DIVA: Applying Decision Theory to Collaborative Filtering

Hien Nguyen*, Peter Haddawy*@

Decision Systems and Artificial Intelligence Lab*Dept. of EE &CS

University of Wisconsin-MilwaukeeMilwaukee, W153201

{ nguyen,haddawy } @ cs.uwm.edu

Intelligent Systems Lab~Faculty of Science & Technology

Assumption UniversityBangkok 10240, Thailandhaddawy@isl.s-t.au.ac.th

AbstractThis paper describes DIVA, a decision-theoreticagent for recommending movies that contains anumber of novel features. DIVA represents userpreferences using pairwise comparisons amongitems, rather than numeric ratings. It uses a novelsimilarity measure based on the concept of theprobability of conflict between two orderings of

¯ items. The system has a rich representation ofpreference, distinguishing between a user’s generaltaste in movies and his immediate interests. It takesan incremental approach to preference elicitation inwhich the user can provide feedback if not satisfiedwith the recommendation list. We empiricallyevaluate the performance of the system using theEachMovie collaborative filtering database.

Introduction

Collaborative filtering has become a popular approachfor eliciting user preferences in order to recommenditems of interest 1. Representation and elicitation ofpreferences have long been studied in Decision Theory(Keeyney & Raiffa 1976), but surprisingly no work collaborative filtering has made use of the wealth oftechniques and formalism available. This paperdescribes the Decision-Theoretic Interactive VideoAdvisor (DIVA), a collaborative filtering system thatprovides movie recommendations. The guidingprinciple behind the system design is the accuraterepresentation and efficient elicitation of userpreferences, following decision-theoretic principleswherever they apply. Following this designmethodology has lead to a number of novel features thatprovide DIVA with distinct advantages over othercollaborative filtering systems.

All other collaborative filtering systems to date

1 AAAI Workshop on Recommender Systems, Madison,

July 1998. AAAI Technical Report WS-98-08.

represent user preferences with numerical ratings. Incontrast, DIVA uses the standard decision-theoreticnotion of a preference order, i.e., pairwise comparisonsamong movies. This provides a fine-grainedrepresentation of preference without forcing the user tothink about a large number of rating categories.

Most collaborative filtering systems, e.g. (Hill et al.1995, Shardanand & Maes 1995), determine similaritybetween preferences of different users following thetechnique used in GroupLens (Resnick 1994), which based on the Pearson correlation coefficient. In contrast,DIVA uses a measure based on the concept of theprobability of conflict between pairwise rankings. Weshow that our measure has several practical advantagesover the GroupLens measure. We empiricallydemonstrate that use of our similarity measure results inmore accurate recommendations than use of theGroupLens measure.

While people can be characterized as having a generaltaste in movies, what they are interested in seeing on anyone occasion may deviate from this. DIVA supports thisdynamic notion of preference by distinguishing betweenlong- and short-term preferences.

In order to minimize the amount of time the user needsto spend providing preference information to the system,DIVA supports the notion of incremental elicitation ofpreferences by permitting the user to provide feedback ifhe is not satisfied with the list movies DIVArecommends. This feedback takes into account thedistinction between long- and short-term preferences.

The rest of this paper is organized as follows. Section 1provides an overview of DIVA’s functionality. Section 2describes the overall architecture and key algorithms.Section 3 presents the results from our empiricalevaluation of the system. Section 4 discusses relatedwork in collaborative filtering and incrementalpreference elicitation, and section 5 presents conclusionsand directions for future research.

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From: AAAI Technical Report WS-99-01. Compilation copyright © 1999, AAAI (www.aaai.org). All rights reserved.

Figure 1: A screenshot of the registration window.

Overview of DIVADIVA’s design emphasizes ease and accuracy ofpreference elicitation. In order not to overburden theuser with unnecessary questions, DIVAtakes an incremental approach topreference elicitation. It starts by elicitingsome preference information and thenquickly provides a list ofrecommendations. If the user is notsatisfied with the recommendations, theuser can critique them in order to provideadditional preference information.

