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BM bmT2`K`F2iǶ 2tKTH2- Bi }M/b i?2 b2i Q7 Bi2Kb r?B+? `2 7`2[m2MiHv Tmi BMiQ i?2 bK2 #bF2i M/ #Qm;?i iQ;2i?2`X JQ`2Qp2`- r2 +QmH/ b2i bmTTQ`i i?`2b?QH/ iQ bT2+B7v ?Qr 7`2[m2Mi Bb 7`2[m2Mi 2MQm;? 7Q` i?2 Bi2Kb2ib iQ #2 b2H2+i2/X
TTHvBM; i?2 b?QTTBM; MHQ;v iQ Qm` b+2M`BQ- mb2` B/ Q7 2+? TQbi Bb M ǵBi2KǶ- M/ 2p2`v jy TQbib BM i?`2/ 7Q`Kb ǵ#bF2iǶ- bQ 2+? 7`2[m2Mi Bi2Kb2i rQmH/ #2 ;`QmT mb2`b i?i 7`2[m2MiHv ǵTT2`2/ iQ;2i?2`Ƕ BM i?`2/bX AM Qm` 2tT2`BK2Mib- 7`2[m2Mi Bi2Kb2i KBMBM; Bb +QM/m+i2/ QM HH i?`2/b BM
#Qi? i`BMBM; b2i M/ i2bi b2i- rBi? i?2 ?2HT Q7 i?2 P`M;2 U.2KȒ` 2i HX-kyRjV HB#``v- M/ /Q2bMǶi BMpQHp2 i?2 mb2 Q7 ;`QmM/ i`mi?X
_i?2` i?M #2BM; bQK2?Qr BM+Q`TQ`i2/ b 72im`2 BM Qm` KQ/2H- i?2 KBM2/
7`2[m2Mi Bi2Kb2ib `2 mb2/ iQ 7m2H bKQQi?BM; T`Q+2bb QM i?2 T`2/B+iBQM QmiTmib Q7 i?2 #b2 KQ/2HkdX AM i?Bb bKQQi?BM; T`Q+2bb- 7Q` 2+? j@2H2K2Mi 7`2[m2Mi Bi2Kb2ik3- r2 // mT i?2 bTKB+BivkNQ7 i?2 mb2`b BM BiX A7 i?2 bmK Bb
#B;;2` i?M i?`2b?QH/- i?2M r2 T`2/B+i HH mb2`b BM i?Bb j@2H2K2Mi Bi2Kb2i iQ #2 bTKK2`bX h?2 Tb2m/Q+Q/2 Q7 i?2 r?QH2 T`Q+2/m`2 Bb BM H;Q`Bi?K 8XdX qBi? i?2 /2b+`B#2/ bKQQi?BM; T`Q+2bb- i?2 6@K2bm`2 `2+?2b e9XeyW- r?B+?
/Q2bMǶi HQQF #/ i HH +QMbB/2`BM; i?2 `iBQ Q7 bTKK2`b BM i2bi b2i Bb QMHv yXN3WX
kdh?2 +m``2Mi KQ/2H 7Q` bTKK2` /2i2+iBQM r2Ƕ`2 BKT`QpBM; mTQMX Aib T2`7Q`KM+2 rb b?QrM BM i#H2 jk
k3A7 i?2`2 `2 #B;;2` 7`2[m2Mi Bi2Kb2ib- r2 bBKTHv iF2 HH j@2H2K2Mi bm#b2ib Q7 i?2KX
kNT`Q##BHBbiB+ T`2/B+iBQM QmiTmi #v Qm` #b2 KQ/2H B7 i?2 mb2` Bb BM i2bi b2i- Q` Dmbi y Q` R ++Q`/BM; iQ i?2 ;`QmM/ i`mi? B7 i?2 mb2` Bb BM i`BMBM; b2i
89
H;Q`Bi?K k h?2 r?QH2 T`Q+2bb +QK#BM2/ rBi? i?2 bKQQi?BM; bi2T
R 7mM+iBQM 6BMHJQ/2HUusersntrain, labelsntrain, usersntest, postsV
k f eaturesntrain← 1ti`+i62im`2bUusersntrainV
j f eaturesntest ← 1ti`+i62im`2bUusersntestV
9 model ← JGT`Q+2/m`2Ufeaturesntrain, labelsntrainV
8 preds, probs← JF2S`2/B+iBQMbUmodel, featuresntestV
e f reqngroups ← 6BM/6`2[m2Mi:`QmTbUpostsV HH TQbib
d preds← aKQQi?S`2/b6`2[:`TbUpreds, probs, freqngroupsV
3 `2im`M preds
N 7mM+iBQM 6BM/6`2[m2Mi:`QmTbUpostsV
Ry threads← BM/2t i?2 posts rBi? i?2B` i?`2/ B/b
RR baskets ← 2KTiv HBbi BMBiBHBx2 i?2 HBbi Q7 ǵ#bF2ibǶ Q` Bi2Kb2ib
