A Bayesian Approach toward Active Learning for Collaborative Filtering

Transcription

1 A Bayesan Appoach towad Actve Leanng fo Collaboatve Flteng Rong Jn Depatment of Compute Scence and Engneeng Mchgan State Unvesty Abstact Collaboatve flteng s a useful technque fo eplotng the pefeence pattens of a goup of uses to pedct the utlty of tems fo the actve use. In geneal, the pefomance of collaboatve flteng depends on the numbe of ated eamples gven by the actve use. The moe the numbe of ated eamples gven by the actve use, the moe accuate the pedcted atngs wll be. Actve leanng povdes an effectve way to acque the most nfomatve ated eamples fom actve uses. Pevous wok on actve leanng fo collaboatve flteng only consdes the epected loss functon based on the estmated model, whch can be msleadng when the estmated model s naccuate. Ths pape takes one step futhe by takng nto account of the posteo dstbuton of the estmated model, whch esults n moe obust actve leanng algothm. Empcal studes wth datasets of move atngs show that when the numbe of atngs fom the actve use s estcted to be small, actve leanng methods only based on the estmated model don t pefom well whle the actve leanng method usng the model dstbuton acheves substantally bette pefomance. 1. Intoducton The apd gowth of the nfomaton on the Intenet demands ntellgent nfomaton agent that can sft though all the avalable nfomaton and fnd out the most valuable to us. Collaboatve flteng eplots the pefeence pattens of a goup of uses to pedct the utlty of tems fo an actve use. Compaed to contentbased flteng appoaches, collaboatve flteng systems have advantages n the envonments whee the contents of tems ae not avalable due to ethe a pvacy ssue o the fact that contents ae dffcult fo a compute to Luo S Language Technoy Insttute School of Compute Scence Canege Mellon Unvesty Pttsbugh, PA ls@cs.cmu.edu analye (e.g. musc and vdeos). One of the key ssues n the collaboatve flteng s to dentfy the goup of uses who shae the smla nteests as the actve use. Usually, the smlaty between uses ae measued based on the atngs ove the same set of tems. Theefoe, to accuately dentfy uses that shae smla nteests as the actve use, a easonably lage numbe of atngs fom the actve use ae usually equed. Howeve, few uses ae wllng to povde atngs fo a lage amount of tems. Actve leanng methods povde a soluton to ths poblem by acqung the atngs fom an actve use that ae most useful n detemnng hs/he nteests. Instead of andomly selectng an tem fo solctng the atng fom the actve use, fo most actve leanng methods, tems ae selected to mame the epected educton n the pedefned loss functon. The commonly used loss functons nclude the entopy of model dstbuton and the pedcton eo. In the pape by Yu et. al. (2003), the epected educton n the entopy of the model dstbuton s used to select the most nfomatve tem fo the actve use. Boutle et. al. (2003) apples the metc of epected value of utlty to fnd the most nfomatve tem fo solctng the atng, whch s to fnd the tem that leads to the most sgnfcant change n the hghest epected atngs. One poblem wth the pevous wok on the actve leanng fo collaboatve flteng s that computaton of epected loss s based only on the estmated model. Ths can be dangeous when the numbe of ated eamples gven by the actve use s small and as a esult the estmated model s usually fa fom beng accuate. A bette stategy fo actve leanng s to take nto account of the model uncetanty by aveagng the epected loss functon ove the posteo dstbuton of models. Wth the full Bayesan teatment, we wll be able to avod the poblem caused by the lage vaance n the model dstbuton. Many studes have been conducted on the actve leanng to take nto account of the model uncetanty. The method of quey by commttee (Seung et. al., 1992; Feud et. al., 1997) smulates the posteo dstbuton of models by constuctng an ensemble of