To accurately represent user preferences,we attempt to account for the dynamicnature of preferences. While people havegeneral taste in movies, the type of moviethey would like to see will typically varyfrom one occasion to another, based onmany environmental factors, such as whatmovies they recently saw. Thus weseparate the elicitation of long- and short-term preferences and we combine the twotypes of preference in a natural andintuitive fashion.

A new user to DIVA is asked to provide auser login name and a password, whichare used to index his preferenceinformation whenever he accesses the system. The useris then shown an alphabetical list of all movies in the

system and asked to indicate some he particularly liked,some he particularly disliked, and some he thought wereabout average (Figure 1). Experience has shown that user must classify a minimum of about 5 movies in eachcategory to get reasonable recommendations from thesystem. This information is used to build an initialpreference structure for the user.

The user may add or change some preferences at anytime by clicking the "View/Update Your Profile" buttonat the top-right corner of Figure 2. After submitting hispreferences, the user may request recommendations.This is done via a page that permits the user to constrainthe search, as shown in Figure 2. The user may specifyactors and actresses, directors, genres, professional starratings, countries of production, release years, MPAAratings, and the running time that he is particularlyinterested in. These constraints give the user a way ofindicating what kind of movie he is particularlyinterested in watching at the current time, i.e. his short-term preferences. They act as an initial filter on theentries in the movie database. The movies that satisfythe constraints are then ranked according to the user’spreferences. The behavior we have endeavored toembody in DIVA is that of someone who knows youwell acting on your behalf with some instruction fromyou. For example, suppose you ask a close friend to goto the video store and rent an adventure film that takesplace in Africa. Within the context of that constraint,she would use her knowledge of your taste in movies,e.g. a preference for films with excellent

Figure 2: A screenshot of the search window

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cinematography, to select the film she thinks you wouldbe most likely to enjoy.

The recommendation list is displayed on a separate page,as shown in Figure 3. By clicking any of the movie titlesin the recommendation list, the user can see all theattribute information about that film. If the user is notinterested in any of the films in the recommendation list,he can provide feedback to the system and then requestanother search. We distinguish between feedbackconcerning long-term preferences (second feedbackcolumn) and feedback concerning short-term preferences(first feedback column). If the user has seen any moviein the list, he can indicate whether he particularly likedor disliked it. Even though he may not have seen a film,the user may know enough about it to be quite confidentthat he would not enjoy seeing it. This is all feedbackconcerning long-term preferences and is added to thestored user preference model. For movies the user hasnot seen, DIVA asks that he indicate if they are close towhat he is interested in watching currently or if they arefar from that. This is feedback concerning short-termpreferences and is used only in the current search

Figure 3: The screenshot of the search result.

session. After providing feedback, the user clicks on the"Continue Search" button (Figure 3) to obtain a new listof recommendations.

Architecture and AlgorithmsWe retrieve movies by first computing the preferenceranking over all movies in our movie database. Then weremove any movies that do not satisfy the user’s short-term constraints and display the top n movies. If thereare not many movies that satisfy all the constraints, werelax the constraints by disjoining them.

Initial preference elicitation

A user’s complete set of preferences in a domainwith no uncertainty (such as the movie domain) can represented as a total ordering over the items in thedomain. A subset of the user’s preferences thencorresponds to a partial order over the items. An initialset of pairwise preferences among movies is obtainedfrom the user’s Like, OK, and Dislike lists (Figure 1).This gives us a partial order over movies: every movie

in the Like list is consideredpreferred to every movie inthe OK list, which is in turnpreferred to every movie inthe Dislike list. Figure 4(b)(without the dashed links andthe filled node) shows thepreferences obtained from theLike, OK, and Dislike lists ofthe user in Figure 1.

Case retrievalThe directly elicited user

preferences are augmentedwith preference informationfrom a case base of userpreference information, usingthe technique described in (Ha& Haddawy 1998). The casebase contains partialpreference structures for allusers of the system. Wecompute the similaritybetween the active user’sinitial partially elicitedpreference structure and thepreference structures in thecase base. We then use thepreferences of the mostsimilar stored structure tosupplement the directlyelicited preferences.

