Abstract. We propose a simple approach to combining first-order logic and probabilistic graphical models in a single representation. A Markov logic network (MLN) is a first-order 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 first-order 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 pseudo-likelihood measure. Optionally, additional clauses are learned using inductive logic programming techniques. Experiments with a real-world database and knowledge base in a university domain illustrate the promise of this approach.

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 Baum-Welch algorithm for HMMs, the Inside-Outside 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 Inside-Outside algorithm. 1.

Most probabilistic inference algorithms are specified and processed on a propositional level. In the last decade, many proposals for algorithms accepting first-order 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 first-order level, but this method is limited to special cases. In this paper we present the first exact inference algorithm that operates directly on a first-order level, and that can be applied to any first-order model (specified in a language that generalizes undirected graphical models). Our experiments show superior performance in comparison with propositional exact inference. 1

Interest in statistical relational learning (SRL) has grown rapidly in recent years. Several key SRL tasks have been identified, and a large number of approaches have been proposed. Increasingly, a

. The state-of-the-art 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 [2-8]. 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...

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 -the-art in probabilistic logic learning through the identification of a number of important probabilistic, logical and learning concepts.

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 Metropolis-Hasting 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 Context-Free Grammars and Markov nets (Muggleton, 1996; Cussens, 1999). However, we need to ask (i) whether this i...

Stochastic processes that involve the creation of objects and relations over time are widespread, but relatively poorly studied. For example, accurate fault diagnosis in factory assembly processes requires inferring the probabilities of erroneous assembly operations, but doing this efficiently and accurately is difficult. Modeled as dynamic Bayesian networks, these processes have discrete variables with very large domains and extremely high dimensionality. In this paper, we introduce relational dynamic Bayesian networks (RDBNs), which are an extension of dynamic Bayesian networks (DBNs) to first-order logic. RDBNs are a generalization of dynamic probabilistic relational models (DPRMs), which we had proposed in our previous work to model dynamic uncertain domains. We first extend the Rao-Blackwellised particle filtering described in our earlier work to RDBNs. Next, we lift the assumptions associated with Rao-Blackwellization in RDBNs and propose two new forms of particle filtering. The first one uses abstraction hierarchies over the predicates to smooth the particle filter’s estimates. The second employs kernel density estimation with a kernel function specifically designed for relational domains. Experiments show these two methods greatly outperform standard particle filtering on the task of assembly plan execution monitoring. 1.

Inductive logic programming (ILP) is built on a foundation laid by research in other areas of machine learning and computational logic. But in spite of this strong foundation, at just over 10 years of age ILP now faces a number of new challenges brought on by exciting areas of application. Research in other areas of machine learning and computational logic can contribute much to help ILP meet these challenges. After a brief review, the paper presents ve future research directions for ILP and points to initial approaches or results where they exist. It is hoped that the paper will motivate research workers in machine learning and computational logic to invest some time into ILP.

Abstract. We are often faced with the challenge of mining data represented in relational form. Unfortunately, most statistical learning methods work only with “flat ” data representations. Thus, to apply these methods, we are forced to convert the data into a flat form, thereby not only losing its compact representation and structure but also potentially introducing statistical skew. These drawbacks severely limit the ability of current statistical methods to mine relational databases. Probabilistic models, in particular probabilistic relational models, allow us to represent a statistical model over a relational domain. These models can represent correlations between attributes within a single table, and between attributes in multiple tables, when these tables are related via foreign key joins. In previous work [4, 6, 8], we have developed algorithms for automatically constructing a probabilistic relational model directly from a relational database. We survey the results here and describe how the methods can be used to discover interesting dependencies the data. We show how this class of models and our construction algorithm are ideally suited to mining multi-relational data. 1