Evaluating Inference Algorithms for the Prolog Factor Language

Abstract

Over the last years there has been some interest in models that combine first-order logic and probabilistic graphical models to describe large scale domains, and in efficient ways to perform inference on these domains. Prolog Factor Language (PFL) is a extension of the Prolog language that allows a natural representation of these first-order probabilistic models (either directed or undirected). PFL is also capable of solving probabilistic queries on these models through the implementation of four inference algorithms: variable elimination, belief propagation, lifted variable elimination and lifted belief propagation. We show how these models can be easily represented using PFL and then we perform a comparative study between the different inference algorithms in four artificial problems.

Lifted graphical models: a survey

“…An overview of lifted inference from the perspective of top-down vs bottom-up inference is given by Kersting (2012), and an in-depth tutorial by Kersting et al (2011). Lifted inference is a very active area of research, and there are many recent publications that have not been discussed here, including work on knowledge compilation Van den Broeck and Davis, 2012;Van den Broeck et al, 2014), message passing Hadiji et al, 2011;Kersting et al, 2010a), online inference (Nath and Domingos, 2010), lifted inference for models with continuous variables and Kalman filtering (Choi et al, 2010(Choi et al, , 2011a, variational inference (Choi and Amir, 2012;Bui et al, 2013), lifted inference with evidence (Bui et al, 2012;Van den Broeck and Davis, 2012;Van den Broeck and Darwiche, 2013), work that examines the completeness of lifted inference formalisms (Van den Broeck, 2011;Taghipour et al, 2013c;Jaeger and Van den Broeck, 2012;Jaeger, 2014), and many other advanced topics, e.g., (Kiddon and Domingos, 2011;Gogate and Domingos, 2011;Choi et al, 2011b;Gomes and Santos Costa, 2012;Jha et al, 2010;Hadiji and Kersting, 2013;Taghipour et al, 2013a;Sarkhel et al, 2014).…”

Expressing preferences in logic programming using an infinite-valued logic

“…Other systems that are related to PrefLog are certain manyvalued extensions of logic programming and in particular the probabilistic ones (such as for example [9,10,14,17,19,22,24]). In probabilistic extensions of logic programming, the programmer is usually required to rank rules (or facts) with a certainty factor or to use a special form of implication in rules that has attached a numerical attenuation factor.…”

Lifted Variable Elimination for Probabilistic Logic Programming

“…As progress has been made on managing large networks, it has become clear that often the same factor appears repeatedly in the network, thus suggesting the use of templates generalizing individual factors, or parametric factors (Kisynski and Poole 2009a). The Prolog Factor Language (PFL) (Gomes and Costa 2012) extends Prolog to support probabilistic reasoning with parametric factors or parfactors. The PFL syntax for a factor is T ype F ; φ ; C. T ype refers to the type of the network over which the parfactor is defined (bayes for directed networks or markov for undirected ones); F is a sequence of Prolog terms that define sets of random variables under the constraints in C. The set of all logical variables in F is named L. C is a list of Prolog goals that impose bindings on the logical variables in L (the successful substitutions for the goals in C are the valid values for the variables in L).…”

“…The lifted ve algorithm of (Gomes and Costa 2012) represents the adaptation of GC-FOVE to the PFL language.…”

“…In (Gomes and Costa 2012), the Prolog Factor Language (PFL, for short) was proposed as a Prolog extension to support probabilistic reasoning with parfactors. PFL exploits the state-of-art algorithm GC-FOVE (Taghipour et al 2013), which redefines the operations described in (Milch et al 2008) to be correct for whatever constraint representation is being used.…”