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173
Markov Logic Networks
 Machine Learning
, 2006
"... Abstract. We propose a simple approach to combining firstorder logic and probabilistic graphical models in a single representation. A Markov logic network (MLN) is a firstorder knowledge base with a weight attached to each formula (or clause). Together with a set of constants representing objects ..."
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Cited by 569 (34 self)
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Abstract. We propose a simple approach to combining firstorder logic and probabilistic graphical models in a single representation. A Markov logic network (MLN) is a firstorder knowledge base with a weight attached to each formula (or clause). Together with a set of constants representing objects in the domain, it specifies a ground Markov network containing one feature for each possible grounding of a firstorder formula in the KB, with the corresponding weight. Inference in MLNs is performed by MCMC over the minimal subset of the ground network required for answering the query. Weights are efficiently learned from relational databases by iteratively optimizing a pseudolikelihood measure. Optionally, additional clauses are learned using inductive logic programming techniques. Experiments with a realworld database and knowledge base in a university domain illustrate the promise of this approach.
A Knowledge Compilation Map
 Journal of Artificial Intelligence Research
, 2002
"... We propose a perspective on knowledge compilation which calls for analyzing different compilation approaches according to two key dimensions: the succinctness of the target compilation language, and the class of queries and transformations that the language supports in polytime. ..."
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Cited by 162 (24 self)
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We propose a perspective on knowledge compilation which calls for analyzing different compilation approaches according to two key dimensions: the succinctness of the target compilation language, and the class of queries and transformations that the language supports in polytime.
Lifted firstorder probabilistic inference
 In Proceedings of IJCAI05, 19th International Joint Conference on Artificial Intelligence
, 2005
"... Most probabilistic inference algorithms are specified and processed on a propositional level. In the last decade, many proposals for algorithms accepting firstorder specifications have been presented, but in the inference stage they still operate on a mostly propositional representation level. [Poo ..."
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Cited by 88 (7 self)
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Most probabilistic inference algorithms are specified and processed on a propositional level. In the last decade, many proposals for algorithms accepting firstorder specifications have been presented, but in the inference stage they still operate on a mostly propositional representation level. [Poole, 2003] presented a method to perform inference directly on the firstorder level, but this method is limited to special cases. In this paper we present the first exact inference algorithm that operates directly on a firstorder level, and that can be applied to any firstorder model (specified in a language that generalizes undirected graphical models). Our experiments show superior performance in comparison with propositional exact inference. 1
Defaultreasoning with models
"... Reasoning with modelbased representations is an intuitive paradigm, which has been shown to be theoretically sound and to possess some computational advantages over reasoning with formulabased representations of knowledge. In this paper we present more evidence to the utility of such representatio ..."
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Cited by 79 (18 self)
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Reasoning with modelbased representations is an intuitive paradigm, which has been shown to be theoretically sound and to possess some computational advantages over reasoning with formulabased representations of knowledge. In this paper we present more evidence to the utility of such representations. In real life situations, one normally completes a lot of missing "context" information when answering queries. We model this situation by augmenting the available knowledge about the world with contextspecific information; we show that reasoning with modelbased representations can be done efficiently in the presence of varying context information. We then consider the task of default reasoning. We show that default reasoning is a generalization of reasoning within context, in which the reasoner has many "context" rules, which may be conflicting. We characterize the cases in which modelbased reasoning supports efficient default reasoning and develop algorithms that handle efficiently fragments of Reiter's default logic. In particular, this includes cases in which performing the default reasoning task with the traditional, formulabased, representation is intractable. Further, we argue that these results support an incremental view of reasoning in a natural way.
The Computational Complexity of Probabilistic Planning
 Journal of Artificial Intelligence Research
, 1998
"... We examine the computational complexity of testing and finding small plans in probabilistic planning domains with both flat and propositional representations. The complexity of plan evaluation and existence varies with the plan type sought; we examine totally ordered plans, acyclic plans, and loopin ..."
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Cited by 77 (5 self)
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We examine the computational complexity of testing and finding small plans in probabilistic planning domains with both flat and propositional representations. The complexity of plan evaluation and existence varies with the plan type sought; we examine totally ordered plans, acyclic plans, and looping plans, and partially ordered plans under three natural definitions of plan value. We show that problems of interest are complete for a variety of complexity classes: PL, P, NP, coNP, PP, NP PP, coNP PP , and PSPACE. In the process of proving that certain planning problems are complete for NP PP , we introduce a new basic NP PP complete problem, EMajsat, which generalizes the standard Boolean satisfiability problem to computations involving probabilistic quantities; our results suggest that the development of good heuristics for EMajsat could be important for the creation of efficient algorithms for a wide variety of problems.
Discriminative training of markov logic networks
 In Proc. of the Natl. Conf. on Artificial Intelligence
, 2005
"... Many machine learning applications require a combination of probability and firstorder logic. Markov logic networks (MLNs) accomplish this by attaching weights to firstorder clauses, and viewing these as templates for features of Markov networks. Model parameters (i.e., clause weights) can be lear ..."