In order to find the closest matching preferencestructure, we need a method of computing the similaritybetween two preference structures. We define the dis-

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similarity between two complete preference structures asthe probability that two randomly chosen elements areranked differently by the two preference structures. Thissimilarity measure satisfies all the properties of adistance metric and has range [0,1].

But the preference information in our case base and thepreference information for the active user are onlypartial. So we need a similarity measure over partiallyspecified preference structures. A partial preferencestructure can be thought of as the set of linear extensionsconsistent with the partial order. We define the dis-similarity between two partial preference structuressimply as the average dis-similarity between all pairs oflinear extensions in the two sets. This measure also hasrange [0 1] and satisfies the triangel inequality, but it isnot a metric because the distance between two identicalpartial orders that are not complete orders is alwayspositive. But this is desirable if the two orders representthe preferences of two different users, since the completepreference orders of the two may actually differ.

Computing this distance measure is closely related to theproblem of computing the number of linear extensionsof a finite partial order. That problem is known to be #P- complete (Brightwell & Winkler 1991). We use theMarkov chain based approximationalgorithm of (Bubley & Dyer 1998), whichalmost uniformly samples the space oflinear extensions and runs in polynomialtime. To generate each sample linearextension, the algorithm involves running aMonte Carlo simulation of a Markov chainfor a fixed number of iterations. Thecomplexity of the distance measurealgorithm used in DIVA is O(nm2) in whichn is the number of users in the case base andm is the number of movies in the moviedatabase.

After computing the distance between theactive user and each preference structure inthe database, we choose the most similarpreference structure and then choose thesampled linear extension for the active userthat is most similar to that preferencestructure. In this way we retain all thedirectly elicited user preferences and obtaina complete preference structure for theactive user, guided by the preferences in thecase base. In effect, the preferencestructures in the case base are used asattractors, indicating in which direction tocomplete the partial preference structure ofthe active user. In order to savecomputation time, we compute the similarity only overthe top 100 ranked movies in each pair of partialpreference structures.

Incorporating user feedback

DIVA permits the user to provide feedback concerninglong-term and short-term preferences. The long-termpreference feedback is added to the stored partialpreference structure obtained from the originalLike/OK/Dislike list. If the user saw a movie and likedit, the movie is added to the Like list, as shown in Figure4(b). If the user saw a movie and disliked it or if didn’t see a movie but is confident he wouldn’t like it,the movie is added to the Dislike list. The short-termpreference feedback is stored separately from the long-term preferences and is forgotten after the current searchis ended. Movies the user tags as being a near miss areconsidered preferred to those tagged as being not evenclose. A preference link is created from every near missmovie to every not even close movie, as shown in Figure4(a).

The new preference structure representing the user isnow the union of the updated long-term preferencestructure and the structure resulting from the short-termfeedback. The process of generating a recommendationlist is now rerun, using the new updated preferencestructure as the input to the case retrieval algorithm.

(b)

Figure 4: Preference structure of the user feedback asseen in Figure 3. (a) Temporary feedback information (b)Permanent feedback information is incorporated into theuser’s initial preferences.

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Databases

DIVA contains both a movie database and a userpreference case base. We built the initial case base usingthe EachMovie collaborative filtering database providedby Digital Equipment Corporation. The Digital systemsresearch center assembled the database by running acollaborative filtering system for 18 months. TheEachMovie database contains 72916 users, 2811983numeric ratings and 1628 movies. To represent userpreferences, EachMovie use numeric rating scaleranging from 0 (awful) to 1 (excellent), in increments 0.2. To populate our case base, we chose 500 users outof the 72916 users such that each user rated at least 20movies. The average number of ratings per user over all500 users is around 70 movies.

Since the EachMovie database did not contain sufficientattribute information for our purposes, we obtainedmovie attributes from the Microsoft Cinemania 94CDROM. Our movie database contains 2000 movieswith 9 attributes including actors/actresses, director,genre, professional film critic star rating, MPAA rating,country of production, running time, year released andtitle. Of the 1628 movies in EachMovie, only 500 appearin the Cinemania database. So we removed from theEachMovie rankings for all those movies that are notpresent in Cinemania. We then converted the preferencestructures represented as numeric ratings in Eachmovieto partial order preference structures in the obvious way:For each user, a movie sl is preferable to movie s2 if theuser’s rating for movie sl is greater than that for movies2.

