emnlp emnlp2010 emnlp2010-57 knowledge-graph by maker-knowledge-mining
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Author: Adria de Gispert ; Juan Pino ; William Byrne
Abstract: We report on investigations into hierarchical phrase-based translation grammars based on rules extracted from posterior distributions over alignments of the parallel text. Rather than restrict rule extraction to a single alignment, such as Viterbi, we instead extract rules based on posterior distributions provided by the HMM word-to-word alignmentmodel. We define translation grammars progressively by adding classes of rules to a basic phrase-based system. We assess these grammars in terms of their expressive power, measured by their ability to align the parallel text from which their rules are extracted, and the quality of the translations they yield. In Chinese-to-English translation, we find that rule extraction from posteriors gives translation improvements. We also find that grammars with rules with only one nonterminal, when extracted from posteri- ors, can outperform more complex grammars extracted from Viterbi alignments. Finally, we show that the best way to exploit source-totarget and target-to-source alignment models is to build two separate systems and combine their output translation lattices.
Reference: text
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1 uk }@ Abstract We report on investigations into hierarchical phrase-based translation grammars based on rules extracted from posterior distributions over alignments of the parallel text. [sent-6, score-1.176]
2 Rather than restrict rule extraction to a single alignment, such as Viterbi, we instead extract rules based on posterior distributions provided by the HMM word-to-word alignmentmodel. [sent-7, score-0.808]
3 We define translation grammars progressively by adding classes of rules to a basic phrase-based system. [sent-8, score-0.634]
4 We assess these grammars in terms of their expressive power, measured by their ability to align the parallel text from which their rules are extracted, and the quality of the translations they yield. [sent-9, score-0.64]
5 In Chinese-to-English translation, we find that rule extraction from posteriors gives translation improvements. [sent-10, score-1.031]
6 We also find that grammars with rules with only one nonterminal, when extracted from posteri- ors, can outperform more complex grammars extracted from Viterbi alignments. [sent-11, score-0.633]
7 Finally, we show that the best way to exploit source-totarget and target-to-source alignment models is to build two separate systems and combine their output translation lattices. [sent-12, score-0.614]
8 1 Introduction Current practice in hierarchical phrase-based translation extracts regular phrases and hierarchical rules from word-aligned parallel text. [sent-13, score-0.954]
9 Alignment models estimated over the parallel text are used to generate these alignments, but these models are then typically used no further in rule extraction. [sent-14, score-0.445]
10 This is less than ideal because these alignment models, even if they 545 are not suitable for direct use in translation, can still provide a great deal of useful information beyond a single best estimate of the alignment of the parallel text. [sent-15, score-0.832]
11 Our aim is to use alignment models to generate the statistics needed to build translation grammars. [sent-16, score-0.614]
12 There are two aspects to hierarchical phrase-based translation grammars which concern us. [sent-19, score-0.524]
13 For a grammar with given types of rules, larger rule sets will yield greater expressive power. [sent-22, score-0.604]
14 This motivates studies of grammars based on the rules which are extracted and the movement the grammar allows. [sent-23, score-0.717]
15 These posteriors allow us to build larger rule sets with improved translation accuracy. [sent-27, score-0.898]
16 tc ho2d0s10 in A Nsastoucira tlio Lnan fogru Cagoem Ppruotcaetisosninagl, L pinag eusis 5t4ic5s–5 4, To make this approach feasible, we consider only phrase-to-phrase alignments with a high posterior probability under the alignment models. [sent-32, score-0.587]
17 In this way, the alignment model probabilities guide rule extraction. [sent-33, score-0.703]
18 Section 2 reviews related work on using posteriors to extract phrases, as well as other approaches that tightly integrate word alignment and rule extraction. [sent-35, score-1.019]
19 Section 3 describes rule extraction based on word and phrase posterior distributions provided by the HMM word-to-word alignment model. [sent-36, score-0.954]
20 In Section 4 we define translation grammars progressively by adding classes of rules to a basic phrase-based system, motivating each rule type by the phrase movement it is intended to achieve. [sent-37, score-1.082]
