Hierarchical Probabilistic Relational Models

1
Hierarchical Probabilistic Relational Models for
Collaborative Filtering
Jack Newton (newton_at_cs.ualberta.ca) and Russ
Greiner (greiner_at_cs.ualberta.ca)
Introduction, Problem Set Up
Our Approach
Experiments and Results
Introduction
PRMs
The EachMovie Dataset

• Personalized Recommender Systems recommend
  specific products
• For example Amazon.coms 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 users 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.

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

Algorithm Absolute Deviation
CR 1.257
BC 1.127
BN 1.143
VSIM 2.113
PRM 1.26
Algorithm Absolute Deviation
CR 0.994
BC 1.103
BN 1.066
VSIM 2.136
hPRM 1.060
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 Johns Vote on Star Wars to help
  predict
• Johns Vote on T3
• Freds Vote on Star Wars
• (Why? PRMs 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 4352, 1998. FGKP99 Nir Friedman,
Lise Getoor, Daphne Koller, and Avi Pfeffer.
Learning probabilistic relational models. In
IJCAI-99, pages 13001309, 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 580587, Madison, WI, 1998.