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SLGAD Resolution for Inference on logic programs with annotated disjunctions

FUNDAMENTA INFORMATICAE 2010年第3-4期102卷 429-466页

作者： Riguzzi, Fabrizio Univ Ferrara ENDIF I-44100 Ferrara Italy

logic programs with annotated disjunctions (LPADs) allow to express probabilistic information in logic programming. The semantics of an LPAD is given in terms of the well-founded models of the normal logic programs obtained by selecting one disjunct from each ground LPAD clause. Inference on LPADs can be performed using either the system Ailog2, that was developed for the Independent Choice logic, or SLDNFAD, an algorithm based on SLDNF. However, both of these algorithms run the risk of going into infinite loops and of performing redundant computations. In order to avoid these problems, we present SLGAD resolution that computes the (conditional) probability of a ground query from a range-restricted LPAD and is based on SLG resolution for normal logic programs. As SLG, it uses tabling to avoid some infinite loops and to avoid redundant computations. The performances of SLGAD are evaluated on classical benchmarks for normal logic programs under the well-founded semantics, namely a 2-person game and the ancestor relation, and on games of dice. SLGAD is compared with Ailog2 and SLDNFAD on the problems in which they do not go into infinite loops, namely those that are described by a modularly acyclic program. The results show that SLGAD is sometimes slower than Ailog2 and SLDNFAD but, if the program requires the repeated computations of the same goals, as for the dice games, then SLGAD is faster than both.

关键词： Probabilistic logic Programming Well-Founded Semantics logic programs with annotated disjunctions SLG Resolution

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ALLPAD: approximate learning of logic programs with annotated disjunctions

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MACHINE LEARNING 2008年第2-3期70卷 207-223页

作者： Riguzzi, Fabrizio Univ Ferrara Dipartimento Ingn I-44100 Ferrara Italy

logic programs with annotated disjunctions (LPADs) provide a simple and elegant framework for representing probabilistic knowledge in logic programming. In this paper we consider the problem of learning ground LPADs starting from a set of interpretations annotated with their probability. We present the system ALLPAD for solving this problem. ALLPAD modifies the previous system LLPAD in order to tackle real world learning problems more effectively. This is achieved by looking for an approximate solution rather than a perfect one. A number of experiments have been performed on real and artificial data for evaluating ALLPAD, showing the feasibility of the approach.

关键词： inductive logic programming probabilistic logic programming statistical relational learning logic programs with annotated disjunctions

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Approximate Inference for logic programs with annotated disjunctions

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20th International Conference on Inductive logic Programming (ILP)

作者： Bragaglia, Stefano Riguzzi, Fabrizio Univ Ferrara ENDIF Univ Bologna DEIS I-44100 Ferrara Italy

ISBN: (纸本)9783642212949;9783642212956

logic programs with annotated disjunctions (LPADs) are a promising language for Probabilistic Inductive logic Programming. In order to develop efficient learning systems for LPADs, it is fundamental to have high-performing inference algorithms. The existing approaches take too long or fail for large problems. In this paper we adapt to LPAD the approaches for approximate inference that have been developed for ProbLog, namely k-best and Monte Carlo. k-Best finds a lower bound of the probability of a query by identifying the k most probable explanations while Monte Carlo estimates the probability by smartly sampling the space of programs. The two techniques have been implemented in the cplint suite and have been tested on real and artificial datasets representing graphs. The results show that both algorithms are able to solve larger problems often in less time than the exact algorithm.

关键词： Probabilistic Inductive logic Programming logic programs with annotated disjunctions ProbLog

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The Most Probable Explanation for Probabilistic logic programs with annotated disjunctions 1

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24th International Conference on Inductive logic Programming (ILP)

作者： Shterionov, Dimitar Renkens, Joris Vlasselaer, Jonas Kimmig, Angelika Meert, Wannes Janssens, Gerda KULeuven Leuven Belgium

ISBN: (数字)9783319237084

ISBN: (纸本)9783319237084;9783319237077

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.

