A* Search via Approximate Factoring

We present a novel method for creating A∗ estimates for structured search problems originally described in Haghighi, DeNero, & Klein (2007). In our approach, we project a complex model onto multiple simpler models for which exact inference is efficient. We use an optimization framework to estimate parameters for these projections in a way which bounds the true costs. Similar to Klein & Manning (2003), we then combine completion estimates from the simpler models to guide search in the original complex model. We apply our approach to bitext parsing and demonstrate its effectiveness. Introduction Inference tasks in natural language processing (NLP) often involve searching for an optimal output from a large set of structured outputs. Example output spaces include sentences (machine translation and automatic speech recognition), partitions (coreference analysis), and trees (syntactic parsing). For many complex models, selecting the highest scoring output for a given observation is slow or even intractable. One general technique to increase efficiency while preserving optimality is A∗ search (Hart, Nilsson, & Raphael 1968); however, successfully using A∗ search is challenging in practice. The design of admissible (or nearly admissible) heuristics which are both effective (close to actual completion costs) and also efficient to compute is a difficult, open problem in most domains. As a result, most work on search has focused on nonoptimal methods, such as beam search or pruning based on approximate models (Collins 1999), though in certain cases admissible heuristics are known (Zhang & Gildea 2006). For example, Klein & Manning (2003) show a class of projection-based A∗ estimates, but their application is limited to models which have a very restrictive kind of score decomposition. In this work, we broaden their projection-based technique to give A∗ estimates for models which do not factor in this restricted way. Like Klein & Manning (2003), we focus on search problems where there are multiple projections or Copyright c © 2007, American Association for Artificial Intelligence (www.aaai.org). All rights reserved. 3.0 4.0 3.0 2.0 2.0 1.0