Minimum Error Rate Training Semiring

Minimum Error Rate Training Semiring Artem Sokolov Franc¸ois Yvon LIMSI-CNRS LIMSI-CNRs & Uni. Paris Sud BP-133, 91 403 Orsay, France {artem.sokolov, francois.yvon}@limsi.fr Abstract Modern Statistical Machine Translation (SMT) systems make their decisions based on multiple information sources, which as- sess various aspects of the match between a source sentence and its possible trans- lation(s). Tuning a SMT system consists in finding the right balance between these sources so as to produce the best possi- ble output, and is usually achieved through Minimum Error Rate Training (MERT) (Och, 2003). In this paper, we recast the operations implied in MERT in the terms of operations over a specific semir- ing, which, in particular, enables us to de- rive a simple and generic implementation of MERT over word lattices. 1 Introduction Inference (decoding) in phrase-based statistical machine translation (SMT) systems is typically based on a log-linear model of the probability p(e|f) = Z(f)−1 exp(¯λ · ¯h(e, f)) of obtaining a target sentence e given an input sentence f. For such model, the MAP decision rule selects ˜ef as : ˜ef(¯λ) = arg max e∈E p(e|f) = arg max e∈E ¯λ · ¯h(e, f), (1) where E is the set of reachable translations, ¯h(e, f) is the vector of feature functions representing var- ious compatibility measures of f and e, and ¯λ is a parameter vector, each component λi of which regulates the influence of the feature hi(e, f). c⃝ 2011 European Association for Machine Translation. The set of reachable translations E (also re- ferred to as the search space) in modern decoders is based on a set of heuristics that define the set of possible translation of each word or phrase (up to a maximum limit) and specify the range of possi- ble reorderings of words or phrases during trans- lation. Assuming that the components of E have been defined, the actual tuning step of a SMT sys- tem consists in finding ¯λ∗ that maximizes the em- pirical gain G on a development set F = {(f, rf)} made of pairs of a source sentence f and corre- sponding reference translation(s) rf: ¯λ∗ = arg max ¯λ G(F; ¯λ) (2) where the computation of the gain function G, typ- ically the BLEU score (Papineni et al., 2002) 1, depends on the actual translations {˜ef(¯λ), f ∈ F} achieved for a given value of ¯λ according to (1). For the sake of performing this optimization ef- ficiently, the search space of the decoder is often approximated using an explicit list of n-best hy- potheses or a directed acyclic graph (lattice) en- coding a large number of potential translations. Because of the form of the inference rule (1), the learning criterion (2) is neither convex nor dif- ferentiable. Furthermore, its exact computation is made intractable by the typical size of E, hence the recourse to various heuristic optimization strate- gies. The most successful to date is the proposal of (Och, 2003), usually referred to as Minimum Er- ror Rate Training (MERT). This proposal has how- …

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