|Pr1], 226 P1=P 227 ; 228 Pr=Pr1, 229 P1=P0 230 ), 231 FP1 is FP+1, 232 TN1 is TN-1, 233 compute_curve_points(T,P1,TP,FP1,FN,TN1,Pr1). 234 235compute_curve_points([P- _|T],P0,TP,FP,FN,TN,Pr):-!, 236 (P<P0-> 237 Prec is TP/(TP+FP), 238 Rec is TP/(TP+FN), 239 Pr=[Rec-Prec|Pr1], 240 P1=P 241 ; 242 Pr=Pr1, 243 P1=P0 244 ), 245 TP1 is TP+1, 246 FN1 is FN-1, 247 compute_curve_points(T,P1,TP1,FP,FN1,TN,Pr1). 248 249area([],_Flag,_Pos,_TPA,_FPA,A,A,PR,PR). 250 251area([R0-P0|T],Flag,Pos,TPA,FPA,A0,A,PR0,PR):- 252 TPB is R0*Pos, 253 (TPB=:=0-> 254 A1=A0, 255 FPB=0, 256 PR2=PR0, 257 PR=[R0-P0|PR3] 258 ; 259 R_1 is TPA/Pos, 260 (TPA=:=0-> 261 (Flag=false-> 262 P_1=P0, 263 PR=[0.0-P0|PR3] 264 ; 265 P_1=0.0, 266 PR=[0.0-0.0|PR3] 267 ) 268 ; 269 P_1 is TPA/(TPA+FPA), 270 PR=PR3 271 ), 272 FPB is TPB*(1-P0)/P0, 273 N is TPB-TPA+0.5, 274 (N<1.0-> 275 append(PR0,[R0-P0],PR2), 276 A1=A0 277 ; 278 interpolate(1,N,Pos,R_1,P_1,TPA,FPA,TPB,FPB,A0,A1,[],PR1), 279 append(PR0,PR1,PR2) 280 ) 281 ), 282 area(T,Flag,Pos,TPB,FPB,A1,A,PR2,PR3). 283 284interpolate(I,N,_Pos,_R0,_P0,_TPA,_FPA,_TPB,_FPB,A,A,PR,PR):-I>N,!. 285 286interpolate(I,N,Pos,R0,P0,TPA,FPA,TPB,FPB,A0,A,PR0,[R-P|PR]):- 287 R is (TPA+I)/Pos, 288 P is (TPA+I)/(TPA+I+FPA+(FPB-FPA)/(TPB-TPA)*I), 289 A1 is A0+(R-R0)*(P+P0)/2, 290 I1 is I+1, 291 interpolate(I1,N,Pos,R,P,TPA,FPA,TPB,FPB,A1,A,PR0,PR)
auc
This module computes the Area Under the Receiving Operating Characteristics and Precision Recall curves using the method of Davis, Jesse, and Mark Goadrich. "The relationship between Precision-Recall and ROC curves." Proceedings of the 23rd international conference on Machine learning. ACM, 2006.