A Regression-Based Approach for Scaling-Up Personalized Recommender Systems in E-Commerce

Transcription

1 A Regresson-Bsed Approch for Sclng-Up Personlzed Recommender Systems n E-Commerce Slobodn Vucetc 1 nd Zorn Obrdovc 1, svucetc@eecs.wsu.edu, zorn@cs.temple.edu 1 Electrcl Engneerng nd Computer Scence, Wshngton Stte Unversty, Pullmn, WA Center for Informton Scence nd Technology, Temple Unversty, Phldelph, PA 191, USA ABSTRACT Automted collbortve flterng s one of the key technques for provdng customzton for E- commerce stes. Vrous neghbor-bsed recommendton methods re populr choces for collbortve flterng. However, ther ltency cn be serous drwbck for sclng up to lrge number of requests tht should be processed n rel-tme. In ths pper we propose n lterntve regresson-bsed pproch tht serches for reltonshps mong tems nsted of lookng for smlrtes mong users. Experments on move dtbse provde evdence tht the proposed regresson-bsed pproch provdes sgnfcntly better ccurcy nd s two orders of mgntude fster thn the neghbor-bsed lterntves. Even fster tme response wth ccurcy smlr to neghbor-bsed recommendtons ws obtned by djustng the generc recommendtons wth only the verge preference of n ctve user. 1. INTRODUCTION In tody s socety there s n ncresng need for utomted systems provdng personlzed recommendtons to user fced wth lrge number of choces. For exmple, n ncresng choce of vlble products s cused by compnes shftng towrds developng customzed products tht meet specfc needs of dfferent groups of customers [11]. The products customzton trend coupled wth E-commerce where customers were not provded wth n opton to exmne the products off-shelf n trdtonl sense, mke the problem of provdng ccurte personlzed recommendtons very mportnt. Incresng the qulty of personlzed recommendtons would ncrese customer stsfcton nd loylty, t the sme tme reducng the costs cused by product return. Another exmple where personlzed recommendtons re extremely useful s n nformton overlod stuton wth n mount of dt vlble through Internet nd other med lrgely exceedng the blty of person even gettng glnce of t. Here, utomted methods re needed to provde lrge number of users wth the blty to effcently locte nd retreve nformton ccordng to ther preferences. Personlzed recommender systems cn be clssfed nto two mn ctegores: content-bsed nd collbortve flterng. In content-bsed flterng, mostly used for retrevng relevnt textul documents [6, 1], serch s performed for tems wth content most smlr to users nterests. The tsk of collbortve flterng s to predct preferences of n ctve user gven dtbse of preferences of other users, where the preferences re typclly expressed s numercl evluton scores. Scores cn be obtned explctly by recordng votes from ech user on subset of vlble tems, or mplctly, nferrng from user behvor or rectons regrdng gven set of tems. Memory-bsed collbortve flterng lgorthms mntn dtbse of prevous users preferences nd perform certn clcultons on dtbse ech tme new predcton s needed [3]. The most common representtves re neghbor-bsed lgorthms where subset of users most smlr to n ctve user s chosen nd weghted verge of ther scores s used to estmte preferences of n ctve user on other tems [5, 13]. In contrst, model-bsed lgorthms frst develop descrpton model from dtbse nd use t to mke predctons for n ctve user. Publshed systems of ths type nclude Byesn clusterng, Byesn networks [3] nd clssfcton-bsed lgorthms [, 9]. Neghbor-bsed collbortve flterng lgorthms re known to be superor to model-bsed n terms of ccurcy [3]. However, ther hgh ltency n gvng predctons for ctve users cn be serous drwbck n systems wth lrge number of requests tht should be processed n rel-tme. Also, prevous results [4] show tht s the number of tems evluted by n ctve user decreses, the predcton ccurcy of neghborhoodbsed lgorthms deterortes drmtclly (demndng n extensve user s effort for successful proflng cn

