Probabilistic graphical models are an elegant framework which combines uncertainty (probabilities) and logical structure (independence constraints) to compactly represent complex, real-world phenomena. The framework is quite general in that many of the commonly proposed statistical models (Kalman filters, hidden Markov models, Ising models) can be described as graphical models. Graphical models have enjoyed a surge of interest in the last two decades, due both to the flexibility and power of the representation and to the increased ability to effectively learn and perform inference in large networks.

}, author = {Daphne Koller and Nir Friedman and Lise Getoor and Benjamin Taskar}, editor = {Lise Getoor and Benjamin Taskar} } @book {getoor:prm-ch-srl-book07, title = {Probabilistic Relational Models}, series = {An Introduction to Statistical Relational Learning}, volume = {1}, year = {2007}, pages = {129--174}, publisher = {MIT Press}, organization = {MIT Press}, edition = {1}, chapter = {5}, abstract = {Probabilistic relational models (PRMs) are a rich representation language for structured statistical models. They combine a frame-based logical representation with probabilistic semantics based on directed graphical models (Bayesian networks). This chapter gives an introduction to probabilistic relational models, describing semantics for attribute uncertainty, structural uncertainty, and class uncertainty. For each case, learning algorithms and some sample results are presented.

}, author = {Lise Getoor and Nir Friedman and Daphne Koller and Avi Pfeffer and Benjamin Taskar}, editor = {Lise Getoor and Benjamin Taskar} } @book {getoor:rdm-book01, title = {Learning Probabilistic Relational Models}, series = {Relational Data Mining}, volume = {1}, year = {2001}, pages = {307--335}, publisher = {Springer-Verlag}, organization = {Springer-Verlag}, edition = {1}, chapter = {13}, abstract = {Probabilistic relational models (PRMs) are a language for describing statistical models over typed relational domains. A PRM models the uncertainty over the attributes of objects in the domain and uncertainty over the relations between the objects. The model specifies, for each attribute of an object, its (probabilistic) dependence on other attributes of that object and on attributes of related objects. The dependence model is defined at the level of classes of objects. The class dependence model is instantiated for any object in the class, as appropriate to the particular context of the object (i.e., the relations between this objects and others). PRMs can also represent uncertainty over the relational structure itself, e.g., by specifying a (class-level) probability that two objects will be related to each other. PRMs provide a foundation for dealing with the noise and uncertainty encountered in most real-world domains. In this chapter, we show that the compact and natural representation of PRMs allows them to be learned directly from an existing relational database using well-founded statistical techniques. We give an introduction to PRMs and an overview of methods for learning them. We show that PRMs provide a new framework for relational data mining, and offer new challenges for the endeavor of learning relational models for real-world domains.

}, author = {Lise Getoor and Nir Friedman and Daphne Koller and Avi Pfeffer}, editor = {Saso Dzeroski and Nada Lavrac} }