Probabilistic Relational Models

Daphne Koller

Computer Science Department, Stanford University, Stanford, CA 94305-9010
http://robotics.stanford.edu/~koller
koller@cs.stanford.edu



Abstract. Probabilistic models provide a sound and coherent foundation 
for dealing with the noise and uncertainty encountered in most realworld domains. 
Bayesian networks are a language for representing complex 
probabilistic models in a compact and natural way. A Bayesian
network can be used to reason about any attribute in the domain, given
any set of observations. It can thus be used for a variety tasks, including
prediction, explanation, and decision making. The probabilistic semantics 
also gives a strong foundation for the task of learning models from
data. Techniques currently exist for learning both the structure and the
parameters, for dealing with missing data and hidden variables, and for
discovering causal structure.
One of the main limitations of Bayesian networks is that they represent
the world in terms of a fixed set of attributes . Like propositional logic,
they are incapable of reasoning explicitly about entities, and thus cannot
represent models over domains where the set of entities and the relations
between them are not fixed in advance. As a consequence, Bayesian networks 
are limited in their ability to model large and complex domains.
Probabilistic relational models are a language for describing probabilistic 
models based on the significantly more expressive basis of relational
logic. They allow the domain to be represented in terms of entities, their
properties, and the relations between them. These models represent the
uncertainty over the properties of an entity, representing its probabilistic
dependence both on other properties of that entity and on properties of
related entities. They can even represent uncertainty over the relational
structure itself. Some of the techniques for Bayesian network learning
can be generalized to this setting, but the learning problem is far from
solved. Probabilistic relational models provide a new framework, and new
challenges, for the endeavor of learning relational models for real-world
domains.
References

1.	G.F. Cooper. The computational complexity of probabilistic inference using
Bayesian belief networks. Artificial Intelligence, 42:393405, 1990.
2.	A. Dempster, N. Laird, and D. Rubin. Maximum likelihood from incomplete data
via the EM algorithm. Journal of the Royal Statistical Society, 39 (Series B):138,
1977.
3.	N. Friedman. Learning belief networks in the presence of missing values and hidden
variables. In Proc. ICML, 1997.
4.	N. Friedman, L. Getoor, D. Koller, and A. Pfeffer. Learning probabilistic relational
models. In Proc. IJCAI, 1999.
5.	D. Heckerman. A tutorial on learning with Bayesian networks. Technical Report
MSR-TR-95-06, Microsoft Research, 1995.
6.	D. Koller and A. Pfeffer. Learning probabilities for noisy first-order rules. In Proc.
IJCAI, pages 13161321, 1997.
7.	D. Koller and A. Pfeffer. Probabilistic frame-based systems. In Proc. AAAI, 1998.
8.	S. L. Lauritzen. The EM algorithm for graphical association models with missing
data. Computational Statistics and Data Analysis, 19:191201, 1995.
9.	Steffen L. Lauritzen and David J. Spiegeihalter. Local computations with probabilities 
on graphical structures and their application to expert systems. Journal of
the Royal Statistical Society, B 50(2):157224, 1988.
10.	L. Ngo and P. Haddawy. Answering queries from context-sensitive probabilistic
knowledge bases. Theoretical Computer Science, 1996.
11.	J. Pearl. Probabilistic Reasoning in Intelligent Systems: Networks of Plausible
Inference. Morgan Kaufmann, 1988.
12.	A. Pfeffer, D. Koller, B. Milch, and K. Takusagawa. SPOOK: A system for probabilistic 
object-oriented knowledge representation. Submitted to UAI 99, 1999.
13.	D. Poole. Probabilistic Horn abduction and Bayesian networks. Artificial Intelligence, 
64:81129, 1993.
14.	P. Spirtes, C. Glymour, and R. Scheines. Causation, prediction, and search.
Springer Verlag, 1993.