Empirical Analysis

We evaluated the quality of DIVA’s recommendationsand those generated using the GroupLens (Resnick1994) collaborative filtering technique over our databaseof 500 users. We used the precision and recall metricscommonly used in information retrieval (Salton 1983) our evaluation criteria. In the present context, precisionindicates how many movies in a recommended list wereactually liked by the user. Recall indicates how manymovies out of all movies liked by the user were predictedcorrectly. We formed our test set by randomly takingout 10 users from the case base. For each user in the testset, we divided the user’s partial preference structureinto two sets that are observed set O1 and unobserved set02. Since the partial value function used by DIVA addsinformation not in the preference structure stored in thecase base, we disabled this portion of the system.Hence, the recommendations were generated using onlythe case-based elicitation portion of the system.

We ran the evaluation of DIVA by using the preferencestructure of the observed set to simulate elicitation froma new user. Based on the closest matching preferencestructure, we predicted unobserved items in 02, i.e. thebulk of the Like list. We generated a recommendationlist of length 1/6 of all movies that the user rated, whichfor all users in the experimental set was a subset of thenumber of items in 02. We chose the value 1/6 in orderto maximize precision at the expense of recall becausefrom a user standpoint, the desirability of the items inthe recommendation list is more important than findingall items of interest in the data base.

We ran 100 experiments with each of 10 users. We setthe number of iterations in our sampling algorithm to 50,100, and 150 and the number of linear set to 10, 30, and50. For each user, we randomly kept 3 movies from his"Like" list and tried to predict the remaining movies inhis original "Like" list. The results are shown in Table 1,averaged over all 10 users.

We observed that if the number of linear extensions isgreater than 30 and the number of iterations is greaterthan 100, the precision and recall do not change much.

We ran the same set of experiments using the GroupLenscollaborative filtering technique. GroupLens (Resniek etal 1994, Konstan et al 1998) is a collaborative filteringsystem that helps News readers to find articles ofinterest. Each News reader rates a number of articles on a5 point numeric scale. The system uses these ratings todetermine which users are most similar to each other andthen predicts how much the user will like new articlesbased on ratings from similar users.

Number of 10 30 50linearextensionsNumber of 50,100,150 50,100,150 50,100,150iterationsPrecision 80%,83%,83%81%, 86%,86%84%,85%,86%

38%,40%,40%38%,40%,40%40%,40%,40%RecallTable 1: Average precision and recall for DIVA’s case-based

elicitation algorithm.

GroupLens uses a similarity metric based on the Pearsoncorrelation coefficient (Pindyck & Rubinfeld 1991). Themeasure assumes that preferences are represented withnumeric ratings. Thus, for this portion of the experimentwe worked with the original numeric ratingrepresentation of the preferences in our case base of 500users. The correlation between the user K and any user Lin the case base defined as follows:

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~,~ ( gi- Kavg ) ( Li- Lave i

~i (gi-gavg)2 ~i (Zi-Zavg)2

In which K,v~, L~v8 are the average ratings of user K andL, respectively. K~, L~ are the rating of the users K and Lto the article i. The summations over i are over the itemsfor which both users K and L have rated. The correlationcoefficient weights between -1 (disagree) and 1(completely agree). It indicates how much the user Ktends to agree with the user L on those articles that theyboth rated. Predictions for movies that one user did notrate are then produced by using the correlation toproduce a weighted sum over all users in the case base.The precision and recall using GroupLens techniquewere 65% and 35% respectively. The best precision andrecall for DIVA were 86% and 40%, respectively, so thecase-based elicitation technique in DIVA outperformedthe GroupLens technique along both dimensions.

