Translation as weighted deduction

Abstract

We present a unified view of many translation algorithms that synthesizes work on deductive parsing, semiring parsing, and efficient approximate search algorithms. This gives rise to clean analyses and compact descriptions that can serve as the basis for modular implementations. We illustrate this with several examples, showing how to build search spaces for several disparate phrase-based search strategies, integrate non-local features, and devise novel models. Although the framework is drawn from parsing and applied to translation, it is applicable to many dynamic programming problems arising in natural language processing and other areas.

Products of weighted logic programs

“…We will summarize how the PRODUCT transformation was applied to a simple form of phrase-to-phrase translation (Koehn et al 2003) by Lopez (2009). Lopez (2009) suggested a deductive view of algorithms for machine translation, similar to the view of parsing given by Shieber et al (1995).…”

“…Lopez (2009) discusses more powerful translation algorithms that permit, for example, reordering of phrases.…”

“…We will summarize how the PRODUCT transformation was applied to a simple form of phrase-to-phrase translation (Koehn et al 2003) by Lopez (2009). Lopez (2009) suggested a deductive view of algorithms for machine translation, similar to the view of parsing given by Shieber et al (1995). Lopez used the PRODUCT transformation to derive an algorithm for phrase translation from two different factor programs, one which attempts to enforce fluency (a measure of the grammaticality of a sentence) in the translated sentence and one which attempts to enforce adequacy (a measure of how much of the meaning of an original sentence is preserved in the translation.…”

Exact Decoding for Phrase-Based Statistical Machine Translation

“…It is denoted by [C, r, γ] (also known as carry), where: C is a coverage vector, necessary to impose the non-overlapping constraint; r is the rightmost position most recently covered, necessary for the computation of δ; and γ is the last n − 1 words 1 Preventing phrases from overlapping requires an exponential number of constraints (the powerset of x) rendering the problem NP-complete (Knight, 1999). 2 Weighted logics have been extensively used to describe weighted sets (Lopez, 2009), operations over weighted sets (Chiang, 2007;Dyer and Resnik, 2010), and a variety of dynamic programming algorithms (Cohen et al, 2008). , that is, an instantiated biphrase which covers the span x i i and yields y j j with weight φ r .…”

First- and second-order expectation semirings with applications to minimum-risk training on translation forests

“…For example, we may want to run the Viterbi algorithm to find the most probable derivation tree in the hypergraph, or the k most probable trees. Semiring-weighted logic programming is a general framework to specify these algorithms (Pereira and Warren, 1983;Shieber et al, 1994;Goodman, 1999;Eisner et al, 2005;Lopez, 2009). Goodman (1999) describes many useful semirings (e.g., Viterbi, inside, and Viterbin-best).…”