21 In Section 5 we assess these grammars in terms of their expressive power and the quality of the translations they yield in Chinese-toEnglish, showing that rule extraction from posteriors gives translation improvements. [sent-38, score-1.386]
22 We also find that the best way to exploit source-to-target and targetto-source alignment models is to build two separate systems and combine their output translation lattices. [sent-39, score-0.614]
23 2 Related Work Some authors have previously addressed the limitation caused by decoupling word alignment models from grammar extraction. [sent-41, score-0.56]
24 (2008) extract rules from n-best lists of alignments for a syntax-augmented hierarchical system. [sent-43, score-0.513]
25 (2009) to create a structure called weighted alignment matrices that approximates word-to-word link posterior probabilities, from which phrases are extracted for a phrase-based system. [sent-45, score-0.619]
26 Alignment posteriors have been used before for extracting phrases in non-hierarchical phrase-based translation (Venugopal et al. [sent-46, score-0.641]
27 In order to simplify hierarchical phrase-based grammars and make translation feasible with rela- tively large parallel corpora, some authors discuss the need for various filters during rule extraction (Chiang, 2007). [sent-49, score-1.102]
28 We also note approaches to tighter coupling between translation grammars and alignments. [sent-55, score-0.407]
29 (2009) report improvement on a phrase-based system where word alignment has been trained with an inversion transduction grammar (ITG) rather than IBM models. [sent-58, score-0.633]
30 We take a different approach in that we aim to start with very strong word alignment models and use them to guide grammar extraction. [sent-66, score-0.56]
31 3 Rule Extraction from Alignment Posteriors The goal of rule extraction is to generate a set of good-quality translation rules from a parallel corpus. [sent-67, score-1.068]
32 Rules are of the form X→hγ,α,∼i , where γ, α ∈ {X s∪ a T}+ are eth feo source →ahndγ target ,si wdehse roef tγh,eα rule, XT ∪de Tno}tes the set of terminals (words) and ∼ is a bijective function1 relating source and target ∼no inste arm biinjeaclsti Xe uofn etaiocnh rule (Chiang, 2007). [sent-68, score-0.491]
33 Given a sentence pair (f1J, e1I), the extraction algorithm traverses the source sentence and, for each sequence of terminals it considers all possible fjj12, eii21 as translation target-side sequences candidates. [sent-74, score-0.517]
34 In this section we will explore variations of this rule extraction procedure involving alternative definitions of the ranking and counting functions, fR and fC, based on probabilities over alignment models. [sent-78, score-0.836]
35 , 2003) takes a set of word alignment links L and defines the alignment constraints CA so that there is a consistency between tchoen sltirnakins isn C the phrase pair. [sent-80, score-0.826]
36 We call this extraction Viterbi-based, as the set of alignment links is generally obtained after applying a symmetrization heuristic to sourceto-target and target-to-source Viterbi alignments. [sent-83, score-0.597]
37 In the following section we depart from this approach and apply novel functions to rank and count target-side translations according to their quality in the context of each parallel sentence, as defined by the word alignment models. [sent-84, score-0.581]
38 We also depart from common practice in that we do not use a set of links as alignment constraints. [sent-85, score-0.422]
39 1 Word-to-word Alignment Posterior Probabilities Word-to-word alignment posterior probabilities p(lji |f1J, e1I) express how likely it is that the words in source position j and target position iare aligned 547 given a sentence pair. [sent-91, score-0.55]
40 We note that Equation 1 can be computed using link posteriors provided by alignment models trained on either source-to-target or target-to-source translation directions. [sent-104, score-0.985]
41 2 Phrase-to-phrase Alignment Posterior Probabilities Rather than limit ourselves to word-to-word link posteriors we can define alignment probability distributions over phrase alignments. [sent-107, score-0.777]
42 The grammar expressivity is greater as more types of rules are included. [sent-111, score-0.436]
43 In addition to the rules shown in the respective columns, G1, G2 and G3 also contain the rules of G0. [sent-112, score-0.454]
44 These phrase posteriors directly define a probability distribution over the alignments of translation candidates, so we use them both for ranking and scoring extracted rules, that is fR = fC = p. [sent-115, score-0.833]
45 548 Once all rules over the entire collection of parallel sentences have been extracted, we require each rule to occur at least nobs times and with a forward translation probability p(α|γ) > 0. [sent-125, score-1.047]
