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67
ProbLog: a probabilistic Prolog and its application in link discovery
 In Proceedings of 20th International Joint Conference on Artificial Intelligence
, 2007
"... We introduce ProbLog, a probabilistic extension of Prolog. A ProbLog program defines a distribution over logic programs by specifying for each clause the probability that it belongs to a randomly sampled program, and these probabilities are mutually independent. The semantics of ProbLog is then defi ..."
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Cited by 87 (14 self)
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We introduce ProbLog, a probabilistic extension of Prolog. A ProbLog program defines a distribution over logic programs by specifying for each clause the probability that it belongs to a randomly sampled program, and these 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. The key contribution of this paper is the introduction of an effective solver for computing success probabilities. It essentially combines SLDresolution with methods for computing the probability of Boolean formulae. Our implementation further employs an approximation algorithm that combines iterative deepening with binary decision diagrams. We report on experiments in the context of discovering links in real biological networks, a demonstration of the practical usefulness of the approach. 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 49 (6 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
Logical hidden markov models
 Journal of Artificial Intelligence Research
, 2006
"... Logical hidden Markov models (LOHMMs) upgrade traditional hidden Markov models to deal with sequences of structured symbols in the form of logical atoms, rather than flat characters. This note formally introduces LOHMMs and presents solutions to the three central inference problems for LOHMMs: evalu ..."
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Cited by 42 (10 self)
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Logical hidden Markov models (LOHMMs) upgrade traditional hidden Markov models to deal with sequences of structured symbols in the form of logical atoms, rather than flat characters. This note formally introduces LOHMMs and presents solutions to the three central inference problems for LOHMMs: evaluation, most likely hidden state sequence and parameter estimation. The resulting representation and algorithms are experimentally evaluated on problems from the domain of bioinformatics. 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 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.
Blog: Relational modeling with unknown objects
 ICML 2004 Workshop on Statistical Relational Learning and Its Connections
, 2004
"... In many realworld probabilistic reasoning problems, one of the questions we want to answer is: how many objects are out there? Examples of such problems range from multitarget tracking to extracting information from text documents. However, most probabilistic modeling formalisms — even firstorder o ..."
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Cited by 30 (1 self)
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In many realworld probabilistic reasoning problems, one of the questions we want to answer is: how many objects are out there? Examples of such problems range from multitarget tracking to extracting information from text documents. However, most probabilistic modeling formalisms — even firstorder ones — assume a fixed, known set of objects. We introduce a language called Blog for specifying probability distributions over relational structures that include varying sets of objects. In this paper we present Blog informally, by means of example models for multitarget tracking and citation matching. We discuss some attractive features of Blog models and some avenues of future work. 1.
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 25 (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
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.
The Independent Choice Logic and Beyond
"... Abstract. The Independent Choice Logic began in the early 90’s as a way to combine logic programming and probability into a coherent framework. The idea of the Independent Choice Logic is straightforward: there is a set of independent choices with a probability distribution over each choice, and a l ..."
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Cited by 18 (5 self)
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Abstract. The Independent Choice Logic began in the early 90’s as a way to combine logic programming and probability into a coherent framework. The idea of the Independent Choice Logic is straightforward: there is a set of independent choices with a probability distribution over each choice, and a logic program that gives the consequences of the choices. There is a measure over possible worlds that is defined by the probabilities of the independent choices, and what is true in each possible world is given by choices made in that world and the logic program. ICL is interesting because it is a simple, natural and expressive representation of rich probabilistic models. This paper gives an overview of the work done over the last decade and half, and points towards the considerable work ahead, particularly in the areas of lifted inference and the problems of existence and identity. 1
Firstorder probabilistic languages: Into the unknown
 PROCEEDINGS OF THE 16TH INTERNATIONAL CONFERENCE ON INDUCTIVE LOGIC PROGRAMMING. (2007
, 2007
"... This paper surveys firstorder probabilistic languages (FOPLs), which combine the expressive power of firstorder logic with a probabilistic treatment of uncertainty. We provide a taxonomy that helps make sense of the profusion of FOPLs that have been proposed over the past fifteen years. We also e ..."
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Cited by 16 (0 self)
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This paper surveys firstorder probabilistic languages (FOPLs), which combine the expressive power of firstorder logic with a probabilistic treatment of uncertainty. We provide a taxonomy that helps make sense of the profusion of FOPLs that have been proposed over the past fifteen years. We also emphasize the importance of representing uncertainty not just about the attributes and relations of a fixed set of objects, but also about what objects exist. This leads us to Bayesian logic, or BLOG, a new language for defining probabilistic models with unknown objects. We give a brief overview of BLOG syntax and semantics, and emphasize some of the design decisions that distinguish it from other languages. Finally, we consider the challenge of constructing FOPL models automatically from data.
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 16 (9 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