MAP Inference in Probabilistic Answer Set Programs

Abstract

Reasoning with uncertain data is a central task in artificial intelligence. In some cases, the goal is to find the most likely assignment to a subset of random variables, named query variables, while some other variables are observed. This task is called Maximum a Posteriori (MAP). When the set of query variables is the complement of the observed variables, the task goes under the name of Most Probable Explanation (MPE). In this paper, we introduce the definitions of cautious and brave MAP and MPE tasks in the context of Probabilistic Answer Set Programming under the credal semantics and provide an algorithm to solve them. Empirical results show that the brave version of both tasks is usually faster to compute. On the brave MPE task, the adoption of a state-of-the-art ASP solver makes the computation much faster than a naive approach based on the enumeration of all the worlds.

Inference in Probabilistic Answer Set Programming Under the Credal Semantics

“…Increasing instances are: i2 = i1 ∪ {person (3). }, i3 = i2 ∪ {person (4). }, i4 = i3 ∪ {0.2::influences(2, 3).…”

“…}, i4 = i3 ∪ {0.2::influences(2, 3). }, i5 = i4 ∪ {0.7::influences (3,4). }, i6 = i5 ∪ {0.9::influences(4, 1).}.…”

“…For instance, model counting requires counting the models while probabilistic inference, e.g., in the probabilistic logic language ProbLog [11], requires summing the probabilities associated with the different models. Other tasks, such as decision theoretic inference [7], MAP and MPE inference [4,5,22], and probabilistic inference under the smProbLog language [23], require to aggregate the results obtained via inference, so they need two levels of aggregations. These tasks they were recently identified as Second Level Algebraic Model Counting (2AMC) tasks [17].…”

“…3 we cast inference in PASP as a 2AMC task and in Sect. 4 we test an implementation on top of the aspmc solver against the PASTA solver. Section 5 concludes the paper.…”