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Shay B. Cohen

Publications and source records attributed to Shay B. Cohen.

97 records · Page 6Linked to original sources
arXiv2016

Optimizing Spectral Learning for Parsing

We describe a search algorithm for optimizing the number of latent states when estimating latent-variable PCFGs with spectral methods. Our results show that contrary to the common belief that the number of latent states for each nonterminal in an L-PCFG can be decided in isolation with spectral methods, parsing results significantly improve if the number of latent states for each nonterminal is globally optimized, while taking into account interactions between the different nonterminals. In addition, we contribute an empirical analysis of spectral algorithms on eight morphologically rich languages: Basque, French, German, Hebrew, Hungarian, Korean, Polish and Swedish. Our results show that our estimation consistently performs better or close to coarse-to-fine expectation-maximization techniques for these languages.

cs.CL↗
arXiv2016

Parsing Linear Context-Free Rewriting Systems with Fast Matrix Multiplication

We describe a matrix multiplication recognition algorithm for a subset of binary linear context-free rewriting systems (LCFRS) with running time $O(n^{ωd})$ where $M(m) = O(m^ω)$ is the running time for $m \times m$ matrix multiplication and $d$ is the "contact rank" of the LCFRS -- the maximal number of combination and non-combination points that appear in the grammar rules. We also show that this algorithm can be used as a subroutine to get a recognition algorithm for general binary LCFRS with running time $O(n^{ωd + 1})$. The currently best known $ω$ is smaller than $2.38$. Our result provides another proof for the best known result for parsing mildly context sensitive formalisms such as combinatory categorial grammars, head grammars, linear indexed grammars, and tree adjoining grammars, which can be parsed in time $O(n^{4.76})$. It also shows that inversion transduction grammars can be parsed in time $O(n^{5.76})$. In addition, binary LCFRS subsumes many other formalisms and types of grammars, for some of which we also improve the asymptotic complexity of parsing.

cs.CL↗
arXiv2015

Low-Rank Approximation of Weighted Tree Automata

We describe a technique to minimize weighted tree automata (WTA), a powerful formalisms that subsumes probabilistic context-free grammars (PCFGs) and latent-variable PCFGs. Our method relies on a singular value decomposition of the underlying Hankel matrix defined by the WTA. Our main theoretical result is an efficient algorithm for computing the SVD of an infinite Hankel matrix implicitly represented as a WTA. We provide an analysis of the approximation error induced by the minimization, and we evaluate our method on real-world data originating in newswire treebank. We show that the model achieves lower perplexity than previous methods for PCFG minimization, and also is much more stable due to the absence of local optima.

cs.LG↗
arXiv2015

Diversity in Spectral Learning for Natural Language Parsing

We describe an approach to create a diverse set of predictions with spectral learning of latent-variable PCFGs (L-PCFGs). Our approach works by creating multiple spectral models where noise is added to the underlying features in the training set before the estimation of each model. We describe three ways to decode with multiple models. In addition, we describe a simple variant of the spectral algorithm for L-PCFGs that is fast and leads to compact models. Our experiments for natural language parsing, for English and German, show that we get a significant improvement over baselines comparable to state of the art. For English, we achieve the $F_1$ score of 90.18, and for German we achieve the $F_1$ score of 83.38.

cs.CL↗
arXiv2012

Elimination of Spurious Ambiguity in Transition-Based Dependency Parsing

We present a novel technique to remove spurious ambiguity from transition systems for dependency parsing. Our technique chooses a canonical sequence of transition operations (computation) for a given dependency tree. Our technique can be applied to a large class of bottom-up transition systems, including for instance Nivre (2004) and Attardi (2006).

cs.CL↗
arXiv2010

Products of Weighted Logic Programs

Weighted logic programming, a generalization of bottom-up logic programming, is a well-suited framework for specifying dynamic programming algorithms. In this setting, proofs correspond to the algorithm's output space, such as a path through a graph or a grammatical derivation, and are given a real-valued score (often interpreted as a probability) that depends on the real weights of the base axioms used in the proof. The desired output is a function over all possible proofs, such as a sum of scores or an optimal score. We describe the PRODUCT transformation, which can merge two weighted logic programs into a new one. The resulting program optimizes a product of proof scores from the original programs, constituting a scoring function known in machine learning as a ``product of experts.'' Through the addition of intuitive constraining side conditions, we show that several important dynamic programming algorithms can be derived by applying PRODUCT to weighted logic programs corresponding to simpler weighted logic programs. In addition, we show how the computation of Kullback-Leibler divergence, an information-theoretic measure, can be interpreted using PRODUCT.

cs.AI↗