Stochastic Attribute-Value Grammars

Probabilistic analogues of regular and context-free grammars are well-known in computational linguistics, and currently the subject of intensive research. To date, however, no satisfactory probabilistic analogue of attribute-value grammars has been proposed: previous attempts have failed to define a correct parameter-estimation algorithm. In the present paper, I define stochastic attribute-value grammars and give a correct algorithm for estimating their parameters. The estimation algorithm is adapted from Della Pietra, Della Pietra, and Lafferty (1995). To estimate model parameters, it is necessary to compute the expectations of certain functions under random fields. In the application discussed by Della Pietra, Della Pietra, and Lafferty (representing English orthographic constraints), Gibbs sampling can be used to estimate the needed expectations. The fact that attribute-value grammars generate constrained languages makes Gibbs sampling inapplicable, but I show how a variant of Gibbs sampling, the Metropolis-Hastings algorithm, can be used instead.Comment: 23 pages, 21 Postscript figures, uses rotate.st

Empirical Risk Minimization with Approximations of Probabilistic Grammars

Probabilistic grammars are generative statistical models that are useful for compositional and sequential structures. We present a framework, reminiscent of structural risk minimization, for empirical risk minimization of the parameters of a fixed probabilistic grammar using the log-loss. We derive sample complexity bounds in this framework that apply both to the supervised setting and the unsupervised setting.

Unsupervised Statistical Learning of Context-free Grammar

In this paper, we address the problem of inducing (weighted) context-free grammar (WCFG) on data given. The induction is performed by using a new model of grammatical inference, i.e., weighted Grammar-based Classifier System (wGCS). wGCS derives from learning classifier systems and searches grammar structure using a genetic algorithm and covering. Weights of rules are estimated by using a novelty Inside-Outside Contrastive Estimation algorithm. The proposed method employs direct negative evidence and learns WCFG both form positive and negative samples. Results of experiments on three synthetic context-free languages show that wGCS is competitive with other statistical-based method for unsupervised CFG learning

XRate: a fast prototyping, training and annotation tool for phylo-grammars

BACKGROUND: Recent years have seen the emergence of genome annotation methods based on the phylo-grammar, a probabilistic model combining continuous-time Markov chains and stochastic grammars. Previously, phylo-grammars have required considerable effort to implement, limiting their adoption by computational biologists. RESULTS: We have developed an open source software tool, xrate, for working with reversible, irreversible or parametric substitution models combined with stochastic context-free grammars. xrate efficiently estimates maximum-likelihood parameters and phylogenetic trees using a novel "phylo-EM" algorithm that we describe. The grammar is specified in an external configuration file, allowing users to design new grammars, estimate rate parameters from training data and annotate multiple sequence alignments without the need to recompile code from source. We have used xrate to measure codon substitution rates and predict protein and RNA secondary structures. CONCLUSION: Our results demonstrate that xrate estimates biologically meaningful rates and makes predictions whose accuracy is comparable to that of more specialized tools

Structured parameter estimation for LFG-DOP using Backoff

Despite its state-of-the-art performance, the Data Oriented Parsing (DOP) model has been shown to suffer from biased parameter estimation, and the good performance seems more the result of ad hoc adjustments than correct probabilistic generalization over the data. In recent work, we developed a new estimation procedure, called Backoff Estimation, for DOP models that are based on Phrase-Structure annotations (so called Tree-DOP models). Backoff Estimation deviates from earlier methods in that it treats the model parameters as a highly structured space of correlated events (backoffs), rather than a set of disjoint events. In this paper we show that the problem of biased estimates also holds for DOP models that are based on Lexical-Functional Grammar annotations (i.e. LFG-DOP), and that the LFG-DOP parameters also constitute a hierarchically structured space. Subsequently, we adapt the Backoff Estimation algorithm from Tree-DOP to LFG-DOP models. Backoff Estimation turns out to be a natural solution to some of the specific problems of robust parsing under LFGDOP