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Cited by 77 (15 self)
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Many machine learning applications require a combination of probability and firstorder logic. Markov logic networks (MLNs) accomplish this by attaching weights to firstorder clauses, and viewing these as templates for features of Markov networks. Model parameters (i.e., clause weights) can be learned by maximizing the likelihood of a relational database, but this can be quite costly and lead to suboptimal results for any given prediction task. In this paper we propose a discriminative approach to training MLNs, one which optimizes the conditional likelihood of the query predicates given the evidence ones, rather than the joint likelihood of all predicates. We extend Collins’s (2002) voted perceptron algorithm for HMMs to MLNs by replacing the Viterbi algorithm with a weighted satisfiability solver. Experiments on entity resolution and link prediction tasks show the advantages of this approach compared to generative MLN training, as well as compared to purely probabilistic and purely logical approaches.
Entity Resolution with Markov Logic
 In ICDM
, 2006
"... Entity resolution is the problem of determining which records in a database refer to the same entities, and is a crucial and expensive step in the data mining process. Interest in it has grown rapidly in recent years, and many approaches have been proposed. However, they tend to address only isolate ..."
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Cited by 76 (9 self)
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Entity resolution is the problem of determining which records in a database refer to the same entities, and is a crucial and expensive step in the data mining process. Interest in it has grown rapidly in recent years, and many approaches have been proposed. However, they tend to address only isolated aspects of the problem, and are often ad hoc. This paper proposes a wellfounded, integrated solution to the entity resolution problem based on Markov logic. Markov logic combines firstorder logic and probabilistic graphical models by attaching weights to firstorder formulas, and viewing them as templates for features of Markov networks. We show how a number of previous approaches can be formulated and seamlessly combined in Markov logic, and how the resulting learning and inference problems can be solved efficiently. Experiments on two citation databases show the utility of this approach, and evaluate the contribution of the different components. 1
On Markov chains for independent sets
 Journal of Algorithms
, 1997
"... Random independent sets in graphs arise, for example, in statistical physics, in the hardcore model of a gas. A new rapidly mixing Markov chain for independent sets is defined in this paper. We show that it is rapidly mixing for a wider range of values of the parameter than the LubyVigoda chain, ..."
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Cited by 72 (20 self)
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Random independent sets in graphs arise, for example, in statistical physics, in the hardcore model of a gas. A new rapidly mixing Markov chain for independent sets is defined in this paper. We show that it is rapidly mixing for a wider range of values of the parameter than the LubyVigoda chain, the best previously known. Moreover the new chain is apparently more rapidly mixing than the LubyVigoda chain for larger values of (unless the maximum degree of the graph is 4). An extension of the chain to independent sets in hypergraphs is described. This chain gives an efficient method for approximately counting the number of independent sets of hypergraphs with maximum degree two, or with maximum degree three and maximum edge size three. Finally, we describe a method which allows one, under certain circumstances, to deduce the rapid mixing of one Markov chain from the rapid mixing of another, with the same state space and stationary distribution. This method is applied to two Markov ch...
The Complexity of Counting in Sparse, Regular, and Planar Graphs
 SIAM Journal on Computing
, 1997
"... We show that a number of graphtheoretic counting problems remain NPhard, indeed #Pcomplete, in very restricted classes of graphs. In particular, it is shown that the problems of counting matchings, vertex covers, independent sets, and extremal variants of these all remain hard when restricted to ..."
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Cited by 71 (0 self)
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We show that a number of graphtheoretic counting problems remain NPhard, indeed #Pcomplete, in very restricted classes of graphs. In particular, it is shown that the problems of counting matchings, vertex covers, independent sets, and extremal variants of these all remain hard when restricted to planar bipartite graphs of bounded degree or regular graphs of constant degree. To achieve these results, a new interpolationbased reduction technique which preserves properties such as constant degree is introduced. In addition, the problem of approximately counting minimum cardinality vertex covers is shown to remain NPhard even when restricted to graphs of maximal degree 3. Previously, restrictedcase complexity results for counting problems were elusive; we believe our techniques may help obtain similar results for many other counting problems. 1 Introduction Ever since the introduction of NPcompleteness in the early 1970's, the primary focus of complexity theory has been on decision ...
Learning to reason
 Journal of the ACM
, 1994
"... Abstract. We introduce a new framework for the study of reasoning. The Learning (in order) to Reason approach developed here views learning as an integral part of the inference process, and suggests that learning and reasoning should be studied together. The Learning to Reason framework combines the ..."
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Cited by 57 (24 self)
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Abstract. We introduce a new framework for the study of reasoning. The Learning (in order) to Reason approach developed here views learning as an integral part of the inference process, and suggests that learning and reasoning should be studied together. The Learning to Reason framework combines the interfaces to the world used by known learning models with the reasoning task and a performance criterion suitable for it. In this framework, the intelligent agent is given access to its favorite learning interface, and is also given a grace period in which it can interact with this interface and construct a representation KB of the world W. The reasoning performance is measured only after this period, when the agent is presented with queries � from some query language, relevant to the world, and has to answer whether W implies �. The approach is meant to overcome the main computational difficulties in the traditional treatment of reasoning which stem from its separation from the “world”. Since the agent interacts with the world when constructing its knowledge representation it can choose a representation that is useful for the task at hand. Moreover, we can now make explicit the dependence of the reasoning performance on the environment the agent interacts with. We show how previous results from learning theory and reasoning fit into this framework and