Hierarchical Probabilistic Relational Models
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Hierarchical Probabilistic Relational Models for Collaborative Filtering. John.Age. StarWars.TheaterStatus. John.Education. StarWars.VideoStatus. John.Gender. Vote JohnOnStarWars .Score. Jack Newton ([email protected]) and Russ Greiner ([email protected]).

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Hierarchical Probabilistic Relational Models for Collaborative Filtering

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Hierarchical probabilistic relational models for collaborative filtering

Hierarchical Probabilistic Relational Models

for Collaborative Filtering

John.Age

StarWars.TheaterStatus

John.Education

StarWars.VideoStatus

John.Gender

VoteJohnOnStarWars.Score

Jack Newton ([email protected]) and Russ Greiner ([email protected])

Introduction, Problem Set Up

Our Approach

Experiments and Results

Introduction

PRMs

The EachMovie Dataset

  • Personalized Recommender Systems recommend specific products

    • For example: Amazon.com’s book recommender; Yahoo!’s LAUNCHcast music recommender

    • Very popular!

  • We designed/built a recommender system – “tadpole” – using

    • Probabilistic Relational Models (PRMs) [KP98]

    • Hierarchical PRMs (hPRMs) [Get02]

    • applied to EachMovie dataset

  • A PRM encodes

    • class-Level dependencies

    • used to make inferences about a particular instance of a class.

  • Learning

  • Must first learn PRM from the data [FGK99]

    • algorithm for learning a legal structure for a PRM

    • estimating parameters for that PRM.

  • Often used to test recommender systems

  • 72,916 users, 1,628 movies, 2,811,983 votes

  • Composed of three tables:

    • Person: describes people; fields: age, gender, zip code, …

    • Movie: describes movies; fields: genre, …

    • Vote: user’s rating on movie; {0,1,2,3,4,5}

Person

Action-Movie

Age

Theater Status

Score

Person

Movie

Video Status

Movie

Education

Age

Action-Vote

Theater Status

AVG

Romantic-Comedy-Movie

Theater Status

Score

Gender

Education

Video Status

Romantic-

Comedy-Vote

Comedy

Thriller

AVG

Action

Recommender Systems

Video Status

Slapstick-Comedy-Movie

Theater Status

Gender

Score

Video Status

Slapstick-Comedy-Vote

RomanticComedy

SlapstickComedy

Thriller-Movie

Score

Theater Status

  • Content-based recommenders

    • use only facts about products and individual (potential) purchaser

    • Eg: a movie recommender system: just People  Movies database

      • Each tuple

        •  25, Male, Calif, … ,  Action, Budget, …, 4 

      • lists facts about a person, facts about a movie, a vote  {1,.., 5}

      • Use dataset to learn a classifier, that predicts vote for novel person/movie pairs.

  • Collaborative Filtering-based recommenders

    • base recommendations on ratings other “similar” users have assigned to similar products.

    • If person P1 appears similar to person P2

      • (perhaps based on their previous “liked movies”)

      • and P2 liked X,

      • perhaps P1 will like X.

  • Our goal: a cohesive framework for combining all types of information:

    • properties of product

    • properties of user,

    • voting patterns of all users,

    • As well voting patterns of a given user

    • to make accurate recommendations.

  • Probabilistic Relational Models, and an extension to PRMs called Hierarchical PRMs (hPRMs), offer a probabilistic framework we can apply to the recommender system problem domain [Get02].

  • Evaluation: applying the PRM framework to the EachMovie dataset.

Video Status

Score

Thriller-Vote

Figure 3a: A class hierarchy

Figure 3b: An hPRM learned on the EachMovie dataset

Vote

Results

Figure 1: A standard PRM

  • Inference

  • Given PRM encoding the class-level dependencies,

  • Generate a Ground Bayesian Network for each specific object

    • Use same structure/parameters for each instance of class

  • Use standard Bayesian Network inference algorithm

    • Different results for child nodes as different data for parents, …

  • Compared to

    • Correlation (CR), Bayesian Clustering (BC), Bayesian Network (BN),

    • Vector Similarity (VSIM) as presented in [BHK98]

  • Metric: Mean Absolute Error (MAE) [BHK98]

  • 5-fold cross-validation

Figure 2: A ground Bayesian Network

Hierarchical PRMs

Contributions

  • Two limitation of PRMs (which motivate hPRMs):

    • Vote.Score can depend on attributes of related objects,

      • such as Person.Age,

      • but Vote.Score can NOT depend on itself in any way.

      • BAD: want John’s Vote on Star Wars to help predict

        • John’s Vote on T3

        • Fred’s Vote on Star Wars

      • (Why? PRM’s class-level dependency structure must be DAG)

    • Restricted to one dependency graph for Vote.Score

      • However, you could may want one dependency graph for movies of the Comedy genre, and another for the Action genre

  • hPRMs [Get02] address both problems:

    • hPRMs use a class hierarchy such as that in Figure 3a,

    • to learn the hPRM in Figure 3b:

  • Built PRM and hPRM models – learning, inference algorithms

  • Show that (h)PRMs can apply to recommender systems in general

  • Evaluated in context of EachMovie database, demonstrated competitive results against existing algorithms

  • Demonstrate superiority of hPRMs over standard PRMs.

Acknowledgements

Lise Getoor, for useful discussion, encouragement to pursue this line of work, and access to software and data that aided us in building our tadpole system.

Alberta Ingenuity, NSERC, and iCORE for funding.

References

[BHK98] John S. Breese, David Heckerman, and Carl Kadie. Empirical analysis of predictive algorithms

for collaborative filtering. In UAI98, pages 43–52, 1998.

[FGKP99] Nir Friedman, Lise Getoor, Daphne Koller, and Avi Pfeffer. Learning probabilistic relational

models. In IJCAI-99, pages 1300–1309, 1999.

[Get02] L. Getoor. Learning Statistical Models from Relational Data. PhD thesis, Stanford University, 2002.

[KP98] D. Koller and A. Pfeffer. Probabilistic frame based systems. In AAAI-98,pages 580–587, Madison, WI, 1998.


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