2 models and the eample wth the lagest uncetanty n pedcton s selected fo use s feedback. In the wok by Tong and Kolle (2000), a full Bayesan analyss of the actve leanng fo paamete estmaton n Bayesan Netwoks s used, whch takes nto account of the model uncetanty n computng the loss functon. In ths pape, we wll apply the full Bayesan analyss to the actve leanng fo collaboatve flteng. Patculaly, n ode to smplfy the computaton, we appomate the posteo dstbuton of model wth a smple Dchlet dstbuton, whch leads to an analytc epesson fo the epected loss functon. The est of the pape s aanged as follows: Secton 2 descbes the elated wok n both collaboatve flteng and actve leanng. Secton 3 dscusses the poposed actve leanng algothm fo collaboatve flteng. The epements ae eplaned and dscussed n Secton 4. Secton 5 concludes ths wok and the futue wok. 2. Related Wok In ths secton, we wll fst befly dscuss the pevous wok on collaboatve flteng, followed by the pevous wok on actve flteng. The pevous wok on actve leanng fo collaboatve flteng wll be dscussed at the end of ths secton. 2.1 Pevous Wok on Collaboatve Flteng Most collaboatve flteng methods fall nto two categoes: Memoy-based algothms and Model-based algothms (Beese et al. 1998). Memoy-based algothms stoe atng eamples of uses n a tanng database. In the pedcatng phase, they pedct the atngs of an actve use based on the coespondng atngs of the uses n the tanng database that ae smla to the actve use. In contast, model-based algothms constuct models that well eplan the atng eamples fom the tanng database and apply the estmated model to pedct the atngs fo actve uses. Both types of appoaches have been shown to be effectve fo collaboatve flteng. In ths subsecton, we focus on the model-based collaboatve flteng appoaches, ncludng the Aspect Model (AM), the Pesonalty Dagnoss (PD) and the Fleble Mtue Model (FMM). Fo the convenence of dscusson, we wll fst ntoduce the annotaton. Let tems denoted by X { 1, 2,..., M }, uses denoted by Y { y1, y2,..., y N }, and the ange of atngs denoted by { 1,..., R }. A tuple (, y, ) means that atng s assgned to tem by use y. Let X ( y) denote the set of tems ated by use y, and R y () stand fo and the atng of tem by use y, espectvely. Aspect model s a pobablstc latent space model, whch models ndvdual pefeences as a conve combnaton of pefeence factos (Hofmann & Pucha 1999; Hofmann, 2003). The latent class vaable Z,,..., } { 1 2 K s assocated wth each pa of a use and an tem. The aspect model assumes that uses and tems ae ndependent fom each othe gven the latent class vaable. Thus, the pobablty fo each obsevaton tuple (, y, ) s calculated as follows: p (, y) p(, ) p( y) (1) Z whee p( y) stands fo the lkelhood fo use y to be n class and p(,) stands fo the lkelhood of assgnng tem wth atng by uses n class. In ode to acheve bette pefomance, the atngs of each use ae nomaled to be a nomal dstbuton wth eo mean and vaance as 1 (Hofmann, 2003). The paamete p(,) s appomated as a Gaussan dstbuton N ( µ, σ ) and p( y) as a multnomal dstbuton. Pesonalty dagnoss appoach teats each use n the tanng database as an ndvdual model. To pedcate the atng of the actve use on cetan tems, we fst compute the lkelhood fo the actve use to be n the model of each tanng use, whch s appomated usng a Gaussan dstbuton: p( y y) e X ( y ) t ( R ( ) R y y 2 ( )) 2σ whee σ stands fo the vaance of Gaussan dstbutons. The atngs fom the tanng use on the same tems ae then weghted by the computed lkelhood. The weghted aveage s used as the estmaton of atngs fo the actve use. Pevous empcal studes have shown that the pesonalty dagnoss method s able to outpefom seveal othe