2 be dscourgng from usng the recommender system). Fnlly, t s unlkely tht two users hve exctly the sme tste over ll possble tems whle t s more probble tht the smlrty s lrger over certn subsets of tems (e.g., two users of move recommendton system cn shre the opnons n drms whle dsgreeng n scence fcton). In ths pper we propose regresson-bsed pproch to collbortve flterng tht serches for smlrtes between tems, bulds collecton of experts n the form of smple lner models, nd combnes them to provde preference predctons for n ctve user. For exmple, n move recommendton system, f lrge postve correlton n votes for moves 1 Monkeys nd Seven s dentfed n the dtbse, hgh evluton score for the move 1 Monkeys by n ctve user mples hgher then verge recommendton for the move Seven. Lner regresson models descrbng reltonshp between prs of moves re used n predcton s locl experts nd they re ntegrted usng vrous procedures for combnng the experts.. BACKGROUND In ths secton more forml descrpton of recommendton problem s followed by descrpton of severl recommendton lgorthms tht wll be used for comprson wth our pproch. Performnce mesures used to compre dfferent lgorthms re lso ntroduced n ths secton..1. Descrpton of the personlzed recommendton tsk Assumng dtbse of I tems prtlly evluted by U users, we re gven U I mtrx R wth element r u representng n evluton score of tem by user u. In relstc systems the mtrx R s usully very sprse snce users re lkely to vote just for smll subset of vlble tems. By r u*, r *, nd r ** we denote n verge score for ech user, n verge score for ech tem, nd n overll verge score, respectvely. Snce ech user does not vote for ech tem, by I u we denote subset of tems rted by user u. Smlr, U denotes subset of users tht evluted tem. Gven the evluton scores of n ctve user on tems I the recommender system tsk s to estmte scores of user on the remnng tems I/I... Smple nd neghbor-bsed lgorthms We propose three smple recommendton lgorthms estblshng ccurcy lower bounds on more complex recommendton systems. The frst, MEAN, uses the overll verge score r ** s score on predcton of ny user on ny tem. The second, GENERIC, uses the verge scores r * of ech tem s predctons of new user s preferences. The predctons of ADJUSTED_GENERIC for user re obtned s predctons from GENERIC djusted by the dfference r between the verge score of user nd n verge score of n verge user over the sme set of tems, I, defned s r = (r r ). (1) I For neghbor-bsed lgorthms, Person correlton s used to mesure smlrty between user u nd ctve user [4]. Here, (r r )(ru ru ) I Iu w, u = u, () where σ nd σ u re stndrd devtons of scores clculted over I I u. The score of user for tem s predcted s weghted sum of the votes of other users p computed s, w, u (ru ru* ) u U p = r + w. (3) u U, u If two unrelted users hve smll number of co-rted tems, t s probble tht ther Person correlton s hgh. Exstence of such flse neghbors cn sgnfcntly deterorte the ccurcy. Sgnfcnce weghtng [4] s proposed to reduce the weghts f the number of co-rted tems, n, s smller thn some predetermned number N. If ths s the cse, the obtned weght s multpled by n/n. Neghborhood selecton s ntroduced to retn only smll subset of the most smlr users for predcton [4]. Predctng n tem cn be done effectvely by retnng K of the most smlr users from U. The reported benefts re twofold: computtonl tme needed for ech predcton s decresed nd slght mprovements n ccurcy cn be observed. Both modfctons re mplemented n neghborbsed lgorthm used for comprson wth the proposed regresson-bsed lgorthm. We denote the neghbor-bsed lgorthm wth these modfctons s NEIGHBOR(N,K), where N nd K re djustble sgnfcnce nd selecton prmeters of the lgorthm.

