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.

One of the basic problems in knowledge discovery in databases (KDD) is the following: given a data set r, a class L of sentences for defining subgroups of r, and a selection predicate, find all sentences of L deemed interesting by the selection predicate. We analyze the simple levelwise algorithm for finding all such descriptions. We give bounds for the number of database accesses that the algorithm makes. For this, we introduce the concept of the border of a theory, a notion that turns out to be surprisingly powerful in analyzing the algorithm. We also consider the verification problem of a KDD process: given r and a set of sentences S ` L, determine whether S is exactly the set of interesting statements about r. We show strong connections between the verification problem and the hypergraph transversal problem. The verification problem arises in a natural way when using sampling to speed up the pattern discovery step in KDD.

The recent growth of online information available in the form of natural language documents creates a greater need for computing systems with the ability to process those documents to simplify access to the information. One type of processing appropriate for many tasks is information extraction, a type of text skimming that retrieves specific types of information from text. Although information extraction systems have existed for two decades, these systems have generally been built by hand and contain domain specific information, making them difficult to port to other domains. A few researchers have begun to apply machine learning to information extraction tasks, but most of this work has involved applying learning to pieces of a much larger system. This paper presents a novel rule representation specific to natural language and a learning system, Rapier, which learns information extraction rules. Rapier takes pairs of documents and filled templates indicating the information to be ext...

This paper presents a method for inducing logic programs from examples that learns a new class of concepts called first-order decision lists, defined as ordered lists of clauses each ending in a cut. The method, called Foidl, is based on Foil (Quinlan, 1990) but employs intensional background knowledge and avoids the need for explicit negative examples. It is particularly useful for problems that involve rules with specific exceptions, such as learning the past-tense of English verbs, a task widely studied in the context of the symbolic/connectionist debate. Foidl is able to learn concise, accurate programs for this problem from significantly fewer examples than previous methods (both connectionist and symbolic). 1. Introduction Inductive logic programming (ILP) is a growing subtopic of machine learning that studies the induction of Prolog programs from examples in the presence of background knowledge (Muggleton, 1992; Lavrac & Dzeroski, 1994). Due to the expressiveness of first-order...

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 score-based 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.

Markov logic networks (MLNs) combine logic and probability by attaching weights to first-order clauses, and viewing these as templates for features of Markov networks. In this paper we develop an algorithm for learning the structure of MLNs from relational databases, combining ideas from inductive logic programming (ILP) and feature induction in Markov networks. The algorithm performs a beam or shortestfirst search of the space of clauses, guided by a weighted pseudo-likelihood measure. This requires computing the optimal weights for each candidate structure, but we show how this can be done efficiently. The algorithm can be used to learn an MLN from scratch, or to refine an existing knowledge base. We have applied it in two real-world domains, and found that it outperforms using off-the-shelf ILP systems to learn the MLN structure, as well as pure ILP, purely probabilistic and purely knowledge-based approaches. 1.

Knowledge discovery in databases and data mining aim at semiautomatic tools for the analysis of large data sets. We consider some methods used in data mining, concentrating on levelwise search for all frequently occurring patterns. We show how this technique can be used in various applications. We also discuss possibilities for compiling data mining queries into algorithms, and look at the use of sampling in data mining. We conclude by listing several open research problems in data mining and knowledge discovery.

We present positive PAC-learning results for the nonmonotonic inductive logic programming setting. In particular, we show that first order range-restricted clausal theories that consist of clauses with up to k literals of size at most j each are polynomialsample polynomial-time PAC-learnable with one-sided error from positive examples only. In our framework, concepts are clausal theories and examples are finite interpretations. We discuss the problems encountered when learning theories which only have infinite non-trivial models and propose a way to avoid these problems using a representation change called flattening. Finally, we compare our results to PAC-learnability results for the normal inductive logic programming setting. 1

Several data mining problems can be formulated as problems of finding maximally specific sentences that are interesting in a database. We first show that this problem has a close relationship with the hypergraph transversal problem. We then analyze two algorithms that have been previously used in data mining, proving upper bounds on their complexity. The first algorithm is useful when the maximally specific interesting sentences are "small". We show that this algorithm can also be used to efficiently solve a special case of the hypergraph transversal problem, improving on previous results. The second algorithm utilizes a subroutine for hypergraph transversals, and is applicable in more general situations, with complexity close to a lower bound for the problem. We also relate these problems to the model of exact learning in computational learning theory, and use the correspondence to derive some corollaries. 1

Inductive logic programming, or relational learning, is a powerful paradigm for machine learning or data mining. However, in order for ILP to become practically useful, the efficiency of ILP systems must improve substantially. To this end, the notion of a query pack is introduced: it structures sets of similar queries. Furthermore, a mechanism is described for executing such query packs. A complexity analysis shows that considerable efficiency improvements can be achieved through the use of this query pack execution mechanism. This claim is supported by empirical results obtained by incorporating support for query pack execution in two existing learning systems.