Dimitar Sht. Shterionov

Inference and Learning in Probabilistic Logic Programs using Weighted Boolean Formulas

Probabilistic logic programs are logic programs in which some of the facts are annotated with probabilities. This paper investigates how classical inference and learning tasks known from the graphical model community can be tackled for probabilistic logic programs. Several such tasks such as computing the marginals given evidence and learning from (partial) interpretations have not really been addressed for probabilistic logic programs before. The rst contribution of this paper is a suite of ecient algorithms for various inference tasks. It is based on a conversion of the program and the queries and evidence to a weighted Boolean formula. This allows us to reduce the inference tasks to well-studied tasks such as weighted model counting, which can be solved using state-of-the-art methods known from the graphical model and knowledge compilation literature. The second contribution is an algorithm for parameter estimation in the learning from interpretations setting. The algorithm employs Expectation Maximization, and is built on top of the developed inference algorithms. The proposed approach is experimentally evaluated. The results show that the inference algorithms improve upon the state-of-the-art in probabilistic logic programming and that it is indeed possible to learn the parameters of a probabilistic logic program from interpretations.

The Most Probable Explanation for Probabilistic Logic Programs with Annotated Disjunctions

Probabilistic logic languages, such as ProbLog and CP-logic, are probabilistic generalizations of logic programming that allow one to model probability distributions over complex, structured domains. Their key probabilistic constructs are probabilistic facts and annotated disjunctions to represent binary and mutli-valued random variables, respectively. ProbLog allows the use of annotated disjunctions by translating them into probabilistic facts and rules. This encoding is tailored towards the task of computing the marginal probability of a query given evidence MARG, but is not correct for the task of finding the most probable explanation MPE with important applications e.g., diagnostics and scheduling. In this work, we propose a new encoding of annotated disjunctions which allows correct MARG and MPE. We explore from both theoretical and experimental perspective the trade-off between the encoding suitable only for MARG inference and the newly proposed general approach.

Implementation and Performance of Probabilistic Inference Pipelines

In order to handle real-world problems, state-of-the-art probabilistic logic and learning frameworks, such as ProbLog, reduce the expensive inference to an efficient Weighted Model Counting. To do so ProbLog employs a sequence of transformation steps, called an inference pipeline. Each step in the probabilistic inference pipeline is called a pipeline component. The choice of the mechanism to implement a component can be crucial to the performance of the system. In this paper we describe in detail different ProbLog pipelines. Then we perform a empirical analysis to determine which components have a crucial impact on the efficiency. Our results show that the Boolean formula conversion is the crucial component in an inference pipeline. Our main contributions are the thorough analysis of ProbLog inference pipelines and the introduction of new pipelines, one of which performs very well on our benchmarks.

Compacting Boolean Formulae for Inference in Probabilistic Logic Programming

Knowledge compilation converts Boolean formulae for which some inference tasks are computationally expensive into a representation where the same tasks are tractable. ProbLog is a state-of-the-art Probabilistic Logic Programming system that uses knowledge compilation to reduce the expensive probabilistic inference to an efficient weighted model counting. Motivated to improve ProbLog’s performance we present an approach that optimizes Boolean formulae in order to speed-up knowledge compilation. We identify 7 Boolean subformulae patterns that can be used to re-write Boolean formulae. We implemented an algorithm with polynomial complexity which detects and compacts 6 of these patterns. We employ our method in the inference pipeline of ProbLog and conduct extensive experiments. We show that our compaction method improves knowledge compilation and consecutively the overall inference performance. Furthermore, using compaction reduces the number of time-outs, allowing us to solve previously unsolvable problems.

Crucial components in probabilistic inference pipelines

ProbLog [7, 10] is a general purpose Probabilistic Logic Programming (PLP) language. It extends Prolog with uncertain knowledge encoded as probabilistic facts. A probabilistic fact, p: f states that the fact f is true with probability p.