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.

Abstract not found

Conditional random fields (Lafferty et al., 2001) are quite effective at sequence labeling tasks like shallow parsing (Sha and Pereira, 2003) and namedentity extraction (McCallum and Li, 2003). CRFs are log-linear, allowing the incorporation of arbitrary features into the model. To train on unlabeled data, we require unsupervised estimation methods for log-linear models; few exist. We describe a novel approach, contrastive estimation. We show that the new technique can be intuitively understood as exploiting implicit negative evidence and is computationally efficient. Applied to a sequence labeling problem—POS tagging given a tagging dictionary and unlabeled text—contrastive estimation outperforms EM (with the same feature set), is more robust to degradations of the dictionary, and can largely recover by modeling additional features. 1

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

Recent work on loglinear models in probabilistic constraint logic programming is applied to first-order probabilistic reasoning. Probabilities are defined directly on the proofs of atomic formulae, and by marginalisation on the atomic formulae themselves. We use Stochastic Logic Programs (SLPs) composed of labelled and unlabelled definite clauses to define the proof probabilities. We have a conservative extension of first-order reasoning, so that, for example, there is a one-one mapping between logical and random variables. We show how, in this framework, Inductive Logic Programming (ILP) can be used to induce the features of a loglinear model from data. We also compare the presented framework with other approaches to first-order probabilistic reasoning. Keywords: loglinear models, constraint logic programming, inductive logic programming 1 Introduction A framework which merges first-order logical and probabilistic inference in a theoretically sound and applicable manner promises ma...

We describe a novel training criterion for probabilistic grammar induction models, contrastive estimation [Smith and Eisner, 2005], which can be interpreted as exploiting implicit negative evidence and includes a wide class of likelihood-based objective functions. This criterion is a generalization of the function maximized by the Expectation-Maximization algorithm [Dempster et al., 1977]. CE is a natural fit for log-linear models, which can include arbitrary features but for which EM is computationally difficult. We show that, using the same features, log-linear dependency grammar models trained using CE can drastically outperform EMtrained generative models on the task of matching human linguistic annotations (the MATCHLIN-GUIST task). The selection of an implicit negative evidence class—a “neighborhood”—appropriate to a given task has strong implications, but a good neighborhood one can target the objective of grammar induction to a specific application. 1

This thesis is about estimating probabilistic models to uncover useful hidden structure in data; specifically, we address the problem of discovering syntactic structure in natural language text. We present three new parameter estimation techniques that generalize the standard approach, maximum likelihood estimation, in different ways. Contrastive estimation maximizes the conditional probability of the observed data given a “neighborhood” of implicit negative examples. Skewed deterministic annealing locally maximizes likelihood using a cautious parameter search strategy that starts with an easier optimization problem than likelihood, and iteratively moves to harder problems, culminating in likelihood. Structural annealing is similar, but starts with a heavy bias toward simple syntactic structures and gradually relaxes the bias. Our estimation methods do not make use of annotated examples. We consider their performance in both an unsupervised model selection setting, where models trained under different initialization and regularization settings are compared by evaluating the training objective on a small set of unseen, unannotated development data, and supervised model selection, where the most accurate model on the development set (now with annotations)

We present an extension to Jaynes' maximum entropy principle that handles latent variables. The principle of latent maximum entropy we propose is di#erent from both Jaynes' maximum entropy principle and maximum likelihood estimation, but often yields better estimates in the presence of hidden variables and limited training data. We first show that solving for a latent maximum entropy model poses a hard nonlinear constrained optimization problem in general. However, we then show that feasible solutions to this problem can be obtained e#ciently for the special case of log-linear models---which forms the basis for an e#cient approximation to the latent maximum entropy principle. We derive an algorithm that combines expectation-maximization with iterative scaling to produce feasible log-linear solutions. This algorithm can be interpreted as an alternating minimization algorithm in the information divergence, and reveals an intimate connection between the latent maximum entropy and maximum likelihood principles.

Semantic parsing is the construction of a complete, formal, symbolic meaning representation of a sentence. While it is crucial to natural language understanding, the problem of semantic parsing has received relatively little attention from the machine learning community. Recent work on natural language understanding has mainly focused on shallow semantic analysis, such as word-sense disambiguation and semantic role labeling. Semantic parsing, on the other hand, involves deep semantic analysis in which word senses, semantic roles and other components are combined to produce useful meaning representations for a particular application domain (e.g. database query). Prior research in machine learning for semantic parsing is mainly based on inductive logic programming or deterministic parsing, which lack some of the robustness that characterizes statistical learning. Existing statistical approaches to semantic parsing, however, are mostly concerned with relatively simple application domains in which a meaning representation is no more than a single semantic frame. In this proposal, we present a novel statistical approach to semantic parsing, WASP, which can handle meaning representations with a nested structure. The WASP algorithm learns a semantic parser given a set of sentences annotated with their correct meaning representations. The parsing model is based on the