appoaches fo collaboatve flteng (Pennock et al., 2000). Fleble Mtue Model ntoduces two sets of hdden vaables {, y}, wth fo the class of tems and y fo the class of uses (S and Jn, 2003; Jn et. al., 2003). Smla to aspect model, the pobablty fo each obseved tuple (, y, ) s factoed nto a sum ove dffeent classes fo tems and uses,.e., p(, y, ), y p( ) P( ) P( ) P( y ) P(, ) y All the paametes ae estmated usng Epectaton Mamaton algothm (EM) (Dumpste et. al., 1976). The multple-cause vecto quantaton (MCVQ) model (Boutle, Zemel and Maln 2003) uses the smla dea fo collaboatve flteng. 2.2 Pevous Wok on Actve Leanng The goal of actve leanng s to lean the coect model usng only a small numbe of labeled eamples. The geneal appoach s to fnd the eample fom the pool of unlabeled data that gves the lagest educton n the epected loss functon. The loss functons used by most actve leanng methods can be categoed nto two y 2 y (2) (3)

3 goups: the loss functons based on model uncetanty and the loss functon based on pedcton eos. Fo the fst type of loss functons, the goal s to acheve the lagest educton ato n the space of hypothess. One commonly used loss functon s the entopy of the model dstbuton. Methods wthn ths categoy usually select the eample fo whch the model has the lagest uncetanty n pedctng the label (Seung et. al., 1992; Feud et. al, 1997; Abe and Mamtsuka, 1998; Campbell et. al., 2000; Tong and Kolle, 2000). The second type of loss functons nvolved the pedcton eos. The lagest educton n the volume of hypothess space may not necessaly be effectve n cuttng the pedcton eo. Feud et. al. showed an eample n (1997), n whch the lagest educton n the space of hypothess does not bng the optmal mpovement to the educton of pedcton eos. Empcal studes n Bayesan Netwok (Tong and Kolle, 2000) and tet categoaton (Roy and MaCallum, 2001) have shown that usng the loss functon that dectly tagets on the pedcton eo s able to acheve bette pefomance than the loss functon that s only based on the model uncetanty. The commonly used loss functon wthn ths categoy s the entopy of the dstbuton of pedcted labels. In addton to the choce of loss functon, how to estmate the epected loss s anothe mpotant ssue fo actve leanng. Many actve leanng methods compute the epected loss only based on the cuently estmated model wthout takng nto account of the model uncetanty. Even though ths smple stategy woks fne fo many applcatons, t can be vey msleadng, patculaly when the estmated model s fa fom the tue model. As an eample, consdeng leanng a classfcaton model fo the data dstbuton n Fgue 1, whee sphees epesent data ponts of one class and stas epesent data ponts of the othe class. The fou labeled eamples ae hghlghted by the lne-shaded ellpss. Based on these fou tanng eamples, the most lkely decson bounday s the hoontal lne (.e., the dash lne) whle the tue decson bounday s a vetcal lne (.e., the dot lne). If we only ely on the estmated model fo estmatng the epected loss, the eamples that wll be selected fo use s feedback ae most lkely fom the dot-shaded aeas, whch ae neffectve n adustng the estmated decson bounday (.e. the hoontal lne) to the coect decson bounday (.e. the vetcal). On the othe hand, f we can use the model dstbuton fo computng the epected loss, we wll be able to adust the decson bounday moe effectvely snce decson boundaes othe than the estmated one (.e. hoontal lne) ae consdeed n the computaton of epected loss. Thee have been seveal studes on actve leanng that utle the posteo dstbuton of models fo estmatng the epected loss. The quey by commttee appoach smulates the model dstbuton by samplng a set of models out of the posteo dstbuton. In the wok of actve leanng fo paamete estmaton n Bayesan f 1 Estmated Decson Bounday Coect Decson