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58
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 92 (19 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 77 (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.
A Perspective on Inductive Logic Programming
"... . The stateoftheart in inductive logic programming is surveyed by analyzing the approach taken by this field over the past 8 years. The analysis investigates the roles of 1) logic programming and machine learning, of 2) theory, techniques and applications, of 3) various technical problems address ..."
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Cited by 55 (8 self)
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. The stateoftheart in inductive logic programming is surveyed by analyzing the approach taken by this field over the past 8 years. The analysis investigates the roles of 1) logic programming and machine learning, of 2) theory, techniques and applications, of 3) various technical problems addressed within inductive logic programming. 1 Introduction The term inductive logic programming was first coined by Stephen Muggleton in 1990 [1]. Inductive logic programming is concerned with the study of inductive machine learning within the representations offered by computational logic. Since 1991, annual international workshops have been organized [28]. This paper is an attempt to analyze the developments within this field. Particular attention is devoted to the relation between inductive logic programming and its neighboring fields such as machine learning, computational logic and data mining, and to the role that theory, techniques and implementations, and applications play. The analysis...
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 34 (8 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.
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 26 (7 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 24 (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 23 (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...
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 21 (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.
A comparison of stochastic logic programs and Bayesian logic programs
 In IJCAI03 Workshop on Learning Statistical Models from Relational Data. IJCAI
, 2003
"... Firstorder probabilistic models are recognized as efficient frameworks to represent several realworld problems: they combine the expressive power of firstorder logic, which serves as a knowledge representation language, and the capability to model uncertainty with probabilities. Among existing mod ..."
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Cited by 16 (3 self)
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Firstorder probabilistic models are recognized as efficient frameworks to represent several realworld problems: they combine the expressive power of firstorder logic, which serves as a knowledge representation language, and the capability to model uncertainty with probabilities. Among existing models, it is usual to distinguish the domainfrequency approach from the possibleworlds approach. Bayesian logic programs (BLPs, which conveniently encode possibleworlds semantics) and stochastic logic programs (SLPs, often referred to as a domainfrequency approach) are promising probabilistic logic models in their categories. This paper is aimed at comparing the respective expressive power of these frameworks. We demonstrate relations between SLPs ’ and BLPs ’ semantics, and argue that SLPs can encode the same knowledge as a subclass of BLPs. We introduce extended SLPs which lift the latter result to any BLP. Converse properties are reviewed, and we show how BLPs can define the same semantics as complete, rangerestricted, nonrecursive SLPs. Algorithms that translate BLPs into SLPs (and vice versa) are provided, as well as worked examples of the intertranslations of SLPs and BLPs. 1
View learning for statistical relational learning: With an application to mammography
 Proceeding of the 19th International Joint Conference on Artificial Intelligence
, 2005
"... Statistical relational learning (SRL) constructs probabilistic models from relational databases. A key capability of SRL is the learning of arcs (in the Bayes net sense) connecting entries in different rows of a relational table, or in different tables. Nevertheless, SRL approaches currently are con ..."
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Cited by 15 (8 self)
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Statistical relational learning (SRL) constructs probabilistic models from relational databases. A key capability of SRL is the learning of arcs (in the Bayes net sense) connecting entries in different rows of a relational table, or in different tables. Nevertheless, SRL approaches currently are constrained to use the existing database schema. For many database applications, users find it profitable to define alternative “views ” of the database, in effect defining new fields or tables. Such new fields or tables can also be highly useful in learning. We provide SRL with the capability of learning new views. 1