Rk 7Q` t← threads /Q
Rj 7Q` β ← 2+? jy +QMb2+miBp2 TQbi2`bǶ B/b BM i?`2/ t /Q
R9 TT2M/ β iQ baskets
R8 f reqngroups ← 6`2[m2MiAi2Kb2iJBMBM;UbasketsV ǵP`M;2Ƕ
Re `2KQp2 i?2 ;`QmTb rBi? support <3 7`QK freqngroups
Rd `2im`M f reqngroups
R3 7mM+iBQM aKQQi?S`2/b6`2[:`TbUpreds, probs, f reqngroupsV
RN 7Q` f reqngroup← freqngroups /Q
ky 7Q` f reqntriple← 2+? j@Bi2K bm#b2i Q7 freqngroup /Q
kR sum ← 0 BMBiBHBx2 i?2 ǵbTKB+BivǶ Q7 i?2 i`BTH2
kk 7Q` uid ← freqntriple /Q
kj B7 uid∈ usersntrain i?2M
k9 sum ← sum + labelsntrain[uid] 1 B7 bTKK2`
k8 2Hb2
ke sum ← sum + probs[uid] T`Q##HBiv Q7 bTKK2`
kd B7 sum > 1.2 i?2M ǵbTKB+BivǶ ?B;?2` i?M i?`2b?QH/
k3 7Q` uid ← freqntriple /Q
kN preds[uid] ← 1 T`2/B+i HH j b bTKK2`b
jy `2im`M preds
88
T`2+BbBQM `2+HH 6@K2bm`2
edX8jW eRXNyW e9XeyW
h#H2 jj, T`Q}H2b- KtnbTKB+Bivn7Tb- #m`biBM2bbni?`Qrrvn`2;-rBi? i?2 bKQQi?BM; T`Q+2bb
;BM- i?2 7+i i?i Qm` #2bi KQ/2H 7Q` bTK /2i2+iBQM 7Q` }`bi TQbib ?TT2Mb iQ ?p2 ?B;?2` T`2+BbBQM i?M `2+HH ?2HTbX Ai bQK2?Qr +mb2b i?2 #b2 KQ/2H i`BM2/ rBi? KtnbTKB+Bivn7Tb 72im`2 iQ ?p2 ?B;?2` T`2+BbBQM b r2HHX aBM+2 i?Bb bKQQi?BM; T`Q+2bb BMimBiBp2Hv ;2`b iQr`/ BKT`QpBM; i?2 `2+HH-i?2 HQr2` `2+HH Q7 `2+HH-i?2 #b2 KQ/2H H2p2b #B; `QQK 7Q` i?Bb T`Q+2bb iQ #QQbi i?2 T2`7Q`KM+2X
8Xd *p2i
AM b2+iBQM 8XeX9- i?2 #m`biBM2bb 72im`2 +?2+F2/ UbQ`i Q7V B7 i?2 ++QmMi rb
`2;Bbi2`2/ /m`BM; i?2 bK2 T2`BQ/ b bQK2 i?`Qrrv bTKK2` ++QmMib BM i?2 i`BMBM; b2iX h?2 mb27mHM2bb Q7 bm+? 72im`2 /2T2M/b QM i?2 7+i i?i Qm`
i2bi b2i Bb i2KTQ`HHv +QMiB;mQmb rBi? i`BMBM; b2iX PM i?2 +QMi``v- B7 i?2 i`BMBM; b2i M/ i2bi b2i r2`2 +QHH2+i2/ 7`QK kyRy M/ kyRk- `2bT2+iBp2Hv-i?2 QM2 v2` ;T Kv KF2 bm+? 72im`2 H2bb mb27mH- #2+mb2 `2bT2+iBp2Hv-i?2`2 Bb bHBK@
K2` +?M+2 i?2`2 Bb i?`Qrrv bTKK2` ++QmMib BM i2bi b2i r?B+? rb
`2;Bbi2`2/ BM i?2 bK2 #i+? b i?2 QM2b BM i`BMBM; b2iX
AM b2+iBQM 8XeX8- r?2M M ++QmMi BM KBM2/ 7`2[m2Mi Bi2Kb2i Bb BM i?2 i`BMBM;
b2i- i?2 H;Q`Bi?K /B`2+iHv HQQF mT i?2 ;`QmM/ i`mi? 7Q` Bib bTKB+Biv UHBM2 k9 BM H;Q`Bi?K VX ;BM- i?2 T`Q+2bb `2HB2b QM i?2 7+i i?2 ++QmMib BM i`BMBM;
b2i M/ i2bi b2i +QmH/ #2 BM i?2 bK2 ;`QmT i?i 7`2[m2MiHv TT2`2/ iQ;2i?2`X h?2 i?BM; Bb i?Bb r?QH2 /ib2i Bb p2`v iB;?iHv +QmTH2/ iQ;2i?2`- r?B+?