3 The bottleneck of neghbor-bsed lgorthms s ther on-lne speed. To perform predcton for new user, Person correltons over U exstng users should be clculted frst usng (), whch scles s O(UI), where I s the totl number of tems. Reducng to the K most smlr users for ech tem to be predcted nd pplyng (3) stll scles s O(UI). Also, whole dtbse R of sze O(UI) should be mntned for the modfed lgorthm. Assumng n ncresng number of users nd tems n dtbse such sclng cn be lmtton fctor to the prctcl pplctons of the neghborbsed lgorthms..3. Performnce mesures The coverge, men bsolute error nd ROC senstvty were used to compre exmned recommendton lgorthms. In ths study the coverge s beng clculted s percentge of tems from test set for whch gven lgorthm hs been ble to gve predctons. Men Averge Error (MAE) of predcted scores s sttstcl ccurcy mesure used for collbortve flterng lgorthms [4, 13], whle ROC senstvty s mesure of dgnostc power of predcton lgorthms [4]. One of the mn purposes of recommender systems s to dentfy tems whch new user s lkely to prefer. So, threshold θ 1 s used to obtn subset of tems wth predcted scores hgher then θ 1. ROC curve s plot of senstvty gnst (1 specfcty) of the gven predctons. Senstvty s the probblty of cceptng good tem, whle specfcty s the probblty of rejectng bd tem. A recommender system cn be regrded s successful f ts ROC curve s hgh. As byproduct of ROC curve clculton, one cn clculte the ccurcy of the recommender system. We denote s ROC(θ 1, θ ) the ccurcy of the system whch regrds ll tems wth scores bove θ 1 s good tems, nd declres ech predcton bove θ s recommendton. 3. A REGRESSION-BASED COLLABO- RATIVE FILTERING METHOD For customzed predctons the proposed pproch reles on nherent reltonshps between tems nsted of lookng t smlrtes between users. Assumng dtbse consstng of lrge number of users votng for most tems nd gven unlmted computtonl nd storge resources, exmples from smll neghborhood of n I-dmensonl pont correspondng to scores of n ctve user would represent ts profle. If n ctve user provdes the scores for tems n set I the tsk s to estmte scores for the set I/I of non-rted tems. In theory, ths predcton problem could be pproched by lernng nonlner mppng f (I ): R I R nd usng ths functon to optmlly predct preferences of the ctve user wth respect to the tem. An ctve user cn provde scores for one of I 1 possble subsets of tems, nd so lernng I I 1 functons would optmlly solve the recommendton problem. Lernng ths mny functons s computtonlly unrelstc even for smll tem sets. In ddton, the prctcl dtbses re sprse nd wth nsuffcent number of users to llow even smll-scle verson of the del world pproch. Therefore, we use frst order pproxmton of nonlner mppngs f (I ) s regresson-bsed pproch to collbortve flterng. The frst order pproxmton to predctng score p of user on tem bsed on I cn be expressed s p = w j, f j, j I, (r ), (4) j where f j, re functons descrbng the reltonshp between tems j nd, nd w j, re the correspondng weghts. So, ssumng method for choosng the weghts w j, s known, lernng I(I 1) one-dmensonl functons s suffcent for solvng the pproxmted recommendton problem. From dfferent stndpont, functon f j, cn be consdered s n expert for predctng the score on tem, gven score on tem j. If the ctve user voted for tems from I, then for ech tem from I/I there re I vlble experts. The recommendton problem cn now be pproched s n dentfcton of n optml combnton of experts. To mke the soluton computtonlly more effcent we model experts s lner functons, f j, ( x) x j, + j, =, (5) where α j, nd β j, re the only two prmeters to be estmted for ech expert. The two prmeters re estmted usng ordnry lest squres, nd s byproduct we obtn n estmton of the error vrnce for ech expert, σ j,, whch s useful n determnng the weghts w j,. If the vlue of α j, s ner zero, ths s n ndctor tht the expert resembles the men predctor, nd tht there s no correlton between tems nd j. On the other extreme, f α j, s close to +1 or 1, the expert s n lmost perfect predctor of the score for tem.