Bounday Fgue 1: A leanng scenao when the estmated model s fa fom the tue model. The vetcal lne coesponds to the coect decson bounday and the hoontal lne coesponds to the estmated decson bounday. The fou labeled eamples ae hghlghted by the lne-shaded aeas. Netwok, a Dchlet dstbuton fo the paametes s used to estmate the change n the entopy functon. Howeve, the geneal dffculty wth the full Bayesan analyss fo actve leanng s the computatonal complety. Fo complcated models, usually t s athe dffcult to obtan the eact posteo dstbuton fo models. As a esult, samplng appoaches such as Makov Chan Mote Calo (MCMC) and Gbbs samplng ae used to appomate the Bayesan aveage. In ths pape, we follow an dea smla to the Laplace appomaton used n gaphc model (MacKay, 1992). Instead of accuately computng the posteos, we appomate the posteo dstbuton wth an analytc epesson and apply the appomated posteo dstbuton to estmate the epected loss. Compaed to the samplng appoaches, ths appoach substantally smplfes the computaton by avodng geneatng a lage numbe of models and calculatng the loss functon values ove the geneated models. 2.3 Pevous Wok on Actve Leanng fo Collaboatve Flteng Thee have been only a few studes on actve leanng fo collaboatve flteng. In the pape by Ka et al (2003), a method smla to Pesonalty Dagnoss (PD) s used fo collaboatve flteng. Each eample s selected fo use s feedback n ode to educe the entopy of the lkemndness dstbuton o p( y y ) n Equaton (2). In the pape by Boutle et al (2003), the Multple-cause vecto quantfcaton method (smla to the FMM model) s used fo collaboatve flteng. Unlke many othe collaboatve flteng eseaches, whch ty to mnme f 2

4 the pedcton eo, ths pape only concens wth the tems that ae stongly ecommended by the system. The loss functon s based on the epected value of nfomaton (EVOI), whch s computed based on the cuently estmated model. One poblem wth both studes on actve leanng fo collaboatve flteng s that, the epected loss s computed only based on a sngle model, namely the cuently estmated model. As llustated by the eample n Fgue 1, the estmaton based on only a sngle model can be msleadng, patculaly when the numbe of ated eamples gven by the actve use s small and meanwhle the numbe of paametes to be estmated s lage. In the late epements, we wll show that the selecton based on the epected loss functon usng only the cuently estmated model can be even wose than smple andom selecton. 3. A Bayesan Appoach Towad Actve Leanng fo Collaboatve Flteng In ths secton, we wll fst dscuss the appomated analytc epesson fo the posteo dstbuton. Then, the appomated posteo dstbuton wll be used to estmate the epected loss. 3.1 Appomate the Model Posteo Dstbuton Fo the sake of smplcty, we wll focus on the actve leanng of aspect model fo collaboatve flteng. Howeve, the pncple used n ths secton can be easly etended to othe models fo collaboatve flteng. As descbed n Equaton (1), each condtonal lkelhood p(, y ) s decomposed as the sum of p (, ) p ( y ). Fo actve use y, the most mpotant task s to detemne ts use type, o p( y ). Let { p( )} stands fo the paamete space. Usually, paametes ae estmated though the mamum lkelhood estmaton,.e. ag ma p(, y ; ) X ( y) ag ma p(, ) X ( y) Z Then, the posteo dstbuton of model,.e., p( D( y )) whee D( y ) ncludes all the atngs gven the actve use y, can be wtten as: (4) whee Z( D( y )) s the nomalaton facto. In above, a unfom dstbuton s used fo po p ( ). Appaently, the posteo dstbuton n (7) s athe dffcult to be used fo estmatng the epected loss due to the multple poducts and the nomalaton facto Z( D( y )). To appomate the posteo dstbuton, we wll consde the epanson of the posteo functon aound the mamum pont. Let stand fo the mamal paametes that ae obtaned fom EM