Results 1  10
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144
Probabilistic Theorem Proving
"... Many representation schemes combining firstorder logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable elimination and belief propagation, neither of which take logic ..."
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Cited by 70 (23 self)
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Many representation schemes combining firstorder logic and probability have been proposed in recent years. Progress in unifying logical and probabilistic inference has been slower. Existing methods are mainly variants of lifted variable elimination and belief propagation, neither of which take logical structure into account. We propose the first method that has the full power of both graphical model inference and firstorder theorem proving (in finite domains with Herbrand interpretations). We first define probabilistic theorem proving, their generalization, as the problem of computing the probability of a logical formula given the probabilities or weights of a set of formulas. We then show how this can be reduced to the problem of lifted weighted model counting, and develop an efficient algorithm for the latter. We prove the correctness of this algorithm, investigate its properties, and show how it generalizes previous approaches. Experiments show that it greatly outperforms lifted variable elimination when logical structure is present. Finally, we propose an algorithm for approximate probabilistic theorem proving, and show that it can greatly outperform lifted belief propagation. 1
Clp(bn): Constraint logic programming for probabilistic knowledge
 In Proceedings of the 19th Conference on Uncertainty in Artificial Intelligence (UAI03
, 2003
"... Abstract. In Datalog, missing values are represented by Skolem constants. More generally, in logic programming missing values, or existentially quantified variables, are represented by terms built from Skolem functors. The CLP(BN) language represents the joint probability distribution over missing v ..."
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Cited by 63 (7 self)
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Abstract. In Datalog, missing values are represented by Skolem constants. More generally, in logic programming missing values, or existentially quantified variables, are represented by terms built from Skolem functors. The CLP(BN) language represents the joint probability distribution over missing values in a database or logic program by using constraints to represent Skolem functions. Algorithms from inductive logic programming (ILP) can be used with only minor modification to learn CLP(BN) programs. An implementation of CLP(BN) is publicly available as part of YAP Prolog at
and J.Huang. “Using OBDDs for Efficient Query Evaluation on Probabilistic Databases
 In Proc. SUM
, 2008
"... Abstract. We consider the problem of query evaluation for tuple independent probabilistic databases and Boolean conjunctive queries with inequalities but without selfjoins. We approach this problem as a construction problem for ordered binary decision diagrams (OBDDs): Given a query q and a probabi ..."
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Cited by 41 (15 self)
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Abstract. We consider the problem of query evaluation for tuple independent probabilistic databases and Boolean conjunctive queries with inequalities but without selfjoins. We approach this problem as a construction problem for ordered binary decision diagrams (OBDDs): Given a query q and a probabilistic database D, we construct in polynomial time an OBDD such that the probability of q(D) can be computed linearly in the size of that OBDD. This approach is applicable to a large class of queries, including the hierarchical queries, i.e., the Boolean conjunctive queries without selfjoins that admit PTIME evaluation on any tupleindependent probabilistic database, hierarchical queries extended with inequalities, and nonhierarchical queries on restricted databases. 1
On the Implementation of the Probabilistic Logic Programming Language ProbLog
 UNDER CONSIDERATION FOR PUBLICATION IN THEORY AND PRACTICE OF LOGIC PROGRAMMING
, 2003
"... The past few years have seen a surge of interest in the field of probabilistic logic learning and statistical relational learning. In this endeavor, many probabilistic logics have been developed. ProbLog is a recent probabilistic extension of Prolog motivated by the mining of large biological networ ..."
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Cited by 41 (9 self)
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The past few years have seen a surge of interest in the field of probabilistic logic learning and statistical relational learning. In this endeavor, many probabilistic logics have been developed. ProbLog is a recent probabilistic extension of Prolog motivated by the mining of large biological networks. In ProbLog, facts can be labeled with probabilities. These facts are treated as mutually independent random variables that indicate whether these facts belong to a randomly sampled program. Different kinds of queries can be posed to ProbLog programs. We introduce algorithms that allow the efficient execution of these queries, discuss their implementation on top of the YAPProlog system, and evaluate their performance in the context of large networks of biological entities.
Gradientbased boosting for Statistical Relational Learning: The Relational Dependency Network Case
, 2011
"... Abstract. Dependency networks approximate a joint probability distribution over multiple random variables as a product of conditional distributions. Relational Dependency Networks (RDNs) are graphical models that extend dependency networks to relational domains. This higher expressivity, however, co ..."
