Preliminaries and Factor Graphs and Parameterised Factor Graphs

Table of Links

Abstract and 1. Introduction

2. Preliminaries and 2.1 Factor Graphs and Parameterised Factor Graphs

   2.2 The Colour Passing Algorithm

3. The LIFAGU Algorithm

4. Empirical Evaluation

5. Conclusion, Acknowledgements, and References

2 Preliminaries

In this section, we begin by defining FGs as a propositional representation for a joint probability distribution between random variables (randvars) and then introduce PFGs, which combine probabilistic models and first-order logic. Thereafter, we describe the well-known CP algorithm to lift a propositional model, i.e., to transform an FG into a PFG with equivalent semantics.

2.1 Factor Graphs and Parameterised Factor Graphs

Clearly, the size of the FG increases with an increasing number of individuals even though it is not necessary to distinguish between individuals because there are symmetries in the model (the factor f1 occurs two times and the factor f2 occurs four times). In other words, the probability of an epidemic does not depend on knowing which specific individuals are being sick, but only on how many individuals are being sick. To exploit such symmetries in a model, PFGs can be used. We define PFGs, first introduced by Poole [13], based on the definitions given by Gehrke et al. [5]. PFGs combine first-order logic with probabilistic models, using logical variables (logvars) as parameters in randvars to represent sets of indistinguishable randvars, forming parameterised randvars (PRVs).