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,OPXMFEHF5SBDJOH $PSCFUU • "UBTLUPNPEFMIPXUIFTUVEFOU`TBDBEFNJDBCJMJUZ DIBOHFTPWFSUJNF • ,5BJNTUPFTUJNBUFJGIFTIFXJMMBOTXFSUIFOFYU RVFTUJPODPSSFDUMZ q = 13 a = q = 15 a = q = 41 a = ? … q = 13 a = q = 38 a = 4FRVFODF

% %BUBTFU"44*45NFOUTDPSSFDUFE • &BDIRVFTUJPOJTMBCFMFECZBTLJMM ,$ LOPXMFEHF DPODFQU UIBUJTSFRVJSFEUPTPMWFJU • %BUBTFUTDPOUBJOTRVFTUJPOBOTXFSJOHMPHT 4LJMM*% $POUFOU q = 13 a = q = 15 a = q = 41 a = … q = 13 a = q = 38 a = $POUFOUGSPN "44*45NFOUTDPSSFDUFE %BUBTFU 4FRVFODF 4FRVFODF 4FRVFODF

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 JG BOE PUIFSXJTF sq k = ((q, a1), (q, a2), …, (q, aT)) at = 1 t > T − k at = 0

*OWFSUFEQSFEJDUJPOQSPCMFN • 8FJOWFTUJHBUFEUSBJOFE%,5NPEFMTXJUIEVNNZEBUBTFRVFODF 
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.FUIPET

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2VBOUJ fi DBUJPOPGUIFJOWFSUFEQSFEJDUJPOQSPCMFN • &YQSFTTEFHSFF r2 = 1 Q ∑ rq 2 = 1 Q ∑Q q=1 NDCG ( ̂ y (sq 0 , q), …, ̂ y (sq T , q), (0,…, T)) rq=KC98 2 = 0.51 rq=KC83 2 = 0.74 rq=KC30 2 = 0.83 1SFEJDUFE1FSGPSNBODF 0.0 s0 s20 s10 s0 s20 s10 s0 s20 s10 0.5 1.0 0.0 0.5 1.0 0.0 0.5 1.0 1SFEJDUJPODVSWF B q = KC30 1SFEJDUJPODVSWF C q = KC83 1SFEJDUJPODVSWF D q = KC98

1SFUSBJOJOHSFHVMBSJ[BUJPO • "MMXSPOHBOEBMMDPSSFDUTZOUIFUJDEBUBGPSFBDITLJMMT • 1SJPSLOPXMFEHFUIBU X′  wro = {(qi ,0), …, (qi ,0)}, y′  wro = (qi ,0) X′  cor = {(qi ,1), …, (qi ,1)}, y′  cor = (qi ,1) qi a = qi a = qi a = qi a = qi a = qi a = qi a = qi a = … …

1SFUSBJOJOHSFHVMBSJ[BUJPO qi a = qi a = qi a = qi a = qi a = qi a = qi a = qi a = q1 a = q1 a = q2 a = q2 a = qt a = qt+1 a = qt+1 a = qt a = 4ZOUIFUJDEBUB 3FBMEBUB … … … … 1SFUSBJOJOH 5SBJOJOH

3FTVMUT

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