algothm by mamng Equaton (4). Let s consde the ato of p( D( y )) wth espect to p( D( y )), whch can be wtten as: p(, ) p( D( y )) p( D( y )) p(, ) whee p(, ) p(, ) ( α 1) α s defned as p(, ) α + 1 p(, ) (6) (7) Based on the appomaton n Equaton (6), the appomated posteo dstbuton p( D( y )) s a Dchlet wth hype paametes α defned n Equaton (7), o p( D) Γ( α ) α 1 ( α ) Γ whee α α. Futhemoe, the followng elaton between the hype paametes α and optmal paametes s tue: α 1 α 1 Ths s because the optmal paametes obtaned by the EM algothm s actual the fed pont of the followng equaton: (8) (9) 1 p( D( y )) p( D( y ) ) p( ) Z( D( y )) 1 p(, ) Z( D( y )) X ( y) Z (5) p(, ) (10) p(, )

5 Based on the popety n Equaton (9), t s not dffcult to vefy that the optmal pont fo the appomated Dchlet dstbuton n Equaton (8) s eactly. 3.2 Estmate the Epected Loss Smla to many othe actve leanng woks (Tong and Kolle, 2000; Seung et al, 1992; Ka et al, 2003), we use the entopy of the model functon as the loss functon. Many pevous studes on actve leanng ty to fnd the eample that dectly mnmes the entopy of the model paametes wth cuently estmated model. In the case of aspect model, t can be fomulated as the followng optmaton poblem: (11) ag mn,, X p(, ) whee denotes the cuently estmated paametes and denotes the optmal paamete that ae estmated, usng one addtonal ated eample,.e., tem s ated as. The goal of Equaton (11) s to fnd tem such that the epected entopy of dstbuton s mnmed. Thee ae two poblems wth applyng ths smple stategy to collaboatve flteng: 1) The fst poblem comes fom the fact that the epected entopy s computed only based on the cuently estmated model. Accodng to Equaton (11), the epectaton s evaluated ove the dstbuton p(, ). As aleady ponted out n Secton 2, such estmaton could be msleadng patculaly when the cuently estmated model s fa fom the tue model. 2) The second poblem comes fom the chaactestcs of collaboatve flteng. Recall that paamete stands fo the lkelhood fo the actve use to be n the use class. Snce the optmaton n Equaton (11) tes to effcently educe the uncetanty n the type of use class fo the actve use, t wll select eamples that can pufy the class dstbuton. Ths contadcts the pevous studes n collaboatve flteng (S and Jn, 2003), whch found t s moe effectve fo collaboatve flteng to assume a use of multple use types than a sngle type. As a esult of ths obsevaton, we would epect the dstbuton to be of multple modes, not of a sngle model. Based on the above analyss, the optmaton poblem n Equaton (11) s not appopate fo actve leanng of collaboatve flteng. The late empcal studes also ndcate ths fact. In the deal case, f the tue model s gven, the optmal stategy n selectng eample should be: tue tue ag mn (12) X, tue tue p(, ) The goal of Equaton (12) s to fnd an eample such that the updated model paamete, can be adusted tue towad the tue model paamete most effcently. tue Snce the tue model s unknown, we need to appomate the optmaton goal n Equaton (12). One way of appomaton s to eplace the tue model wth the epectaton ove the posteo dstbuton p( D( y )). As a esult of ths appomaton, Equaton (12) s tansfomed nto the followng optmaton poblem: ag mn X, p(, ) p( D( y)) tue (13) Now, the key ssue becomes how to compute the ntegaton effcently snce the samplng methods ae usually tme consumng. Fotunately, the ntegaton n Equaton (13) can be computed analytcally as follows:, p(, ) p( D( y)) p( D( y)) p(, ) d,, p( D( y)) Ψ a + a + ( 2) a Ψ ( a + 1) ( a + 1) a p(, ) a p(, ) a p(, ) a Ψ ( a + 1) p(, ) ( a + 1) a, a ( a + 1) a a p(, ), (, ) a p(, ) a p + a ( a + 1) ( a + 1) a (14) whee Ψ s the dgamma functon. Note that R 1 p(, ) 1 snce a Gaussan appomaton s used to compute p(, ). The above devaton uses the followng popety of dgamma functon: Ψ( α ) Ψ( α ) ~ Dchlet ( α )

