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81
Parameter learning of logic programs for symbolicstatistical modeling
 Journal of Artificial Intelligence Research
, 2001
"... We propose a logical/mathematical framework for statistical parameter learning of parameterized logic programs, i.e. de nite clause programs containing probabilistic facts with a parameterized distribution. It extends the traditional least Herbrand model semantics in logic programming to distributio ..."
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Cited by 124 (21 self)
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We propose a logical/mathematical framework for statistical parameter learning of parameterized logic programs, i.e. de nite clause programs containing probabilistic facts with a parameterized distribution. It extends the traditional least Herbrand model semantics in logic programming to distribution semantics, possible world semantics with a probability distribution which is unconditionally applicable to arbitrary logic programs including ones for HMMs, PCFGs and Bayesian networks. We also propose a new EM algorithm, the graphical EM algorithm, thatrunsfora class of parameterized logic programs representing sequential decision processes where each decision is exclusive and independent. It runs on a new data structure called support graphs describing the logical relationship between observations and their explanations, and learns parameters by computing inside and outside probability generalized for logic programs. The complexity analysis shows that when combined with OLDT search for all explanations for observations, the graphical EM algorithm, despite its generality, has the same time complexity as existing EM algorithms, i.e. the BaumWelch algorithm for HMMs, the InsideOutside algorithm for PCFGs, and the one for singly connected Bayesian networks that have beendeveloped independently in each research eld. Learning experiments with PCFGs using two corpora of moderate size indicate that the graphical EM algorithm can signi cantly outperform the InsideOutside algorithm. 1.
Towards Combining Inductive Logic Programming with Bayesian Networks
, 2001
"... Recently, new representation languages that integrate first order logic with Bayesian networks have been developed. Bayesian logic programs are one of these languages. In this paper, we present results on combining Inductive Logic Programming (ILP) with Bayesian networks to learn both the qualitativ ..."
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Cited by 82 (12 self)
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Recently, new representation languages that integrate first order logic with Bayesian networks have been developed. Bayesian logic programs are one of these languages. In this paper, we present results on combining Inductive Logic Programming (ILP) with Bayesian networks to learn both the qualitative and the quantitative components of Bayesian logic programs. More precisely, we show how to combine the ILP setting learning from interpretations with scorebased techniques for learning Bayesian networks. Thus, the paper positively answers Koller and Pfeffer's question, whether techniques from ILP could help to learn the logical component of first order probabilistic models.
Probabilistic inductive logic programming
 In ALT
, 2004
"... Abstract. Probabilistic inductive logic programming aka. statistical relational learning addresses one of the central questions of artificial intelligence: the integration of probabilistic reasoning with machine learning and first order and relational logic representations. A rich variety of diffe ..."
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Cited by 70 (9 self)
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Abstract. Probabilistic inductive logic programming aka. statistical relational learning addresses one of the central questions of artificial intelligence: the integration of probabilistic reasoning with machine learning and first order and relational logic representations. A rich variety of different formalisms and learning techniques have been developed. A unifying characterization of the underlying learning settings, however, is missing so far. In this chapter, we start from inductive logic programming and sketch how the inductive logic programming formalisms, settings and techniques can be extended to the statistical case. More precisely, we outline three classical settings for inductive logic programming, namely learning from entailment, learning from interpretations, and learning from proofs or traces, and show how they can be adapted to cover stateoftheart statistical relational learning approaches. 1
Probabilistic Logic Learning
 ACMSIGKDD Explorations: Special issue on MultiRelational Data Mining
, 2004
"... The past few years have witnessed an significant interest in probabilistic logic learning, i.e. in research lying at the intersection of probabilistic reasoning, logical representations, and machine learning. A rich variety of di#erent formalisms and learning techniques have been developed. This pap ..."
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Cited by 43 (10 self)
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The past few years have witnessed an significant interest in probabilistic logic learning, i.e. in research lying at the intersection of probabilistic reasoning, logical representations, and machine learning. A rich variety of di#erent formalisms and learning techniques have been developed. This paper provides an introductory survey and overview of the stateof theart in probabilistic logic learning through the identification of a number of important probabilistic, logical and learning concepts.
Naive Bayesian Classification of Structured Data
, 2003
"... In this paper we present 1BC and 1BC2, two systems that perform naive Bayesian classification of structured individuals. The approach of 1BC is to project the individuals along firstorder features. These features are built from the individual using structural predicates referring to related objects ..."
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Cited by 33 (0 self)
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In this paper we present 1BC and 1BC2, two systems that perform naive Bayesian classification of structured individuals. The approach of 1BC is to project the individuals along firstorder features. These features are built from the individual using structural predicates referring to related objects (e.g. atoms within molecules), and properties applying to the individual or one or several of its related objects (e.g. a bond between two atoms). We describe an individual in terms of elementary features consisting of zero or more structural predicates and one property; these features are treated as conditionally independent in the spirit of the naive Bayes assumption. 1BC2 represents an alternative firstorder upgrade to the naive Bayesian classifier by considering probability distributions over structured objects (e.g., a molecule as a set of atoms), and estimating those distributions from the probabilities of its elements (which are assumed to be independent). We present a unifying view on both systems in which 1BC works in language space, and 1BC2 works in individual space. We also present a new, efficient recursive algorithm improving upon the original propositionalisation approach of 1BC. Both systems have been implemented in the context of the firstorder descriptive learner Tertius, and we investigate the differences between the two systems both in computational terms and on artificially generated data. Finally, we describe a range of experiments on ILP benchmark data sets demonstrating the viability of our approach.
