About ProbReM

A Probabilistic Relational Model (PRM), [1], [2], is a directed probabilistic graphical model used in the field of Statistical Relational Learning (SRL). PRMs define a language that can be used to describe the relationships - structural and probabilistic - between classes and variables, and thus allows representing dependencies between sets of objects. Heckerman et al. [4] introduced the directed acyclic probabilistic entity-relationship (DAPER) model which is based on the entity-relationship model used to design relational databases. ProbReM is built on the DAPER specification of a PRM, thus it requires the data to be modelled with a entity-relationship diagram. The probabilistic structure defines the dependencies among the probabilistic attributes of the entity-relationship model. The parent and the child attribute of a dependency can be associated with different entities or relationships; Getoor et al. refer to the path from child to parent attribute the slotchain whereas Heckerman et al. associate a more general constraint with the dependency instead. The traditional slotchain is the most common constraint, ProbReM makes use of both expressions depending which one is more appropriate in the context. Relationships are either of type 1:n or m:n, therefore it is possible that attribute objects have multiple parent attribute objects for the same probabilistic dependency. Aggregation of the parent attribute objects is a common way to deal with this problem, ProbReM allows to define generic aggregation functions (avg, min, max). Different inference methods have been implemented, all of which are based on Markov Chain Monte Carlo methods.

The section Using ProbReM illustrates the approach used in ProbReM, and the example model is a walkthrough with an applied example. For theoretical background, we recommend Introduction to Statistical Relational Learning [3] by Lise Getoor & Ben Taskar for an excellent introduction to the different approaches introduced in the SRL field. For more background on using MCMC in graphical models, D. Koller & N. Friedman’s Probabilistic Graphical Models: Principles and Techniques [5] is an excellent reference.

Related Research

Many different approaches are pursued in relational learning, below an incomplete list of frameworks that have already been published.

• Alchemy by Pedro Domingos‘s research group at the University of Washington.
• Primula by Manfred Jaeger at the Aalborg university in Denmark.
• BLOG by Brian Milch
• IBAL by Avi Pfeffer at Harvard

For a more complete list and more information and about other frameworks, Manfred Jaeger has started a Comparative Study of Probabilistic Logic Languages and Systems that serves as platform to compare different approaches on different challenge problems.

Requirements

• Python
• Numpy / Scipy
• Matplotlib / Pylab
• iPython

Source code

It is hard to draw a line between the core functionality of the framework and the functionality needed by a specific ProbReM project. For this reason the source code will be provided as a folder and the framework has to be added to the PYTHONPATH of the ProbReM project. In the future it might be useful to create a proper Python package. The code is available as is on github.

See Using ProbReM for how to start a new project.

References

[1]	N. Friedman, L. Getoor, D. Koller, and A. Pfeffer. Learning probabilistic relational models. In IJCAI, pages 1300–1309, 1999.

[2]	Lise Getoor. Learning probabilistic relational models. In SARA ’02: Proceedings of the 4th Interna- tional Symposium on Abstraction, Reformulation, and Approximation, pages 322–323. Springer- Verlag, 2000.

[3]	Lise Getoor and Ben Taskar. Introduction to Statistical Relational Learning (Adaptive Computation and Machine Learning). The MIT Press, 2007.

[4]	D. Heckerman, C. Meek, and D. Koller. Probabilistic models for relational data. Technical Report MSR-TR-2004-30, Microsoft Research, 2004.

[5]	D. Koller and N. Friedman. Probabilistic Graphical Models: Principles and Techniques. MIT Press, 2009.