6 Wth the analytc esult n Equaton (14), the ntegaton n Equaton (13) can be effcently computed. The othe computatonal complety comes fom the estmaton of the updated model,. The standad way to obtan the updated model s to eun the full EM algothm wth one moe addtonal ated eample (.e., eample s ated as categoy ). Ths can be etemely epensve snce we wll have an updated model fo evey tem and evey possble atng categoy. A moe effcent way fo computng the updated model s to avod the dectly optmaton of Equaton (4). Instead, we use the followng appomaton, ag ma p(, ) p(, y ; ) X ( y ) ag ma p(, ) p( D( y )) (15) ag ma p(, ) Dchlet( α) α 1 ag ma p(, ) The EM updatng equaton fo the above obectve functon s: p(, ) + α 1 α + ( p(, ) 1) (16) The advantage of the updatng equaton n (16) vesus the moe geneal EM updatng equaton n (10) s that t only depends on the atng and tem whle Equaton (10) has to go though all the tems ated by the actve use. In summay, we popose a Bayesan teatment of actve leanng fo collaboatve flteng, whch uses the model posteo dstbuton to compute the estmaton of loss functon. To smplfy the computaton, we appomate the mode dstbuton wth a Dchlet dstbuton. As a esult, the epected loss can be calculated analytcally and the use model can be updated moe effcently. Fo late efeence, we call ths method Bayesan method. 4. Epements In ths secton, we pesent epement esults n ode to addess the followng two questons: 1) Whethe the poposed actve leanng algothm s effectve fo collaboatve flteng? In the epement, we wll compae the poposed algothm to the method of andomly acqung eamples fom the actve use. 2) How mpotant s the full Bayesan teatment? In ths pape, we emphase the mpotance of takng nto account the model uncetanty usng the posteo dstbuton. To llustate ths pont, n ths epement, we Table 1: Chaactestcs of MoveRatng and EachMove. MoveRatng EachMove compae the poposed algothm to two commonly used actve leanng methods that ae only based on the estmated model wthout utlng the model dstbuton. The detals of these two actve leanng methods wll be dscussed late. 4.1 Epement Desgn Two datasets of move atngs wee used n ou epements,.e., MoveRatng 1 and EachMove 2. Fo EachMove, we etacted a subset of 2,000 uses wth moe than 40 atngs. The detals of these two datasets ae lsted n Table 1. Fo MoveRatng dataset, we used the fst 200 uses fo tanng and the est uses fo testng. Fo EachMove dataset, the fst 400 uses wee used fo tanng. Fo each test use, we andomly selected thee tems wth the atngs as the statng seed fo the actve leanng algothm to buld the ntal model. Futhemoe, fo each test use, twenty ated tems wee eseved fo evaluatng the pefomance of dffeent actve leanng methods. Fnally, fo each teaton, an actve leanng algothm s allowed to solct atng fo a sngle tem fom the actve use. Totally, t can ask fo atngs of fve dffeent tems and the pefomance s evaluated fo each feedback. Fo smplcty, we assume that the actve use wll always be able to ate the tems pesented by the actve leanng. Of couse, as ponted out n (Ka et al, 2003), ths s not a completely coect assumpton because thee ae tems that the actve use has not seen befoe and theefoe t s mpossble fo hm/he to ate those tems. Snce the focus of ths pape s on the behavo of actve leanng algothms fo collaboatve flteng, we wll leave ths ssue fo futue wok. The aspect model used fo collaboatve flteng has aleady been descbed n the Secton 2. The numbe of use classes used n the epement s set to be 5 fo MoveRatng dataset and 10 fo EachMove datasets based on the pevous empcal studes. The mean absolute eo (MAE) s used to evaluate the pefomance of collaboatve flteng, whch s defned as follows (Beese et al., 1998): whee LTest Numbe of Uses Numbe of Items Avg. # of ated Items/Use Numbe of Ratngs ^ MAE ( l) Ry ( ( ( ) ) l ) l L (17) Test l s the numbe of the test atngs