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Cited by 39 (17 self)
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Abstract. Dependency networks approximate a joint probability distribution over multiple random variables as a product of conditional distributions. Relational Dependency Networks (RDNs) are graphical models that extend dependency networks to relational domains. This higher expressivity, however, comes at the expense of a more complex modelselection problem: an unbounded number of relational abstraction levels might need to be explored. Whereas current learning approaches for RDNs learn a single probability tree per random variable, we propose to turn the problem into a series of relational functionapproximation problems using gradientbased boosting. In doing so, one can easily induce highly complex features over several iterations and in turn estimate quickly a very expressive model. Our experimental results in several different data sets show that this boosting method results in efficient learning of RDNs when compared to stateoftheart statistical relational learning approaches. 1
CPlogic: A Language of Causal Probabilistic Events and Its Relation to Logic Programming
"... We examine the relation between constructive processes and the concept of causality. We observe that causality has an inherent dynamic aspect, i.e., that, in essence, causal information concerns the evolution of a domain over time. Motivated by this observation, we construct a new representation lan ..."
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Cited by 33 (4 self)
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We examine the relation between constructive processes and the concept of causality. We observe that causality has an inherent dynamic aspect, i.e., that, in essence, causal information concerns the evolution of a domain over time. Motivated by this observation, we construct a new representation language for causal knowledge, whose semantics is defined explicitly in terms of constructive processes. This is done in a probabilistic context, where the basic steps that make up the process are allowed to have nondeterministic effects. We then show that a theory in this language defines a unique probability distribution over the possible outcomes of such a process. This result offers an appealing explanation for the usefulness of causal information and links our explicitly dynamic approach to more static causal probabilistic modeling languages, such as Bayesian networks. We also show that this language, which we have constructed to be a natural formalization of a certain kind of causal statements, is closely related to logic programming. This result demonstrates that, under an appropriate formal semantics, a rule of a normal, a disjunctive or a certain kind of probabilistic logic program can be interpreted as a description of a causal event.
The PITA System: Tabling and Answer Subsumption for Reasoning under Uncertainty
 UNDER CONSIDERATION FOR PUBLICATION IN THEORY AND PRACTICE OF LOGIC PROGRAMMING
, 2003
"... Many real world domains require the representation of a measure of uncertainty. The most common such representation is probability, and the combination of probability with logic programs has given rise to the field of Probabilistic Logic Programming (PLP), leading to languages such as the Independen ..."
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Cited by 27 (11 self)
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Many real world domains require the representation of a measure of uncertainty. The most common such representation is probability, and the combination of probability with logic programs has given rise to the field of Probabilistic Logic Programming (PLP), leading to languages such as the IndependentChoice Logic, Logic Programs with Annotated Disjunctions (LPADs), Problog, PRISM and others. These languages share a similar distribution semantics, and methods have been devised to translate programs between these languages. The complexity of computing the probability of queries to these general PLP programs is very high due to the need to combine the probabilities of explanations that may not be exclusive. As one alternative, the PRISM system reduces the complexity of query answering by restricting the form of programs it can evaluate. As an entirely different alternative, Possibilistic Logic Programs adopt a simpler metric of uncertainty than probability. Each of these approaches – general PLP, restricted PLP, and Possibilistic Logic Programming – can be useful in different domains depending on the form of uncertainty to be represented, on the form of programs needed to model problems, and on the scale of
K.: Parameter learning in probabilistic databases: A least squares approach
, 2008
"... Abstract. We introduce the problem of learning the parameters of the probabilistic database ProbLog. Given the observed success probabilities of a set of queries, we compute the probabilities attached to facts that have a low approximation error on the training examples as well as on unseen examples ..."
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Cited by 21 (6 self)
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Abstract. We introduce the problem of learning the parameters of the probabilistic database ProbLog. Given the observed success probabilities of a set of queries, we compute the probabilities attached to facts that have a low approximation error on the training examples as well as on unseen examples. Assuming Gaussian error terms on the observed success probabilities, this naturally leads to a least squares optimization problem. Our approach, called LeProbLog, is able to learn both from queries and from proofs and even from both simultaneously. This makes it flexible and allows faster training in domains where the proofs are available. Experiments on real world data show the usefulness and effectiveness of this least squares calibration of probabilistic databases. 1
Expectation Maximization over Binary Decision Diagrams for Probabilistic Logic Programs
"... 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 M ..."
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Cited by 20 (13 self)
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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 andLogic 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.