Learning the Parameters of Probabilistic Logic Programs from Interpretations

Gutmann, Bernd; Thon, Ingo; Raedt, Luc De

doi:10.1007/978-3-642-23780-5_47

Cited by 50 publications

(70 citation statements)

References 13 publications

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“…ProbLog [6] which is another probabilistic extension of Prolog also employs a BDD-based parameter learning algorithm [7]. However, variational Bayesian inference for ProbLog has not yet been proposed to our knowledge.…”

Section: Conclusion and Related Workmentioning

confidence: 99%

Variational Bayes Inference for Logic-Based Probabilistic Models on BDDs

Ishihata

Kameya

Sato

2012

Inductive Logic Programming

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Abstract. Statistical abduction is an attempt to define a probability distribution over explanations derived by abduction and to evaluate them using their probabilities. In statistical abduction, deterministic knowledge like rules and facts are described as logic formulas. However nondeterministic knowledge like preference and frequency seems difficult to represent as logic. Bayesian inference can reflect such knowledge on a prior and variational Bayes (VB) is known as an approximation method for it. In this paper, we propose VB for logic-based probabilistic models and show that our proposed method is efficient in evaluating abductive explanations about failure in a logic circuit and a metabolic pathway.

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Section: Conclusion and Related Workmentioning

confidence: 99%

Variational Bayes Inference for Logic-Based Probabilistic Models on BDDs

Ishihata

Kameya

Sato

2012

Inductive Logic Programming

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“…k-Best's ability to compile small, approximate BDDs is especially useful in the context of DTProbLog and parameter learning for ProbLog programs (Gutmann et al 2008(Gutmann et al , 2011. These algorithms build and store BDDs for a large number of queries.…”

Section: Examplementioning

confidence: 99%

“…A further disadvantage of k-best is found in parameter learning for ProbLog programs (Gutmann et al 2008(Gutmann et al , 2011 and the use of ProbLog in solving probabilistic decision problems ( Van den Broeck et al 2010). An example of such a decision problem is targeted advertising in social networks: in order to reduce advertising cost, one wishes to identify a small subset of nodes in a social network such that the expected number of people reached is maximized.…”

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confidence: 99%

k-Optimal: a novel approximate inference algorithm for ProbLog

2012

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ProbLog is a probabilistic extension of Prolog. Given the complexity of exact inference under ProbLog's semantics, in many applications in machine learning approximate inference is necessary. Current approximate inference algorithms for ProbLog however require either dealing with large numbers of proofs or do not guarantee a low approximation error. In this paper we introduce a new approximate inference algorithm which addresses these shortcomings. Given a user-specified parameter k, this algorithm approximates the success probability of a query based on at most k proofs and ensures that the calculated probability p is (1 − 1/e)p * ≤ p ≤ p * , where p * is the highest probability that can be calculated based on any set of k proofs. Furthermore a useful feature of the set of calculated proofs is that it is diverse. Our experiments show the utility of the proposed algorithm.

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“…In the present paper and [19], we have discussed a gradient descent approach to parameter learning for ProbLog in which the examples are ground facts together with their target probability. In [57], an approach to learning from interpretations based on an EM algorithm is introduced. There, each example specifies a possible world, that is, a set of ground facts together with their truth value.…”

Section: Related Work In Statistical Relational Learningmentioning

confidence: 99%

Probabilistic Inductive Querying Using ProbLog

Raedt

Kimmig

Gutmann

et al. 2010

Inductive Databases and Constraint-Based Data Mining

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We study how probabilistic reasoning and inductive querying can be combined within ProbLog, a recent probabilistic extension of Prolog. ProbLog can be regarded as a database system that supports both probabilistic and inductive reasoning through a variety of querying mechanisms. After a short introduction to ProbLog, we provide a survey of the different types of inductive queries that ProbLog supports, and show how it can be applied to the mining of large biological networks. IntroductionIn recent years, both probabilistic and inductive databases have received considerable attention in the literature. Probabilistic databases [1] allow one to represent and reason about uncertain data, while inductive databases [2] aim at tight integration of data mining primitives in database query languages. Despite the current interest in these types of databases, there have, to the best of the authors' knowledge, been no attempts to integrate these two trends of research. This chapter wants to contribute to a better understanding of the issues involved by providing a survey of the developments around ProbLog [3] 1 , an extension of Prolog, which supports both inductive and probabilistic querying. ProbLog has been motivated by the need to develop intelligent tools for supporting life scientists analyzing large biological networks. The analysis of such networks typically involves uncertain data, requiring probabilistic representations and inference, as well as the need to find patterns in data, and hence, supporting data mining. ProbLog can be conveniently regarded as a probabilistic database supporting several types of inductive and probabilistic queries. This paper provides an overview of the different types of queries that ProbLog supports.A ProbLog program defines a probability distribution over logic programs (or databases) by specifying for each fact (or tuple) the probability that it belongs to a randomly sampled program (or database), where probabilities are mutually independent. The semantics of ProbLog is then defined by the success probability of a query, which corresponds to the probability that the query succeeds in a randomly sampled program (or database). ProbLog is closely related to other probabilistic logics and probabilistic databases that have been developed over the past two decades to face the general need of combining deductive abilities with reasoning about uncertainty, see e.g. [4,5,6,7,8]. The semantics of ProbLog is studied in Section 10.2. In Section 10.10, we discuss related work in statistical relational learning.We now give a first overview of the types of queries ProbLog supports. Throughout the chapter, we use the graph in Figure 1(a) for illustration, inspired on the application in biological networks discussed in Section 10.9. It contains several nodes (representing entities) as well as edges (representing relationships). Furthermore, the edges are probabilistic, that is, they are present only with the probability indicated. Probabilistic Inference What is the probability that a query...

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Learning the Parameters of Probabilistic Logic Programs from Interpretations

Cited by 50 publications

References 13 publications

Variational Bayes Inference for Logic-Based Probabilistic Models on BDDs

Variational Bayes Inference for Logic-Based Probabilistic Models on BDDs

k-Optimal: a novel approximate inference algorithm for ProbLog

Probabilistic Inductive Querying Using ProbLog

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