7 The poposed algothm s compaed aganst the followng thee actve leanng algothms fo collaboatve flteng: 1) Random Selecton: Ths method andomly selects one tem out of the pool of tems fo use s feedback. We efe ths smple method as andom method. 2) Model Entopy based Sample Selecton. Ths method has aleady been descbed at the begnnng of Secton 3.2. It fnds the tem that effcently educes the entopy of the use class dstbuton fo the actve use (n Equaton (11)). As afoementoned, the poblems wth ths smple selecton stategy ae n two folds: I) Computng the epected loss only based on the cuently estmated model and, II) Conflctng wth the ntuton that each use can be of multple types. By compang ths appoach to the poposed actve leanng method fo collaboatve flteng, we wll be able to see f the dea of usng model dstbuton fo computng epected loss s wothwhle fo collaboatve flteng. We wll efe to ths method as model entopy method. 3) Pedcton Entopy based Sample Selecton. Unlke the pevous method, whch consdes the uncetanty n assgnng the actve use to dffeent use classes, ths method focuses on the uncetanty n pedctng atngs of tems fo the actve use. It selects the tem that s able to educe the entopy of pedcatng atngs fo dffeent tems. Fomally, the selecton cteon can be fomulated as the followng optmaton poblem: ag mn p(,, ) p(,, ) X p(, ) (18) whee notaton, stands fo the updated model usng the eta ated eample (,,y). Smla to the pevous method, ths appoach uses the estmated model fo computng the epected loss. Howeve, unlke the pevous appoach that tes to pufy the dstbuton of use types fo the actve use, ths appoach tagets on the pedcton dstbuton. Theefoe, t s not aganst the ntuton that each use s of multple types. We wll efe ths method as pedcton entopy method. 4.2 Results and Dscusson The esults fo the poposed actve leanng algothm togethe wth the thee baselne models fo database MoveRatng and EachMove ae pesented n Fgue 2 and 3, espectvely. Fst, accodng to Fgue 2 and 3, both the model entopy method and the pedcton entopy method pefom consstently wose than the smple andom method. Ths phenomenon can be eplaned by the fact that the ntal numbe of ated tems gven by the actve use s only thee, whch s elatvely small gven the numbe of paametes to detemne s 5 fo MoveRatng and 10 fo EachMove. As a esult, the epected loss cannot be computed accuately based on the estmated MAE MoveRatng numbe of feedback andom Bayesan model pedcton Fgue 2: MAE esults of fou actve leanng algothms fo collaboatve flteng ove MoveRatng dataset. Legend andom stands fo the andom method, Bayesan fo the Bayesan method, model fo the model entopy method, and pedcaton fo the pedcton entopy method. The smalle the MAE the bette the pefomance Each Move numbe of feedbacks Fgue 3: MAE esults of fou actve leanng algothms fo collaboatve flteng ove EachMove dataset. Legend andom stands fo the andom method, Bayesan fo the Bayesan method, model fo the model entopy method, and pedcaton fo the pedcton entopy method. The smalle the MAE the bette the pefomance. model, and the selected tems wll not be the most nfomatve ones. Futhemoe, compang to the