46 3 Extraction of Rules with Nonterminals Extending the procedure previously described to the case of more complex hierarchical rules including one or even two nonterminals is conceptually straightforward. [sent-128, score-0.414]
47 Optionally, the alignment constraints can also be extended to apply on the nonterminal X. [sent-130, score-0.501]
48 4 Hierarchical Translation Grammar Definition In this section we define the hierarchical phrasebased synchronous grammars we use for translation experiments. [sent-133, score-0.559]
49 Each grammar is defined by the type of hierarchical rules it contains. [sent-134, score-0.553]
50 The rule type can be obtained by replacing every sequence of terminals by a single symbol ‘w’, thus ignoring the identity of the words, but capturing its generalized structure and the kind of reordering it encodes (this was defined as rule pattern in Iglesias et al. [sent-135, score-0.747]
51 The goal is to obtain a grammar with few rule types but which is capable of generating a rich set of translation candidates for a given input sentence. [sent-140, score-0.82]
52 Ttwhios rule types that place the unique nonterminal in an opposite position in each language; we call these ’phrase swap rules’ . [sent-143, score-0.485]
53 a swap must apply after a swap, or the rule is concatenated with the glue rule. [sent-147, score-0.477]
54 This aGdds single Sn{on tXer→mihnwal X rul wes, wwi Xth disjoint terminal sequences, which can encode a mono549 tonic or reordered relationship between them, depending on what their alignment was in the parallel corpus. [sent-155, score-0.522]
55 Although one could expect the movement captured by this phrase-disjoint rule type to be also present in G2 (via two swaps or one concatenation plus one swap), the terminal sequences w may differ. [sent-156, score-0.566]
56 Figure 1 shows an example set of rules indicating to which of the previous grammars each rule belongs, and shows three translation candidates as generated by grammars G1 (left-most tree), G2 (middle tree) and G3 (right-most tree). [sent-157, score-1.126]
57 Note that the middle tree cannot be generated with G1 as it requires monotonic concatenation before reordering with rule R4. [sent-158, score-0.548]
58 The more rule types a hierarchical grammar contains, the more different rule derivations and the greater the search space of alternative translation candidates. [sent-159, score-1.3]
59 This is also connected to how many rules are extracted per rule type. [sent-160, score-0.601]
60 Ideally we would like the grammar to be able to generate the correct translation of a given input sentence, without overgenerating too many other candidates, as that makes the translation task more difficult. [sent-161, score-0.735]
61 By extracting rules from a parallel sentence, we translate them and observe whether the translation grammar is able to produce the parallel target translation. [sent-163, score-0.99]
62 As described in the previous section, the motivation for including rule type X→hw X,w Xi is that the gram- mar nbeg raubllee ytop carry ohuwt Xm,owno Xtoin iics tchoantc thateen gartaimonbefore applying another hierarchical rule with reordering. [sent-168, score-0.747]
63 This movement is permitted by this rule type, but the use of a single nonterminal category X also allows the grammar to apply the concatenation after reordering, that is, immediately before the glue rule is applied. [sent-169, score-1.225]
64 This creates significant redundancy in rule derivations, as this rule type is allowed to act as a glue rule. [sent-170, score-0.797]
65 To avoid this situation we introduce a nonterminal M in the left-hand side of monotonic concatenation rules of G2. [sent-172, score-0.506]
66 All rules are allowed to use nonterminals X and M in their right-hand side, except the glue rules, which can only take X. [sent-173, score-0.433]
67 In the context of our example, R4 is substituted by: R4a: M→hs1 X,t1 Xi so that R4b:: M→hs1 M,t1 Mi only the first derivation is possible: R2,R0,R3,R1, because applying R3,R4a yields anonterminal M that cannot be taken by the glue rule R0. [sent-174, score-0.418]
68 1 Measuring Expressive Power We measure the expressive power of the grammars described in the previous section by running the translation system in alignment mode (de Gispert et al. [sent-197, score-0.91]
69 rules are irrelevant, as only the ability of the grammar to create a desired hypothesis is important. [sent-206, score-0.436]
70 The extraction method iWs brads ePdo on owrsor (dW alignment posteriors hdoedscribed in Section 3. [sent-213, score-0.804]
71 These rules can be obtained either from the posteriors of the sourceto-target (WP-st) or the target-to-source (WPts) alignment models. [sent-216, score-0.898]
72 We apply the alignment constraints and selection criteria described in Section 3. [sent-217, score-0.431]
73 We do not report alignment percentages when using phrase posteriors (as described in Section 3. [sent-219, score-0.779]