关键词： Probabilistic logic programming Statistical relational learning Most Probable Explanation logic programs with annotated disjunctions ProbLog

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Inference with logic programs with annotated disjunctions under the Well Founded Semantics

Inference with Logic Programs with Annotated Disjunctions un...

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24th International Conference on logic Programming (ICLP)

作者： Riguzzi, Fabrizio Univ Ferrara ENDIF I-44100 Ferrara Italy

ISBN: (纸本)9783540899815

logic programs with annotated disjunctions (LPADs) allow to express probabilistic information in logic programming. The semantics of an LPAD is given in terms of well founded models of the normal logic programs obtained by selecting one disjunct from each ground LPAD clause. The paper presents SLGAD resolution that computes the (conditional) probability of a ground query from an LPAD and is based on SLG resolution for normal logic programs. SLGAD is evaluated on classical benchmarks for well founded semantics inference algorithms, namely the stalemate game and the ancestor relation. SLGAD is compared with Cilog2 and SLDNFAD, an algorithm based on SLDNF, on the programs that are modularly acyclic. The results show that SLGAD deals correctly with cyclic programs and, even if it is more expensive than SLDNFAD on problems where SLDNFAD succeeds, is faster than Cilog2 when the query is true in an exponential number of instances.

关键词： Probabilistic logic Programming Well Founded Semantics logic programs with annotated disjunctions SLG resolution

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Reasoning on logic programs with annotated disjunctions

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INTELLIGENZA ARTIFICIALE 2012年第1期6卷 77-96页

作者： Bragaglia, Stefano Univ Bologna DEIS Viale Risorgimento Bologna Italy

Probabilistic Inductive logic Programming and Statistical Relational Learning are families of techniques that are exploited in Machine Learning applications to perform advanced tasks in several domains. Every day the size and complexity of such problems increases and advanced, expressive and efficient tools are needed to successfully solve them. The literature proposes several algorithms to cope with these problems, each of them with its own quirks and perks. Among various solutions, logic Programming with annotated disjunctions (LPAD) is one of the more attractive formalisms, thanks to the expressiveness and readability of its language. Unfortunately, its most advanced implementations are lacking efficient features and techniques that have been introduced for other formalisms, such as ProbLog. In this work, after introducing LPADs and an inference algorithm for computing the probability of a query, we investigate four different approximated algorithms, inspired by similar work done in ProbLog. In particular, we present each algorithm and we evaluate its performances on real and artificial datasets. The results show that our approaches have performances that are usually in line with ProbLog. The Monte Carlo algorithm, however, has performances that are better than the exact approach in terms of both the maximum size of the problems and the execution time, with a neglectable loss in the accuracy of the result.

关键词： Probabilistic Inductive logic Programming logic programs with annotated disjunctions ProbLog

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MCINTYRE: A Monte Carlo System for Probabilistic logic Programming

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FUNDAMENTA INFORMATICAE 2013年第4期124卷 521-541页

作者： Riguzzi, Fabrizio Univ Ferrara Dipartimento Matemat & Informat I-44122 Ferrara Italy

Probabilistic logic Programming is receiving an increasing attention for its ability to model domains with complex and uncertain relations among entities. In this paper we concentrate on the problem of approximate inference in probabilistic logic programming languages based on the distribution semantics. A successful approximate approach is based on Monte Carlo sampling, that consists in verifying the truth of the query in a normal program sampled from the probabilistic program. The ProbLog system includes such an algorithm and so does the cplint suite. In this paper we propose an approach for Monte Carlo inference that is based on a program transformation that translates a probabilistic program into a normal program to which the query can be posed. The current sample is stored in the internal database of the Yap Prolog engine. The resulting system, called MCINTYRE for Monte Carlo INference wiTh Yap REcord, is evaluated on various problems: biological networks, artificial datasets and a hidden Markov model. MCINTYRE is compared with the Monte Carlo algorithms of ProbLog and cplint and with the exact inference of the PITA system. The results show that MCINTYRE is faster than the other Monte Carlo systems.

