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 well-founded, integrated solution to the entity resolution problem based on Markov logic. Markov logic combines first-order logic and probabilistic graphical models by attaching weights to first-order 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

Traditional noun phrase coreference resolution systems represent features only of pairs of noun phrases. In this paper, we propose a machine learning method that enables features over sets of noun phrases, resulting in a first-order probabilistic model for coreference. We outline a set of approximations that make this approach practical, and apply our method to the ACE coreference dataset, achieving a 45 % error reduction over a comparable method that only considers features of pairs of noun phrases. This result demonstrates an example of how a firstorder logic representation can be incorporated into a probabilistic model and scaled efficiently. 1

Formal languages for probabilistic modeling enable re-use, modularity, and descriptive clarity, and can foster generic inference techniques. We introduce Church, a universal language for describing stochastic generative processes. Church is based on the Lisp model of lambda calculus, containing a pure Lisp as its deterministic subset. The semantics of Church is defined in terms of evaluation histories and conditional distributions on such histories. Church also includes a novel language construct, the stochastic memoizer, which enables simple description of many complex non-parametric models. We illustrate language features through several examples, including: a generalized Bayes net in which parameters cluster over trials, infinite PCFGs, planning by inference, and various non-parametric clustering models. Finally, we show how to implement query on any Church program, exactly and approximately, using Monte Carlo techniques. 1

Inductive learning is impossible without overhypotheses, or constraints on the hypotheses considered by the learner. Some of these overhypotheses must be innate, but we suggest that hierarchical Bayesian models help explain how the rest can be acquired. To illustrate this claim, we develop models that acquire two kinds of overhypotheses — overhypotheses about feature variability (e.g. the shape bias in word learning) and overhypotheses about the grouping of categories into ontological kinds like objects and substances.

We develop hierarchical, probabilistic models for objects, the parts composing them, and the visual scenes surrounding them. Our approach couples topic models originally developed for text analysis with spatial transformations, and thus consistently accounts for geometric constraints. By building integrated scene models, we may discover contextual relationships, and better exploit partially labeled training images. We first consider images of isolated objects, and show that sharing parts among object categories improves detection accuracy when learning from few examples. Turning to multiple object scenes, we propose nonparametric models which use Dirichlet processes to automatically learn the number of parts underlying each object category, and objects composing each scene. The resulting transformed Dirichlet process (TDP) leads to Monte Carlo algorithms which simultaneously segment and recognize objects in street and office scenes.

Although classical first-order logic is the de facto standard logical foundation for artificial intelligence, the lack of a built-in, 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 Multi-Entity Bayesian Networks (MEBN), a first-order 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 first-order 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 first-order theory.

The Bayesian Logic (BLOG) language was recently developed for defining first-order probability models over worlds with unknown numbers of objects. It handles important problems in AI, including data association and population estimation. This paper extends BLOG by adopting generative processes over function spaces — known as nonparametrics in the Bayesian literature. We introduce syntax for reasoning about arbitrary collections of objects, and their properties, in an intuitive manner. By exploiting exchangeability, distributions over unknown objects and their attributes are cast as Dirichlet processes, which resolve difficulties in model selection and inference caused by varying numbers of objects. We demonstrate these concepts with application to citation matching. 1

Many recent advances in complex domains such as Natural Language Processing (NLP) have taken a discriminative approach in conjunction with the global application of structural and domain specific constraints. We introduce LBJ, a new modeling language for specifying exact inference systems of this type, combining ideas from machine learning, optimization, First Order Logic (FOL), and Object Oriented Programming (OOP). Expressive constraints are specified declaratively as arbitrary FOL formulas over functions and objects. The language's run-time library translates them to a mathematical programming representation from which an exact solution is computed. In addition, the compiler leverages an existing OOP language: objects and functions are grouped as the OOP objects and methods that encapsulate the user's data.

Uncertainty is a fundamental and irreducible aspect of our knowledge about the world. Probability is the most well-understood and widely applied logic for computational scientific reasoning under uncertainty. As theory and practice advance, general-purpose 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 first-order logic with probability theory. This paper presents such an integrated logical foundation. A formal specification is presented for multi-entity 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 first-order 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 first-order Bayesian knowledge representation, and point the way toward Bayesian languages suitable for general-purpose knowledge representation and computing. Because first-order Bayesian logic contains classical first-order logic as a deterministic subset, it is a natural candidate as a universal representation for integrating domain ontologies expressed in languages based on classical first-order logic or subsets thereof.

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 first-order 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 object-oriented, strongly-typed, functional language. In experimental comparisons to Markov Logic Networks on joint segmentation and coreference, we find our approach to be 3-15 times faster while reducing error by 20-25%—achieving a new state of the art. 1