4 3.1. Experts ntegrton Once I(I 1) lner experts re lerned, they re combned to gve recommendtons. One ntegrton method bsed on smple vergng nd two sttstclly bsed re proposed n ths secton. Averge wth thresholdng In smple vergng, ll I experts re gven the sme weght, w j, = 1/ I. Snce some of the experts cn be no better thn the men predctor, they cn only deterorte predcton by decresng the contrbuton of good experts. Therefore, smple vergng wth thresholdng where only good experts re retned s lkely to mprove predctons. In AVERAGING(θ) we reject ll experts whose R-squred vlue, R j, = 1 j, /, (6) s below θ, where s vrnce of ll the scores from the dtbse for tem. Snce some of the experts re not used for predcton, usng AVERAGING(θ) for lrger θ t s possble tht the coverge s ncomplete. Determnng optml weghts Bck n 1969, Btes nd Grnger [1] hve suggested tht lner combnton of ndvdul predctons cn produce the results tht re superor to ny of the ndvdul predctons. For our problem of combnng lner experts, the optml soluton cn be derved by mnmzng the error vrnce of the lner combnton of experts from (4). The optml weghts w j, cn be found by usng I I covrnce mtrx C of predcton errors wth elements {C j,k } defned s C j,k = E[e j, e k, ], where e j, s the error of expert f j,, e j, = {r, f j, (r,j )}. Weghts cn be clculted s 1 {C } k I j, k w j, = 1, (7) {C } k, j I j, k where {C 1 } j, k re elements of nverse of C [10]. Problems ssocted wth pplyng (7) nclude estmtng C, clcultng ts nverse when experts re hghly correlted nd computng ths suffcently fst. To estmte C j,k, subset of users tht voted for tems, j nd k should be found nd errors of f j, nd f k, should be clculted on ths subset. Snce trnng dtbse s expected to be very sprse, the number of such trples cn be too smll to properly estmte C j,k even for seemngly lrge dtbses. The second problem, s dscussed n [8], s tht n nverse of C cn be unstble for hghly correlted experts. Snce our lner experts wll most often be just slghtly better thn the men predctor, they wll ll be hghly correlted. The thrd problem s computtonl cost, snce the optml pproch requres clculton of n nverse of C whch generlly tkes O( I 3 ) tme. Snce I = O(I) nd I/I = O(I), producng predctons for n ctve user would tke up to O(I 4 ) tme. In the followng, we propose computtonlly effcent pproxmton of ths pproch. Determnng suboptml weghts effcently One of the mn consequences of hghly correlted experts s tht, from (7), two seemngly dentcl experts cn receve very dfferent weghts, the lrger beng ssgned to the slghtly more ccurte one. To llustrte ths, n Tble 1 we show the rto of weghts for two experts wth error vrnces C 11 =1 nd C =1.1, obtned from (7) when ther correlton C 1 s vred from 0 to 1. Therefore, the effect of ncresng C 1 s smlr to the effect of decresng vlues of C 11 nd C by some constnt smller then C 11, whle C 1 =0. We use ths de for determnng weghts effcently. TABLE 1. The effect of correlton between experts on the optml weghts C w 1 / w Frst, we estmte the verge correlton ρ between prs of experts by E[( y1 y ) ] = E[( y y1) ] E[( y y1)( y y )] + E[( y y ) ], (8) where y, y 1 nd y re rndom vrbles. If we ssume tht y 1 nd y re unbsed experts nd y s the true vlue to be predcted, correlton ρ j,k cn be estmted from (8) s j, k 1/ { j, + k, ED j k [( f j, f k, ) ]}, =, (9) j, k, where E [( f f ) ] cn be clculted over ll D j, k j, k, prs of scores for tems nd j from the dtbse R. We propose to clculte vlues ρ,j for severl rndomly chosen trples (, j, k) nd verge them to obtn ρ. Therefore, clculton of ρ, requrng O(I ) tme, needs to be performed just once for the whole dtbse R. Then, new dgonl mtrx C * C = dg( C j, j ) I mn( C j, j ) (10) j