This result is not surprising given the properties of thesimilarity measures. The GroupLens measure has anadvantage that it is fast and easy to implement. However,it has a disadvantage that it is insensitive to the size ofthe set of movies that both users have rated. In anextreme case, the preferences of two users can bemaximally similar if they have only one movie incommon that they rated and they agreed on that rating.In contrast, the distance measure used in DIVAconsiders all movies that the two users have rated.Experiments we conducted to examine the set of usersranked similar to a given user showed that the DIVAmeasure does not rate two users as being similar unlesstheir preferences agree over a set of reasonable size. As aconsequence of this property, the GroupLens measuredoes not satisfy the triangle inequality. In addition tobeing intuitively desirable, the triangle inequality can beexploited to reduce computational effort by computingbounds on similarity.

Related Work

The Automated Travel Assistant (ATA) (Linden 1997) a system for recommending airline flights. It usesdecision-theoretic techniques to determine userpreferences and takes an incremental approach toelicitation. The ATA system elicits some userpreferences concerning airline, price, and non-stop vsindirect, and combines this with default preferences(prefer cheaper flights, prefer fewer stops) to obtain complete preference structure. It then presents the topranked flights to the user, as well as some extremesolutions: cheapest flight, most direct flight. If the useris not satisfied with the recommendations, he can modify

the model of his preferences by manipulating a graphicalrepresentation of the function used to represent thepreferences. ATA and DIVA differ in their approach toincremental elicitation. While DIVA incrementallyobtains increasing amounts of preference informationfrom the user, ATA allows the user to incrementallymodify a always complete preference structure. The userprovides feedback to ATA by directly manipulating thesystem’s internal representation of preferences. Incontrast, the feedback mechanism in DIVA is intended toallow the user to communicate about the proposedsolutions in a way that is natural for the applicationdomain. Finally, whereas ATA applies a single set ofdefaults to every user, the defaults used in DIVA aredetermined by searching the case base, using the initiallyelicited preferences.

Basu et al (Basu 1998) describe an approach generating recommendations that combines contentinformation and collaborative information. The contentinformation includes value for 26 features in the movieselection domain such as genre, actors/actresses, anddirector. The collaborative information is a triple (user,movie, rating). The hybrid feature is created based on theobservation that genre is the content feature that usersmost often think of while choosing a movie. Aftercreating the hybrid features, they then use Ripper (Cohen1995) to learn a user’s preferences. The case basecontains 260 users and 45,000 movie ratings on scale of1 - 10. The average precision and the recall of thesystem are 83% and 34%, respectively.

Conclusions and Future Research

This paper has described the first attempt to usedecision-theoretic techniques in design of a collaborativefiltering system. DIVA addresses several difficultproblems in building recommender systems, includingthe distinction between a user’s general tastes and hisimmediate interests, and provision for the user toprovide feedback if unsatisfied with therecommendations. Several difficult technical problemsremain to be solved. Our representation of short-termpreferences is rather crude. We would like to be able torepresent short-term preferences using as rich arepresentation as that for long-term preferences and to beable to merge the two even when conflicts exist. Inaddition to distinguishing between long and short-termpreferences, a recommender system should be able toaccount for the fact that people’s preferences evolveover time. This would require a system to keep track ofthe time that each piece of preference information wasobtained and to notice when newly expressedpreferences conflict with older preferences.

A problem for DIVA and other collaborative filteringsystems is the computational cost of computingsimilarity when the case base becomes very large. Weare examining the user of hierarchical clustering of the

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case base in order to reduce the computational cost ofcase retrieval. An interesting question is how muchaccuracy we lose in the recommendations produced vshow much computation time we save.

To save computation time, we currently use the roughheuristic of computing similarity over only the top 100ranked movies. We would like to experiment with otherheuristics that involve sampling the preference structurein other ways.

The elicitation of pariwise preferences using the Like,OK, and Dislike lists results in a ranking of movies intoonly three categories. But the internal representationsupports an arbitrary number of categories. We arecurrently working on augmenting the interface so thatthe user can graphically specify a richer set ofpreferences by directly positioning movies within eachlist on a vertical axis. We expect this will improve theaccuracy of the recommendations.

AcknowledgementsThis work was partially supported by NSF grant IRI-9509165. The EachMovie database was generouslyprovided by Digital Equipment Corporation. Thanks toVu Ha, Preerapol Meomeeg and Dr. Hanh Pham for helpwith the implementation and for useful discussions.

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