74 The highest alignment percentages are obtained when merging rules obtained under models trained in each direction (WP-merge), approximately reaching 80% for grammar G3. [sent-226, score-0.84]
75 The maximum rule span in alignment was allowed to be 15 words, so as to be similar to translation, where the maximum rule span is 10 words. [sent-227, score-1.014]
76 2 Translation Results In this section we investigate the translation performance of each hierarchical grammar, as defined by rules obtained from three rule extraction methods: • Viterbi union (V-union). [sent-231, score-1.055]
77 The posteriors are provided by the source-to-target alignment model. [sent-239, score-0.671]
78 Table 2 reports the translation results, as well as the number of extracted rules in each case. [sent-249, score-0.549]
79 This uses rules with up to two nonadjacent non• terminals, but excludes identical rule types such as X→hw X,w Xi or X→hw X1 w X2,w X1 w X2i, wXh→ichhw were reported Xto→ cause computational difficuli-, ties without a clear improvement in translation (Iglesias et al. [sent-253, score-0.805]
80 As expected, for the standard extraction method (see rows entitled V-union), grammar G1 is shown to underperform all other grammars due to its structural limitations. [sent-256, score-0.486]
81 On the other hand, grammar G2 obtains much better scores, nearly generating the same translation quality as the baseline grammar GH. [sent-257, score-0.681]
82 Finally, G3 does not prove able to outperform G2, which suggests that the phrase-disjoint rules with one nonterminal are redundant for the translation grammar. [sent-258, score-0.601]
83 For all grammars, we find that the proposed extraction methods based on alignment posteriors outperform standard Viterbibased extraction, with improvements ranging from 0. [sent-260, score-0.804]
84 This shows that method PP yields wider coverage but with sharper forward rule translation probability distributions than method WP, as the average number of translations per rule is determined by the p(α|γ) > 0. [sent-278, score-1.002]
85 1 we described a strategy to reduce grammar redundancy by introducing an additional nonterminal M for monotonic concatenation rules. [sent-286, score-0.519]
86 Another relevant aspect of this grammar is the actual rule type selected for monotonic concatenation. [sent-290, score-0.598]
87 Table 3: Translation results under grammar G2 with individual rule sets, merged rule sets, and rescoring and system combination with lattice-based MBR (lower-cased BLEU shown) 5. [sent-293, score-0.839]
88 4 Symmetrizing Alignments of Parallel Text In this section we investigate extraction from alignments (and posterior distributions) over parallel text which are generated using alignment models trained in the source-to-target (st) and target-to-source (ts) directions. [sent-294, score-0.85]
89 We find that rules extracted under the source-to-target alignment models (V-st, WP-st and PP-st) consistently perform better than the V-ts, WP-ts and PPts cases. [sent-298, score-0.637]
90 We use the PP rule extraction method to extract two sets of rules, under the st and ts alignment models respectively. [sent-301, score-0.869]
91 The first strategy is PP-merge and merges 553 both rule sets by assigning to each rule the maximum count assigned by either alignment model. [sent-303, score-0.981]
92 The motivation is that MERT can weight rules differently according to the alignment model they were extracted from. [sent-305, score-0.637]
93 , 2010) as produced by rules extracted under each alignment direction (see rows named LMBR(V-st,V-ts) and LMBR(PP-st,PP-ts)). [sent-310, score-0.637]
94 Overall, the best-performing strategy is to extract two sets of translation rules under the phrase pair posteriors in each translation direction, and then to perform translation twice and merge the results. [sent-312, score-1.424]
95 6 Conclusion Rule extraction based on alignment posterior probabilities can generate larger rule sets. [sent-313, score-0.936]
96 Assigning counts equal to phrase posteriors produces better estimation of rule translation probabilities. [sent-315, score-0.953]
97 This more exhaustive rule extraction method permits a grammar simplification, as expressed by the phrase movement allowed by its rules. [sent-317, score-0.823]
98 In particular a simple grammar with rules of only one nonterminal is shown to outperform a more complex grammar built on rules extracted from Viterbi alignments. [sent-318, score-1.042]
99 Finally, we find that the best way to exploit alignment models trained in each translation direction is to extract two rule sets based on alignment posteriors, translate the input independently with each rule set and combine translation output lattices. [sent-319, score-1.891]
100 Improving phrasebased translation via word alignments from stochastic inversion transduction grammars. [sent-422, score-0.507]
