Hierarchical Probabilistic relational models for collaborative Filtering Jack Newton and russell greiner Department of Computing Science University of Alberta Edmonton. AB. Canada T6G 2E8 i newton, greiner ocs. alberta.ca abstract where each tuple lists facts about a person, then facts about a movie, together with a vote(e. g, a numbe This paper applies Probabilistic Relational between 1 and 5. We could build a classifier that Models(PRMs) to the Collaborative Filter predicts this vote, based on facts about a person and ing task, focussing on the EachMovie data movie - here about George and about SoM set. We first learn a standard PRM. and Notice this prediction does not consider other people show that its performance is competitive with (e. g, people "similar"to George)or other movies (like the best known techniques. We then de- SoM) fine a hierarchical PrM, which extends stan- dard PRMs by dynamically refining classes The other main type of recommender system, " collal into hierarchies, which improves the expres- orative filtering", addresses this deficiently, by using siveness as well as the context sensitivity of associations: If person Pl appears similar to persor the PRM. Finally, we show that hierarchical P2(perhaps based on their previous"liked movies") PRMs achieve state-of-the-art results on this and P2 liked x, then perhaps Pi will like X as well. A dataset pure collaboration-only system would use only a ma- ix, whose(i, j) element is the vote that person i gives movie j, which could be blank. The challenge, then 1 Introduction is using this matrix effectively, to acquire the patterns that will help us predict future votes. While there are a number of other techniques that have proven ef- Personlized recommender systems, which recommend specific products(e. g, books, movies) to individuals fective here, such as clustering, PCA, and K-nearest- neighbor [UF98b [UF98al, notice classical Machine have become very prevalent. The challenge faced by learning techniques do not work here, as there is no redicting what each individual will simple way to map this matrix into a simple fixed-size a pure content-based recommender will base this on only facts about the products themselves and about Of course, we would like to use both content and collab- orative information. Here, we can include, as training the individual (potential)purchaser. This enables us data, facts about the people, facts about the movies to express each possible purchase as a simple vector of and a set of (P, M, v)records, which specifies that attributes, some about the product and others about the person. If we also know who previously liked what, Person P gave movie M the vote of v. we can view this as a standard labelled data sample, The challenge is how to use all of this information and use standard machine learning techniques [ Mit97 to predict how George will vote on SoM. Here, we to learn a classifier. which we can later use to deter- want to use facts about george and about SoM, and mine whether a(novel) person will like some (novel) also find and exploit collaborative properties, that deal with people similar to George (in terms of liking sim- To make this concrete. consider a movie recommenda- ar movies), and movies similar to SoM(in terms of tion system which tries to determine whether a spec eing liked by similar people George like SoundOfMusic(SoM)? A cole.g, will Stepping back, the challenge here is learning a distri- fied person will like a specified mo nt-based bution over a set of databases, here descriptions of sets system could use a large Peoplex Movies database, of people and sets of products, as well as their votesHierarchical Probabilistic Relational Models for Collaborative Filtering Jack Newton and Russell Greiner Department of Computing Science University of Alberta Edmonton, AB, Canada T6G 2E8 { newton, greiner }@cs.ualberta.ca Abstract This paper applies Probabilistic Relational Models (PRMs) to the Collaborative Filter￾ing task, focussing on the EachMovie data set. We first learn a standard PRM, and show that its performance is competitive with the best known techniques. We then de- fine a hierarchical PRM, which extends stan￾dard PRMs by dynamically refining classes into hierarchies, which improves the expres￾siveness as well as the context sensitivity of the PRM. Finally, we show that hierarchical PRMs achieve state-of-the-art results on this dataset. 1 Introduction Personlized recommender systems, which recommend specific products (e.g., books, movies) to individuals, have become very prevalent. The challenge faced by these system is predicting what each individual will want. A pure content-based recommender will base this on only facts about the products themselves and about the individual (potential) purchaser. This enables us to express each possible purchase as a simple vector of attributes, some about the product and others about the person. If we also know who previously liked what, we can view this as a standard labelled data sample, and use standard machine learning techniques [Mit97] to learn a classifier, which we can later use to deter￾mine whether a (novel) person will like some (novel) item. To make this concrete, consider a movie recommenda￾tion system which tries to determine whether a spec￾ified person will like a specified movie — e.g., will George like SoundOfMusic (SoM)? A content-based system could use a large People×Movies database, where each tuple lists facts about a person, then facts about a movie, together with a vote (e.g., a number between 1 and 5). We could build a classifier that predicts this vote, based on facts about a person and movie — here about George and about SoM. Notice this prediction does not consider other people (e.g., people “similar” to George) or other movies (like SoM). The other main type of recommender system, “collab￾orative filtering”, addresses this deficiently, by using associations: If person P1 appears similar to person P2 (perhaps based on their previous “liked movies”), and P2 liked X, then perhaps P1 will like X as well. A pure collaboration-only system would use only a ma￾trix, whose hi, ji element is the vote that person i gives to movie j, which could be blank. The challenge, then, is using this matrix effectively, to acquire the patterns that will help us predict future votes. While there are a number of other techniques that have proven ef￾fective here, such as clustering, PCA, and K-nearest￾neighbor [UF98b] [UF98a], notice classical Machine learning techniques do not work here, as there is no simple way to map this matrix into a simple fixed-size vector of attributes. Of course, we would like to use both content and collab￾orative information. Here, we can include, as training data, facts about the people, facts about the movies, and a set of hP, M, Vi records, which specifies that person P gave movie M the vote of V. The challenge is how to use all of this information to predict how George will vote on SoM. Here, we want to use facts about George and about SoM, and also find and exploit collaborative properties, that deal with people similar to George (in terms of liking sim￾ilar movies), and movies similar to SoM (in terms of being liked by similar people). Stepping back, the challenge here is learning a distri￾bution over a set of databases, here descriptions of sets of people and sets of products, as well as their votes