Logical Bayesian Networks and their relation to other probabilistic logical models
 In Proceedings of 15th International Conference on Inductive Logic Pogramming (ILP05), volume 3625 of Lecture Notes in Artificial Intelligence
, 2005
"... We review Logical Bayesian Networks, a language for probabilistic logical modelling, and discuss its relation to Probabilistic Relational Models and Bayesian Logic Programs. 1 Probabilistic Logical Models Probabilistic logical models are models combining aspects of probability theory with aspects of ..."
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Cited by 31 (9 self)
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We review Logical Bayesian Networks, a language for probabilistic logical modelling, and discuss its relation to Probabilistic Relational Models and Bayesian Logic Programs. 1 Probabilistic Logical Models Probabilistic logical models are models combining aspects of probability theory with aspects of Logic Programming, firstorder logic or relational languages. Recently a variety of languages to describe such models has been introduced. For some languages techniques exist to learn such models from data. Two examples are Probabilistic Relational Models (PRMs) [4] and Bayesian Logic Programs (BLPs) [5]. These two languages are probably the most popular and wellknown in the Relational Data Mining community. We introduce a new language, Logical Bayesian Networks (LBNs) [2], that is strongly related to PRMs and BLPs yet solves some of their problems with respect to knowledge representation (related to expressiveness and intuitiveness). PRMs, BLPs and LBNs all follow the principle of Knowledge Based Model Construction: they offer a language that can be used to specify general probabilistic logical knowledge and they provide a methodology to construct a propositional model based on this knowledge when given a specific
Adaptive Bayesian logic programs
 PROCEEDINGS OF THE ELEVENTH CONFERENCE ON INDUCTIVE LOGIC PROGRAMMING (ILP01), VOLUME 2157 OF LNCS
, 2001
"... First order probabilistic logics combine a first order logic with a probabilistic knowledge representation. In this context, we introduce continuous Bayesian logic programs, which extend the recently introduced Bayesian logic programs to deal with continuous random variables. Bayesian logic programs ..."
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Cited by 29 (10 self)
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First order probabilistic logics combine a first order logic with a probabilistic knowledge representation. In this context, we introduce continuous Bayesian logic programs, which extend the recently introduced Bayesian logic programs to deal with continuous random variables. Bayesian logic programs tightly integrate definite logic programs with Bayesian networks. The resulting framework nicely seperates the qualitative (i.e. logical) component from the quantitative (i.e. the probabilistic) one. We also show how the quantitative component can be learned using a gradientbased maximum likelihood method.
Stochastic Logic Programs: Sampling, Inference and Applications
 In Proceedings of the Sixteenth Annual Conference on Uncertainty in Artificial Intelligence (UAI2000
, 2000
"... Algorithms for exact and approximate inference in stochastic logic programs (SLPs) are presented, based respectively, on variable elimination and importance sampling. We then show how SLPs can be used to represent prior distributions for machine learning, using (i) logic programs and (ii) Baye ..."
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Cited by 29 (5 self)
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Algorithms for exact and approximate inference in stochastic logic programs (SLPs) are presented, based respectively, on variable elimination and importance sampling. We then show how SLPs can be used to represent prior distributions for machine learning, using (i) logic programs and (ii) Bayes net structures as examples. Drawing on existing work in statistics, we apply the MetropolisHasting algorithm to construct a Markov chain which samples from the posterior distribution. A Prolog implementation for this is described. We also discuss the possibility of constructing explicit representations of the posterior. 1 Introduction A stochastic logic program (SLP) is a probabilistic extension of a normal logic program that has been proposed as a flexible way of representing complex probabilistic knowledge; generalising, for example, Hidden Markov Models, Stochastic ContextFree Grammars and Markov nets (Muggleton, 1996; Cussens, 1999). However, we need to ask (i) whether this i...
Basic Principles of Learning Bayesian Logic Programs
 Institute for Computer Science, University of Freiburg
, 2002
"... Bayesian logic programs tightly integrate definite logic programs with Bayesian networks in order to... In this paper, we present results on combining Inductive Logic Programming with Bayesian networks to learn both the qualitative and the quantitative components of Bayesian logic programs from data ..."
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Cited by 24 (3 self)
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Bayesian logic programs tightly integrate definite logic programs with Bayesian networks in order to... In this paper, we present results on combining Inductive Logic Programming with Bayesian networks to learn both the qualitative and the quantitative components of Bayesian logic programs from data. More precisely, we show how the qualitative components can be learned by combining the inductive logic programming setting learning from interpretations with scorebased techniques for learning Bayesian networks. The estimation of the quantitative components is reduced to the corresponding problem of (dynamic) Bayesian networks
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 22 (7 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