关键词： Probabilistic logic Programming Monte Carlo Methods logic programs with annotated disjunctions ProbLog

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Speeding Up Inference for Probabilistic logic programs

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COMPUTER JOURNAL 2014年第3期57卷 347-363页

作者： Riguzzi, Fabrizio Univ Ferrara Dipartimento Matemat & Informat I-44122 Ferrara Italy

Probabilistic logic Programming (PLP) allows one to represent domains containing many entities connected by uncertain relations and has many applications in particular in Machine Learning. PITA is a PLP algorithm for computing the probability of queries, which exploits tabling, answer subsumption and Binary Decision Diagrams (BDDs). PITA does not impose any restriction on the programs. Other algorithms, such as PRISM, reduce computation time by imposing restrictions on the program, namely that subgoals are independent and that clause bodies are mutually exclusive. Another assumption that simplifies inference is that clause bodies are independent. In this paper, we present the algorithms PITA(IND,IND) and PITA(OPT). PITA(IND,IND) assumes that subgoals and clause bodies are independent. PITA(OPT) instead first checks whether these assumptions hold for subprograms and subgoals: if they do, PITA(OPT) uses a simplified calculation, otherwise it resorts to BDDs. Experiments on a number of benchmark datasets show that PITA(IND,IND) is the fastest on datasets respecting the assumptions, while PITA(OPT) is a good option when nothing is known about a dataset.

关键词： logic programming Probabilistic logic Programming distribution semantics logic programs with annotated disjunctions PRISM ProbLog

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Summarizing significant subgraphs by probabilistic logic programming

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INTELLIGENT DATA ANALYSIS 2019年第6期23卷 1299-1312页

作者： Bellodi, Elena Satoh, Ken Sugiyama, Mahito Univ Ferrara Dept Engn Ferrara Italy Natl Inst Informat Tokyo Japan PRESTO JST Tokyo Japan

Although recent advances of significant subgraph mining enable us to find subgraphs that are statistically significantly associated with the class variable from graph databases, it is challenging to interpret the resulting subgraphs due to their massive number and their propositional representation. Here we represent graphs by probabilistic logic programming and solve the problem of summarizing significant subgraphs by structure learning of probabilistic logic programs. Learning probabilistic logical models leads to a much more interpretable, expressive and succinct representation of significant subgraphs. We empirically demonstrate that our approach can effectively summarize significant subgraphs with keeping high accuracy.

关键词： Subgraph summarization significant subgraph mining statistical significance probabilistic logic programming logic programs with annotated disjunctions

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Expectation maximization over binary decision diagrams for probabilistic logic programs

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INTELLIGENT DATA ANALYSIS 2013年第2期17卷 343-363页

作者： Bellodi, Elena Riguzzi, Fabrizio Univ Ferrara ENDIF Dipartimento Ingn I-44122 Ferrara Italy

Recently much work in Machine Learning has concentrated on using expressive representation languages that combine aspects of logic and probability. A whole field has emerged, called Statistical Relational Learning, rich of successful applications in a variety of domains. In this paper we present a Machine Learning technique targeted to Probabilistic logic programs, a family of formalisms where uncertainty is represented using logic Programming tools. Among various proposals for Probabilistic logic Programming, the one based on the distribution semantics is gaining popularity and is the basis for languages such as ICL, PRISM, ProbLog and logic programs with annotated disjunctions. This paper proposes a technique for learning parameters of these languages. Since their equivalent Bayesian networks contain hidden variables, an Expectation Maximization (EM) algorithm is adopted. In order to speed the computation up, expectations are computed directly on the Binary Decision Diagrams that are built for inference. The resulting system, called EMBLEM for "EM over Bdds for probabilistic logic programs Efficient Mining", has been applied to a number of datasets and showed good performances both in terms of speed and memory usage. In particular its speed allows the execution of a high number of restarts, resulting in good quality of the solutions.

关键词： Statistical relational learning probabilistic inductive logic programming probabilistic logic programs logic programs with annotated disjunctions expectation maximization binary decision diagrams

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