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Abstract: Extant Statistical Machine Translation (SMT) systems are very complex softwares, which embed multiple layers of heuristics and embark very large numbers of numerical parameters. As a result, it is difficult to analyze output translations and there is a real need for tools that could help developers to better understand the various causes of errors. In this study, we make a step in that direction and present an attempt to evaluate the quality of the phrase-based translation model. In order to identify those translation errors that stem from deficiencies in the phrase table (PT), we propose to compute the oracle BLEU-4 score, that is the best score that a system based on this PT can achieve on a reference corpus. By casting the computation of the oracle BLEU-1 as an Integer Linear Programming (ILP) problem, we show that it is possible to efficiently compute accurate lower-bounds of this score, and report measures performed on several standard benchmarks. Various other applications of these oracle decoding techniques are also reported and discussed. 1 Phrase-Based Machine Translation 1.1 Principle A Phrase-Based Translation System (PBTS) consists of a ruleset and a scoring function (Lopez, 2009). The ruleset, represented in the phrase table, is a set of phrase1pairs {(f, e) }, each pair expressing that the source phrase f can ,bee) r}e,w earicthten p (atirra enxslparteedss)i inngto t a target phrase e. Trarsaens flation hypotheses are generated by iteratively rewriting portions of the source sentence as prescribed by the ruleset, until each source word has been consumed by exactly one rule. The order of target words in an hypothesis is uniquely determined by the order in which the rewrite operation are performed. The search space ofthe translation model corresponds to the set of all possible sequences of 1Following the usage in statistical machine translation literature, use “phrase” to denote a subsequence of consecutive words. we 933 rules applications. The scoring function aims to rank all possible translation hypotheses in such a way that the best one has the highest score. A PBTS is learned from a parallel corpus in two independent steps. In a first step, the corpus is aligned at the word level, by using alignment tools such as Gi z a++ (Och and Ney, 2003) and some symmetrisation heuristics; phrases are then extracted by other heuristics (Koehn et al., 2003) and assigned numerical weights. In the second step, the parameters of the scoring function are estimated, typically through Minimum Error Rate training (Och, 2003). Translating a sentence amounts to finding the best scoring translation hypothesis in the search space. Because of the combinatorial nature of this problem, translation has to rely on heuristic search techniques such as greedy hill-climbing (Germann, 2003) or variants of best-first search like multi-stack decoding (Koehn, 2004). Moreover, to reduce the overall complexity of decoding, the search space is typically pruned using simple heuristics. For instance, the state-of-the-art phrase-based decoder Moses (Koehn et al., 2007) considers only a restricted number of translations for each source sequence2 and enforces a distortion limit3 over which phrases can be reordered. As a consequence, the best translation hypothesis returned by the decoder is not always the one with the highest score. 1.2 Typology of PBTS Errors Analyzing the errors of a SMT system is not an easy task, because of the number of models that are combined, the size of these models, and the high complexity of the various decision making processes. For a SMT system, three different kinds of errors can be distinguished (Germann et al., 2004; Auli et al., 2009): search errors, induction errors and model errors. The former corresponds to cases where the hypothesis with the best score is missed by the search procedure, either because of the use of an ap2the 3the option of Moses, defaulting to 20. dl option of Moses, whose default value is 7. tt l ProceMedITin,g Ms oasfs thaceh 2u0se1t0ts C,o UnSfAer,e n9c-e11 on O Ectmobpeir ic 2a0l1 M0.e ?tc ho2d0s10 in A Nsastouciraatlio Lnan fogru Cagoem Ppruotcaetisosninagl, L pinaggeusis 9t3ic3s–943, proximate search method or because of the restrictions of the search space. Induction errors correspond to cases where, given the model, the search space does not contain the reference. Finally, model errors correspond to cases where the hypothesis with the highest score is not the best translation according to the evaluation metric. Model errors encompass several types oferrors that occur during learning (Bottou and Bousquet, 2008)4. Approximation errors are errors caused by the use of a restricted and oversimplistic class of functions (here, finitestate transducers to model the generation of hypotheses and a linear scoring