5 where dg ( C j, j ) s dgonl mtrx wth elements C j,j, nd I s n dentty mtrx, should be used nsted of C n (7). For the exmple from Tble 1, usng both C nd C * results n the sme weghts when ρ=ρ 1. Observe tht computng the nverse of dgonl mtrx C * requres just O(I) tme, nd so gvng predctons for new user would requre only O(I ) tme. We denote ths lgorthm s WEIGHTED_AVERAGING. 3.. Improved regresson-bsed lgorthm One of the problems when delng wth subjectve rtngs s tht two users wth smlr preferences cn hve dfferent men scores for the sme subset of tems. Ths noton hs been used n AD- JUSTED_GENERIC nd NEIGHBOR lgorthms to djust the predctons ccordng to ech ctve user s men score. Here, to mprove predctons of WEIGHTED_AVERAGING lgorthm we propose n djustment smlr to one used n ADJUSTED_GENERIC. Let us exmne two extreme cses to show tht the dfference r from (1) cnnot be ppled drectly to WEIGHTED_AVERAGING. The frst s the cse of experts tht cn predct the score for tem perfectly (wthout error, R =1, α=1). Ths predcton does not need to be djusted by r snce such n expert lredy descrbes t. The second s the cse of experts tht re men predctors (R =0, α=0). In ths cse the djustment s needed, nd r should be dded to the predcton. Any relstc combnton of experts wll be between these two extremes (0<R <1, 0<α<1). Therefore, we use the slope α of the best expert s the weghtng fctor for djustment. The predcton cn now be expressed s p, = r mx j, + w j, f j, (rj ). (11) j I j I We denote ths lgorthm s ADJUSTED_WEIGH- TED_AVERAGING More bout the complexty of the regresson bsed lgorthm Algorthms AVERAGING nd WEIGHTED_AVERAGING requre O(I ) tme for ech new user whch s n dvntge over O(UI) tme needed by NEIGHB lgorthm snce the number of tems s usully sgnfcntly lower thn the number of users. Effectvely, tkng nto consderton tht ech new user votes just for smll subset of tems, computtonl tme s even lower. If the mxmum number of votes for new user ws upper-bounded by constnt, the computtonl tme of regresson-bsed lgorthms becomes O(I), whle t remns O(UI) for neghbor-bsed lgorthms. Whle on-lne speed of the proposed regresson-bsed lgorthms s clerly superor, they requre lernng of I(I 1) lner models where O(U) tme s requred for ech. Therefore, the ntl lernng of experts requres O(UI ) tme whch, lthough does not scle well wth the number of tems, cn be cceptble snce t s done off-lne. The regresson-bsed lgorthms requre svng two lner prmeters nd n estmte of the error vrnce for ech expert, whch requres storng 3I(I 1) vrbles. For most pplctons ths memory requrement compres fvorbly to memory requrement of neghbor-bsed lgorthms whch scles s O(UI). 4. EXPERIMENTAL EVALUATION In ths secton we compre collbortve flterng lgorthms explned n Sectons nd 3 on move benchmrk dtbse. We frst descrbe the dtbse nd the evluton methodology, nd lter we present summry of the results The EchMove dtbse nd evluton methodology The EchMove dtbse [7] s publcly vlble collbortve flterng benchmrk dtbse collected durng 18-month perod between It contns rtngs from 7,916 users on 1,68 moves wth totl of,456,676 rtngs. Therefore, the mtrx s very sprse wth only.07% rted elements. User rtngs were collected on numerc 6-pont scle between 0 nd 1, but to mke the results more comprehensble we rescled rtngs to ntegers {0, 1,, 5}. To perform number of experments, nd to llow for fr comprson between dfferent lgorthms, we used only subset of the whole dtbse. In our experments the frst 10,000 users represented the trnng set, nd the followng 10,000 users represented set of ctve users. From both sets ll users wth less then 0 scores were fltered out s well s ll the moves recevng less thn 50 scores n the trnng set. Ths resulted n 3,4 users n the trnng set nd 4,790 ActveUsers set wth 503 retned moves. A reltvely low number of trnng users ws desrble for pplyng neghbor-bsed methods, whle low number of moves llowed reltvely fst lernng of 503*50 lner experts needed for regresson-bsed lgorthms (trned n 8 hours on 700MHz NT-bsed computer wth 56MB memory).

