Computing most probable worlds of action probabilistic logic programs: scalable estimation for 1030,000 worlds

Abstract

The semantics of probabilistic logic programs (PLPs) is usually given through a possible worlds semantics. We propose a variant of PLPs called action probabilistic logic programs or ap-programs that use a two-sorted alphabet to describe the conditions under which certain real-world entities take certain actions. In such applications, worlds correspond to sets of actions these entities might take. Thus, there is a need to find the most probable world (MPW) for ap-programs. In contrast, past work on PLPs has primarily focused on the problem of entailment. This paper quickly presents the syntax and semantics of ap-programs and then shows a naive algorithm to solve the MPW problem using the linear program formulation commonly used for PLPs. As such linear programs have an exponential number of variables, we present two important new algorithms, called HOP and SemiHOP to solve the MPW problem exactly. Both these algorithms can significantly reduce the number of variables in the linear programs. Subsequently, we present a 296 S. Khuller et al."binary" algorithm that applies a binary search style heuristic in conjunction with the Naive, HOP and SemiHOP algorithms to quickly find worlds that may not be "most probable." We experimentally evaluate these algorithms both for accuracy (how much worse is the solution found by these heuristics in comparison to the exact solution) and for scalability (how long does it take to compute). We show that the results of SemiHOP are very accurate and also very fast: more than 10 30,000 worlds can be handled in a few minutes. Subsequently, we develop parallel versions of these algorithms and show that they provide further speedups.

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“…Further, there are also good heuristics (cf. [17,18]) that have been shown to provide highly accurate approximations with a reduced-size linear program.…”

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“…In this paper, we assume that information is properly extracted from a set of historic data and hence consistent; (recall that inconsistent information can only be handled in the AM, not the EM). A consistent knowledge base could also be obtained as a result of curation by experts, such that all inconsistencies were removed-see (Khuller et al 2007;Shakarian et al 2011) for algorithms for learning rules of this type.…”