KF2b bQK2 mM/2bB`#H2 BMi2`T`2iiBQMb TQbbB#H2 QM Qm` 2tT2`BK2MiiBQM `2@
bmHibX 6Q` K+?BM2 H2`MBM; Tm`TQb2- r2 bTHBi i?2 /i KBMHv ++Q`/BM;
iQ i?2 i2KTQ`H Q`/2` b /2b+`B#2/ BM b2+iBQM 8Xk- #mi i?2`2 Hrvb b22Kb iQ #2 bQK2 bQ`i Q7 B``2H2pMi +QMM2+iBQM #2ir22M i`BMBM; b2i M/ i2bi b2i i?i +QmH/ ii`B#mi2 i?2 2pHmiBQM `2bmHi iQX 6Q` 2tKTH2- BM bTK /2i2+@
iBQM- bQK2 TQbib BM i`BMBM; M/ i2bi b2i +QmH/ b?`2 i?2 bK2 mi?Q`- bQ r2 +`2i2/ i2bi b2i iQ 2`/B+i2 M Hi2`MiBp2 i?2Q`v i?i Qm` KQ/2H Bb +Tim`BM; bQK2 mb2`@bT2+B}+ #mi MQM@bTK `2Hi2/ #2?pBQ`b- b /Bb+mbb2/
BM b2+iBQM 8XkXRX 1p2M i?2M- /Bz2`2Mi ++QmMib KB;?i biBHH #2 b?`2/ #v i?2 bK2 +imH TQbi2`bX AiǶb p2`v /B{+mHi- B7 MQi BKTQbbB#H2- iQ +QKTH2i2Hv 2t@
+Hm/2 HH FBM/ Q7 B``2H2pMi +QMM2+iBQMb #2ir22M i`BMBM; b2i M/ i2bi b2i- M/
8e
RyyW ii`B#mi2 i?2 T2`7Q`KM+2 Q7 i?2 KQ/2H iQ Bi bm++2bb7mHHv +Tim`BM; i?2 2bb2MiBH Tii2`M Q7 i?Bb +Qp2`i K`F2iBM; +KTB;M UQ` QTBMBQM bTKKBM;
+iBpBiB2bVX
h?2 i2KTQ`H +QMiB;mQmbM2bb K2MiBQM2/ BM i?2 }`bi irQ T`;`T?b BM i?Bb b2+iBQM Bb MQi?2` KMB72biiBQM Q7 iB;?iHv +QmTH2/ Mim`2 Q7 i?2 /ib2iX AMbi2/ Q7 i`vBM; iQ 2t+Hm/2 bm+? 7+iQ`- r?B+? KB;?i #2 BKTQbbB#H2 iQ /Q- r2 H2p2`;2 Bi iQ ?2HT i?2 /2i2+iBQM Q7 bTKK2`bX q2 Dmbi M22/ iQ #2 r`2 Q7 i?2 7+i i?i 7Q` Qm` `2bmHib iQ #2 K2MBM;7mH- i?2 i2KTQ`H +QMiB;mQmbM2bb
bbmKTiBQM #2ir22M i?2 i`BMBM; b2i M/ i?2 i2bi b2i ?b iQ #2 i?2`2X
e 6mim`2 qQ`F
/KBii2/Hv- KQbi Q7 i?2 i2+?MB[m2b r2 /QTi BM bTK M/ bTKK2` /2i2+iBQM r2`2 `i?2` #bB+- r?B+? KB;?i H2p2 bQK2 `QQK 7Q` BKT`Qp2K2MiX AM i?Bb b2+iBQM- r2 bT2+B}+HHv TQBMi Qmi bQK2 TQi2MiBHHv 7`mBi7mH /B`2+iBQMb i?i +QmH/ #2 rQ`F2/ QM BM i?2 7mim`2X