function to discriminate them) to model the translation process. Estimation errors correspond to the use of sub-optimal values for both the phrase pairs weights and the parameters of the scoring function. The reasons behind these errors are twofold: first, training only considers a finite sample of data; second, it relies on error prone alignments. As a result, some “good” phrases are extracted with a small weight, or, in the limit, are not extracted at all; and conversely that some “poor” phrases are inserted into the phrase table, sometimes with a really optimistic score. Sorting out and assessing the impact of these various causes of errors is of primary interest for SMT system developers: for lack of such diagnoses, it is difficult to figure out which components of the system require the most urgent attention. Diagnoses are however, given the tight intertwining among the various component of a system, very difficult to obtain: most evaluations are limited to the computation of global scores and usually do not imply any kind of failure analysis. 1.3 Contribution and organization To systematically assess the impact of the multiple heuristic decisions made during training and decoding, we propose, following (Dreyer et al., 2007; Auli et al., 2009), to work out oracle scores, that is to evaluate the best achievable performances of a PBTS. We aim at both studying the expressive power of PBTS and at providing tools for identifying and quantifying causes of failure. Under standard metrics such as BLEU (Papineni et al., 2002), oracle scores are difficult (if not impossible) to compute, but, by casting the computation of the oracle unigram recall and precision as an Integer Linear Programming (ILP) problem, we show that it is possible to efficiently compute accurate lower-bounds of the oracle BLEU-4 scores and report measurements performed on several standard benchmarks. The main contributions of this paper are twofold. We first introduce an ILP program able to efficiently find the best hypothesis a PBTS can achieve. This program can be easily extended to test various improvements to 4We omit here optimization errors. 934 phrase-base systems or to evaluate the impact of different parameter settings. Second, we present a number of complementary results illustrating the usage of our oracle decoder for identifying and analyzing PBTS errors. Our experimental results confirm the main conclusions of (Turchi et al., 2008), showing that extant PBTs have the potential to generate hypotheses having very high BLEU4 score and that their main bottleneck is their scoring function. The rest of this paper is organized as follows: in Section 2, we introduce and formalize the oracle decoding problem, and present a series of ILP problems of increasing complexity designed so as to deliver accurate lowerbounds of oracle score. This section closes with various extensions allowing to model supplementary constraints, most notably reordering constraints (Section 2.5). Our experiments are reported in Section 3, where we first introduce the training and test corpora, along with a description of our system building pipeline (Section 3. 1). We then discuss the baseline oracle BLEU scores (Section 3.2), analyze the non-reachable parts of the reference translations, and comment several complementary results which allow to identify causes of failures. Section 4 discuss our approach and findings with respect to the existing literature on error analysis and oracle decoding. We conclude and discuss further prospects in Section 5. 2 Oracle Decoder 2.1 The Oracle Decoding Problem Definition To get some insights on the errors of phrasebased systems and better understand their limits, we propose to consider the oracle decoding problem defined as follows: given a source sentence, its reference translation5 and a phrase table, what is the “best” translation hypothesis a system can generate? As usual, the quality of an hypothesis is evaluated by the similarity between the reference and the hypothesis. Note that in the oracle decoding problem, we are only assessing the ability of PBT systems to generate good candidate translations, irrespective of their ability to score them properly. We believe that studying this problem is interesting for various reasons. First, as described in Section 3.4, comparing the best hypothesis a system could have generated and the hypothesis it actually generates allows us to carry on both quantitative and qualitative failure analysis. The oracle decoding problem can also be used to assess the expressive power of phrase-based systems (Auli et al., 2009). Other applications include computing acceptable pseudo-references for discriminative training (Tillmann and Zhang, 2006; Liang et al., 2006; Arun and 5The oracle decoding problem can be extended to the case of multiple references. For the sake of simplicity, we only describe the case of a single