6 In the frst set of experments we hve rndomly selected fve votes from ech ctve user for testng, whle the rest ws used s the set of trnng scores I. We cll ths protocol AllBut5. Therefore, 5*4,790 predctons were mde wth ech lgorthm on the sme testng set, nd these results were used to mesure MAE, ROC curve nd the coverge of dfferent lgorthms. In ccordnce wth [3] we performed nother set of experments llowng smller number of ctve user scores. Here, we rndomly selected, 5, or 10 votes from ech ctve user s the observed scores, nd then predcted remnng scores. The three protocols were nmed Gven, Gven5, nd Gven10. Such smll number of scores gven by ctve user s lkely to be the envronment for relstc recommender systems. 4.. Summry of results In Tble we report the results for dfferent collbortve flterng lgorthms. We used ROC(θ 1 = 4,θ = 3.5) to report the clssfcton ccurcy. Therefore, ech tem wth score of 4 or 5 ws regrded s good tem, nd ech predcton bove 3.5 ws regrded s the recommendton. Out from severl consdered choces of prmeters K nd N, we show performnce results for the best performng neghborbsed lgorthm wth prmeters K=80 nd N=50. As could be seen t hd n lmost complete coverge, but wth ccurcy just slghtly better then AD- JUSTED_GENERIC lgorthm. AVERAGING lgorthms showed lrge senstvty to the threshold, wth θ = 0.06 offerng the best compromse between ccurcy nd coverge. Accurcy for θ = 0.10 ws the best, but wth the coverge of only 84.5%. For WEIGHTED_AVERAGING lgorthm, t ws determned tht n verge correlton between experts ws slghtly lrger then 0.9, nd ths vlue ws used s the defult vlue for equton (10). For llustrton, we lso report the results for ρ = 0.5 nd ρ = It could be seen tht the vlue of ρ = 0.95 mproved results slghtly, effectvely menng tht t s desrble to ssgn n even hgher weght to the best experts. Snce the coverge of WEIGHTED_AVERAGING ws 100%, t cn be concluded tht, overll, t s slghtly more successful thn ADJUSTED_GENERIC, NEIGHBOR nd AVERAGING lgorthms. Algorthm ADJUSTED_WEIGHTED_AVERAGING ws clerly superor to other lgorthms, ndctng tht n ntroduced djustment cn sgnfcntly boost the predcton ccurcy. It should be noted tht smlr djustment cn be ncorported to AVERAGING lgorthm nd tht smlr mprovements could be expected. In Fgure 1 we show ROC curves for NEIGHBOR (K=80, N=50) nd REG_WA(ρ = 0.9) lgorthms, nd t could be seen tht ADJUSTED_WEIGHTED_AVERAGING cheved better ccurcy over the whole curve. Also, n Fgure we plot the MAE of NEIGHBOR nd AD- JUSTED_WEIGHTED_AVERAGING lgorthms for 4 ctegores of users dependng on the number of gven scores, I. As could be noted, whle NEIGHBOR ws very senstve to I, showng the lowest ccurcy for the ctve users gvng less then 5 votes, AD- JUSTED_WEIGHTED_AVERAGING ws just modertely senstve ndctng tht t cn be successfully used even for users provdng just few votes. TABLE. Predcton results of dfferent lgorthms Algorthm MAE ROC(4,3.5) ccurcy Coverge [%] Elpsed tme [s] MEAN GENERIC ADJUSTED_GENERIC NEIGHBOR(K=80,N=50) AVERAGING (θ = 0.00) AVERAGING (θ = 0.06) AVERAGING (θ = 0.10) WEIGHTED_AVERAGING(ρ = 0.9) WEIGHTED_AVERAGING (ρ = 0.5) WEIGHTED_AVERAGING (ρ = 0.95) ADJUSTED_WEIGHTED_AVERAGING (ρ = 0.9) ADJUSTED_WEIGHTED_AVERAGING (ρ = 0.5) ADJUSTED_WEIGHTED_AVERAGING (ρ = 0.95)

7 1 0.8 senstvty Sold - REG WA Sold ADJUSTED_WEIGHTED_AVERAG. Dsh - NEIGHB Dshed - NEIGHBOR specfcty Fgure 1. ROC curves for NEIGHBOR nd ADJUSTED_WEIGHTED_AVERAGING lgorthms As explned n prevous two sectons, regressonbsed lgorthms hve superor on-lne speed to neghbor bsed lgorthms. Our mplementton of these lgorthms n Mtlb on 700MHz NT-bsed computer wth 56MB memory showed tht when performng 5*4,790 predctons ADJUSTED_WEIGH- TED_AVERAGING ws 51 tmes fster then NEIGHBOR, nd tht ADJUSTED_WEIGHTED_AVERAGING ws 5 tmes slower then ADJUSTED_GENERIC (Tble ). Although we do not clm our mplementton s optml, these results vldte results from the nlyss of onlne speed of neghbor-bsed nd the proposed regresson-bsed lgorthms. Comprson of 4 dfferent protocols s presented n Tble 3 where