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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...
MEBN: A Language for FirstOrder Bayesian Knowledge Bases
"... Although classical firstorder logic is the de facto standard logical foundation for artificial intelligence, the lack of a builtin, semantically grounded capability for reasoning under uncertainty renders it inadequate for many important classes of problems. Probability is the bestunderstood and m ..."
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Cited by 45 (18 self)
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Although classical firstorder logic is the de facto standard logical foundation for artificial intelligence, the lack of a builtin, semantically grounded capability for reasoning under uncertainty renders it inadequate for many important classes of problems. Probability is the bestunderstood and most widely applied formalism for computational scientific reasoning under uncertainty. Increasingly expressive languages are emerging for which the fundamental logical basis is probability. This paper presents MultiEntity Bayesian Networks (MEBN), a firstorder language for specifying probabilistic knowledge bases as parameterized fragments of Bayesian networks. MEBN fragments (MFrags) can be instantiated and combined to form arbitrarily complex graphical probability models. An MFrag represents probabilistic relationships among a conceptually meaningful group of uncertain hypotheses. Thus, MEBN facilitates representation of knowledge at a natural level of granularity. The semantics of MEBN assigns a probability distribution over interpretations of an associated classical firstorder theory on a finite or countably infinite domain. Bayesian inference provides both a proof theory for combining prior knowledge with observations, and a learning theory for refining a representation as evidence accrues. A proof is given that MEBN can represent a probability distribution on interpretations of any finitely axiomatizable firstorder theory.
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.
Factorie: Probabilistic programming via imperatively defined factor graphs
 In Advances in Neural Information Processing Systems 22
, 2009
"... Discriminatively trained undirected graphical models have had wide empirical success, and there has been increasing interest in toolkits that ease their application to complex relational data. The power in relational models is in their repeated structure and tied parameters; at issue is how to defin ..."
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Cited by 39 (7 self)
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Discriminatively trained undirected graphical models have had wide empirical success, and there has been increasing interest in toolkits that ease their application to complex relational data. The power in relational models is in their repeated structure and tied parameters; at issue is how to define these structures in a powerful and flexible way. Rather than using a declarative language, such as SQL or firstorder logic, we advocate using an imperative language to express various aspects of model structure, inference, and learning. By combining the traditional, declarative, statistical semantics of factor graphs with imperative definitions of their construction and operation, we allow the user to mix declarative and procedural domain knowledge, and also gain significant efficiencies. We have implemented such imperatively defined factor graphs in a system we call FACTORIE, a software library for an objectoriented, stronglytyped, functional language. In experimental comparisons to Markov Logic Networks on joint segmentation and coreference, we find our approach to be 315 times faster while reducing error by 2025%—achieving a new state of the art. 1
MEBN: A Logic for OpenWorld Probabilistic Reasoning
 Research Paper
, 2004
"... Uncertainty is a fundamental and irreducible aspect of our knowledge about the world. Probability is the most wellunderstood and widely applied logic for computational scientific reasoning under uncertainty. As theory and practice advance, generalpurpose languages are beginning to emerge for which ..."
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Cited by 20 (8 self)
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Uncertainty is a fundamental and irreducible aspect of our knowledge about the world. Probability is the most wellunderstood and widely applied logic for computational scientific reasoning under uncertainty. As theory and practice advance, generalpurpose languages are beginning to emerge for which the fundamental logical basis is probability. However, such languages have lacked a logical foundation that fully integrates classical firstorder logic with probability theory. This paper presents such an integrated logical foundation. A formal specification is presented for multientity Bayesian networks (MEBN), a knowledge representation language based on directed graphical probability models. A proof is given that a probability distribution over interpretations of any consistent, finitely axiomatizable firstorder theory can be defined using MEBN. A semantics based on random variables provides a logically coherent foundation for open world reasoning and a means of analyzing tradeoffs between accuracy and computation cost. Furthermore, the underlying Bayesian logic is inherently open, having the ability to absorb new facts about the world, incorporate them into existing theories, and/or modify theories in the light of evidence. Bayesian inference provides both a proof theory for combining prior knowledge with observations, and a learning theory for refining a representation as evidence accrues. The results of this paper provide a logical foundation for the rapidly evolving literature on firstorder Bayesian knowledge representation, and point the way toward Bayesian languages suitable for generalpurpose knowledge representation and computing. Because firstorder Bayesian logic contains classical firstorder logic as a deterministic subset, it is a natural candidate as a universal representation for integrating domain ontologies expressed in languages based on classical firstorder logic or subsets thereof.