8 pedcton entopy method, we see that the model entopy method pefoms substantally wose. Fo eample, n Fgue 3, fo the model entopy method, the pefomance of collaboatve flteng s almost unchanged whle the pedcaton entopy method s able to educe the MAE eo fom 1.15 to Ths s because the model entopy method tes to naow down a sngle use type fo the actve use. Snce most uses ae of multple types. t s nappopate to apply the model entopy method to collaboatve flteng. On the othe hand, the pedcton entopy method doesn t have ths defect because t focuses on mnmng the uncetanty n pedcatng atngs of tems fo the actve use nstead of the uncetanty n assgnng use types to the actve use. The second obsevaton fom Fgue 2 and 3 s that the poposed actve leanng method pefoms bette than any of the thee based lne models fo both MoveRatng and EachMove datasets. The most mpotant dffeence between the poposed method and the othe methods fo actve leanng s that the poposed method takes nto account the model dstbuton, whch makes t obust when even thee s only thee ated tems gven by the actve use. 5. Concluson In ths pape, we poposed a full Bayesan teatment of actve leanng fo collaboatve flteng. Dffeent fom pevous studes of actve leanng fo collaboatve flteng, ths method takes nto account the model dstbuton when computng the epected loss. In ode to allevate the computaton complety, we appomate the model posteo wth a smple Dchlet dstbuton. As a esult, the estmated loss can be computed analytcally and the model fo the actve use can be updated effcently. Snce ths wok only focuses on the model qualty, we plan to apply the full Bayesan analyss to the pedcton eo, whch s usually moe effectve accodng to the pevous studes of actve leanng. Refeences Beese, J. S., Heckeman, D., Kade C., (1998). Empcal Analyss of Pedctve Algothms fo Collaboatve Flteng. In the Poceedng of the Fouteenth Confeence on Uncetanty n Atfcal Intellgence. Boutle, C., Zemel, R. S., and Maln, B. (2003). Actve collaboatve flteng. In the Poceedngs of Nneteenth Confeence on Uncetanty n Atfcal Intellgence. Dempste, A. P., Lad, N. M., & Rubn, D. B. (1977). Mamum lkelhood fom ncomplete data va the EM algothm. Jounal of the Royal Statstcal Socety, B39: Feund, Y. Seung, H. S., Sham, E. and Tshby. N. (1997) Selectve samplng usng the quey by commttee algothm. Machne Leanng Hofmann, T., & Pucha, J. (1999). Latent class models fo collaboatve flteng. In Poceedngs of Intenatonal Jont Confeence on Atfcal Intellgence. Hofmann, T. (2003). Gaussan latent semantc models fo collaboatve flteng. In Poceedngs of the 26 th Annual Int l ACM SIGIR Confeence on Reseach and Development n Infomaton Reteval. Jn, R., S, L., Zha., C.X. and Callan J. (2003). Collaboatve flteng wth decoupled models fo pefeences and atngs. In Poceedngs of the 12th Intenatonal Confeence on Infomaton and Knowledge Management. MacKay, D. J. C. (1992). A pactcal Bayesan famewok fo back-popagaton netwoks. Neual Computaton 4(3), Roy, N. and McCallum A. (2001). Towad Optmal Actve Leanng though Samplng Estmaton of Eo Reducton. In Poceedngs of the Eghteenth Intenatonal Confeence on Machne Leanng. Pennock, D. M., Hovt, E., Lawence, S., and Gles, C. L. (2000). Collaboatve flteng by pesonalty dagoss: a hybd memoy- and model-based appoach. In Poceedngs of the Steenth Confeence on Uncetanty n Atfcal Intellgence. Seung, H. S., Oppe, M. and Sompolnsky, H. (1992). Quey by commttee. In Computatonal Leang Theoy, pages S, L. and Jn, R. (2003). Fleble mtue model fo collaboatve flteng. In Poceedngs of the Twenteth Intenatonal Confeence on Machne Leanng. Tong, S. and Kolle, D. (2000). Actve Leanng fo Paamete Estmaton n Bayesan Netwoks. In Advances n Neual Infomaton Pocessng Systems. Yu, K., Schwaghofe, A., Tesp, V., Ma, W.-Y. and Zhang, H. J. (2003). Collaboatve ensemble leanng: combnng collaboatve and content-based Infomaton flteng va heachcal Bayes. In Poceedngs of Nneteenth Intenatonal Confeence on Uncetanty n Atfcal Intellgence. Campbell, C., Cstann, N., and Smola, A. (2000). Quey Leanng wth Lage Magn Classfes. In Poceedngs of 17 th Intenatonal Confeence on Machne Leanng. Abe, N. and H. Mamtsuka (1998). Quey leanng stateges usng boostng and baggng. In Poceedngs of the Ffteenth Intenatonal Confeence on Machne Leanng.