AllBut5 re results tken from Tble. As could be seen, the regresson-bsed pproch s very robust to the number of scores gven by n ctve user. It s lso evdent tht performnces of AD- JUSTED_GENERIC nd ADJUSTED_WEIGHTED_AVE- RAGING deterorted sgnfcntly for Gven5 nd Gven protocols. Ths ws to be expected snce estmtes of djustment r usng only or 5 scores hve extremely low confdence. Our work n progress s med towrds usng sttstclly bsed pessmstc estmtes of djustments for mprovng the performnce of both methods Sold ADJUSTED_WEIG- HTED_AVERAGING Dshed - NEIGHBOR 0.85 MAE < > 100 User type I Fgure. Dependence of MAE on the number of scores I gven by the ctve user

8 TABLE 3. MAE of dfferent protocols Algorthm AllBut5 Gven10 Gven5 Gven MEAN GENERIC ADJUSTED_GENERIC NEIGHBOR(K=80,N=50) WEIGHTED_AVERAGING(ρ = 0.9) ADJUSTED_WEIGHTED_AVERAGING (ρ = 0.9) CONCLUSIONS AND FUTURE WORK Automted collbortve flterng s one of the key technques for provdng customzton for E- commerce stes. Vrous neghbor-bsed recommendton methods re populr choces for collbortve flterng. However, ther ltency cn be serous drwbck for sclng up to lrge number of requests tht should be processed n rel-tme. In ths pper we proposed regresson-bsed pproch to collbortve flterng tht serches for smlrtes between tems, bulds collecton of experts n the form of smple lner models, nd combnes them n proper wy to gve predctons for new user. We exmned number of procedures for combnng the experts, rngng from smple verges to sttstclly sound ones. In ddton, we proposed three smple lgorthms for comprson wth neghbor nd regresson-bsed lgorthms. One of them, the ADJUSTED_GENERIC, showed s very robust nd dffcult to outperform despte ts smplcty. Experments on move dtbse provded evdence tht, whle provdng mxml coverge, the proposed regresson-bsed pproch provdes sgnfcntly better ccurcy nd s two orders of mgntude fster thn the neghbor-bsed lterntves. However, the overll ccurcy mprovements over smpler predcton lgorthms were stll nrrow, nd the gol of further reserch s to serch for further ccurcy mprovements. There re severl drectons for mprovng the ccurcy, speed nd memory requrements of the regresson-bsed lgorthm. One of the obvous extensons of our pproch s to use more complex experts nsted of lner ones. To mprove the ccurcy, combnng predctons of dfferent types of known lgorthms cn lso be vble pproch f computtonl tme s of no concern. To mprove the on-lne speed nd memory requrements of the proposed procedure, deletng experts wth poor predctng cpbltes cn be n cceptble lterntve. If there re no vlble experts to predct on gven tem, mxmum coverge could be sved by usng smpler models such s ADJUSTED_GENERIC. Wth such n pproch, the ccurcy would not sgnfcntly deterorte snce deleted experts re not much better thn the men predctor. Snce the error vrnce of ech expert s estmted s prt of the regresson-bsed lgorthms, ths knowledge cn possbly be used for guded on-lne recommender systems where, bsed on the prevous votes, n ctve user s sked to vote on the tems tht would mxmlly decrese overll predcton error. Dervng n optml procedure for guded votng s the topc of our reserch n progress. 6. REFERENCES [1] Btes, J. M., nd Grnger, C. W. J. (1969), The combnton of forecsts, Opertonl Reserch Qurterly, 0, pp , [] Bllsus, Dnel nd Pzzn, Mchel J. (1998), Lernng collbortve nformton flters, Proceedngs of the Ffteenth Interntonl Conference on Mchne Lernng, pp , [3] Breese, John S., Heckermn, Dvd nd Kde, Crl (1998), Emprcl nlyss of predctve lgorthms for collbortve flterng, Proceedngs of the Fourteenth Annul Conference on Uncertnty n Artfcl Intellgence, pp. 43-5, [4] Herlocker, Jonthn L., Konstn, Joseph A., Borchers, Al nd Redl, John (1999), An lgorthmc frmework for performng collbortve flterng. Proceedngs of the nd Annul Interntonl ACM SIGIR Conference on Reserch nd Development n Informton Retrevl, pp , [5] Konstn, Joseph A., Mller, Brdley N., Mltz, Dvd, Herlocker, Jonthn L., Gordon, Lee R., nd Redl, John (1997), GroupLens: pplyng

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