Fisher kernels for logical sequences
 In Proc. of 15th European Conference on Machine Learning (ECML04
, 2004
"... Abstract. One approach to improve the accuracy of classifications based on generative models is to combine them with successful discriminative algorithms. Fisher kernels were developed to combine generative models with a currently very popular class of learning algorithms, kernel methods. Empiricall ..."
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Cited by 13 (5 self)
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Abstract. One approach to improve the accuracy of classifications based on generative models is to combine them with successful discriminative algorithms. Fisher kernels were developed to combine generative models with a currently very popular class of learning algorithms, kernel methods. Empirically, the combination of hidden Markov models with support vector machines has shown promising results. So far, however, Fisher kernels have only been considered for sequences over flat alphabets. This is mostly due to the lack of a method for computing the gradient of a generative model over structured sequences. In this paper, we show how to compute the gradient of logical hidden Markov models, which allow for the modelling of logical sequences, i.e., sequences over an alphabet of logical atoms. Experiments show a considerable improvement over results achieved without Fisher kernels for logical sequences.
Parameter learning for relational bayesian networks
 In Proceedings of the International Conference in Machine Learning
, 2007
"... We present a method for parameter learning in relational Bayesian networks (RBNs). Our approach consists of compiling the RBN model into a computation graph for the likelihood function, and to use this likelihood graph to perform the necessary computations for a gradient ascent likelihood optimizati ..."
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Cited by 12 (2 self)
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We present a method for parameter learning in relational Bayesian networks (RBNs). Our approach consists of compiling the RBN model into a computation graph for the likelihood function, and to use this likelihood graph to perform the necessary computations for a gradient ascent likelihood optimization procedure. The method can be applied to all RBN models that only contain differentiable combining rules. This includes models with nondecomposable combining rules, as well as models with weighted combinations or nested occurrences of combining rules. Experimental results on artificial random graph data explores the feasibility of the approach both for complete and incomplete data. 1.
Learning probabilistic logic models from probabilistic examples
"... Abstract We revisit an application developed originally using abductive Inductive Logic Programming (ILP) for modeling inhibition in metabolic networks. The example data was derived from studies of the effects of toxins on rats using Nuclear Magnetic Resonance (NMR) timetrace analysis of their biof ..."
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Cited by 12 (4 self)
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Abstract We revisit an application developed originally using abductive Inductive Logic Programming (ILP) for modeling inhibition in metabolic networks. The example data was derived from studies of the effects of toxins on rats using Nuclear Magnetic Resonance (NMR) timetrace analysis of their biofluids together with background knowledge representing a subset of the Kyoto Encyclopedia of Genes and Genomes (KEGG). We now apply two Probabilistic ILP (PILP) approaches—abductive Stochastic Logic Programs (SLPs) and PRogramming In Statistical modeling (PRISM) to the application. Both approaches support abductive learning and probability predictions. Abductive SLPs are a PILP framework that provides possible worlds semantics to SLPs through abduction. Instead of learning logic models from nonprobabilistic examples as done in ILP, the PILP approach applied in this paper is based on a general technique for introducing probability labels within a standard scientific experimental setting involving control and treated data. Our results demonstrate that the PILP approach provides a way of learning probabilistic logic models from probabilistic examples, and the PILP models learned from probabilistic examples lead to a significant decrease in error accompanied by improved insight from the learned results compared with the PILP models learned from nonprobabilistic examples.
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 12 (4 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
FirstOrder Bayesian Logic
, 2005
"... Uncertainty is a fundamental and irreducible aspect of our knowledge about the world. Until recently, classical firstorder logic has reigned as the de facto standard logical foundation for artificial intelligence. The lack of a builtin, semantically grounded capability for reasoning under uncertai ..."
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Cited by 8 (3 self)
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Uncertainty is a fundamental and irreducible aspect of our knowledge about the world. Until recently, classical firstorder logic has reigned as the de facto standard logical foundation for artificial intelligence. The lack of a builtin, semantically grounded capability for reasoning under uncertainty renders classical firstorder logic inadequate for many important classes of problems. Generalpurpose languages are beginning to emerge for which the fundamental logical basis is probability. Increasingly expressive probabilistic languages demand a theoretical foundation that fully integrates classical firstorder logic and probability. In firstorder Bayesian logic (FOBL), probability distributions are defined over interpretations of classical firstorder axiom systems. Predicates and functions of a classical firstorder theory correspond to a random variables in the corresponding firstorder Bayesian theory. This is a natural correspondence, given that random variables are formalized in mathematical statistics as measurable functions on a probability space. A formal system called MultiEntity Bayesian Networks (MEBN) is presented for composing distributions on interpretations by instantiating and combining parameterized fragments of directed graphical models. A construction is given of a MEBN theory that assigns a nonzero