reference. Koehn, 2007) or combining machine translation systems in a multi-source setting (Li and Khudanpur, 2009). We have also used oracle decoding to identify erroneous or difficult to translate references (Section 3.3). Evaluation Measure To fully define the oracle decoding problem, a measure of the similarity between a translation hypothesis and its reference translation has to be chosen. The most obvious choice is the BLEU-4 score (Papineni et al., 2002) used in most machine translation evaluations. However, using this metric in the oracle decoding problem raises several issues. First, BLEU-4 is a metric defined at the corpus level and is hard to interpret at the sentence level. More importantly, BLEU-4 is not decomposable6: as it relies on 4-grams statistics, the contribution of each phrase pair to the global score depends on the translation of the previous and following phrases and can not be evaluated in isolation. Because of its nondecomposability, maximizing BLEU-4 is hard; in particular, the phrase-level decomposability of the evaluation × metric is necessary in our approach. To circumvent this difficulty, we propose to evaluate the similarity between a translation hypothesis and a reference by the number of their common words. This amounts to evaluating translation quality in terms of unigram precision and recall, which are highly correlated with human judgements (Lavie et al., ). This measure is closely related to the BLEU-1 evaluation metric and the Meteor (Banerjee and Lavie, 2005) metric (when it is evaluated without considering near-matches and the distortion penalty). We also believe that hypotheses that maximize the unigram precision and recall at the sentence level yield corpus level BLEU-4 scores close the maximal achievable. Indeed, in the setting we will introduce in the next section, BLEU-1 and BLEU-4 are highly correlated: as all correct words of the hypothesis will be compelled to be at their correct position, any hypothesis with a high 1-gram precision is also bound to have a high 2-gram precision, etc. 2.2 Formalizing the Oracle Decoding Problem The oracle decoding problem has already been considered in the case of word-based models, in which all translation units are bound to contain only one word. The problem can then be solved by a bipartite graph matching algorithm (Leusch et al., 2008): given a n m binary matarligxo describing possible t 2r0an08sl)a:ti goinv elinn aks n b×emtw beeinna source words and target words7, this algorithm finds the subset of links maximizing the number of words of the reference that have been translated, while ensuring that each word 6Neither at the sentence (Chiang et al., 2008), nor at the phrase level. 7The (i, j) entry of the matrix is 1if the ith word of the source can be translated by the jth word of the reference, 0 otherwise. 935 is translated only once. Generalizing this approach to phrase-based systems amounts to solving the following problem: given a set of possible translation links between potential phrases of the source and of the target, find the subset of links so that the unigram precision and recall are the highest possible. The corresponding oracle hypothesis can then be easily generated by selecting the target phrases that are aligned with one source phrase, disregarding the others. In addition, to mimic the way OOVs are usually handled, we match identical OOV tokens appearing both in the source and target sentences. In this approach, the unigram precision is always one (every word generated in the oracle hypothesis matches exactly one word in the reference). As a consequence, to find the oracle hypothesis, we just have to maximize the recall, that is the number of words appearing both in the hypothesis and in the reference. Considering phrases instead of isolated words has a major impact on the computational complexity: in this new setting, the optimal segmentations in phrases of both the source and of the target have to be worked out in addition to links selection. Moreover, constraints have to be taken into account so as to enforce a proper segmentation of the source and target sentences. These constraints make it impossible to use the approach of (Leusch et al., 2008) and concur in making the oracle decoding problem for phrase-based models more complex than it is for word-based models: it can be proven, using arguments borrowed from (De Nero and Klein, 2008), that this problem is NP-hard even for the simple unigram precision measure. 2.3 An Integer Program for Oracle Decoding To solve the combinatorial problem introduced in the previous section, we propose to cast it into an Integer Linear Programming (ILP) problem, for which many generic solvers exist. ILP has already been used in SMT to find the optimal translation for word-based (Germann et al., 2001) and to study the complexity of learning phrase alignments (De Nero and Klein, 2008) models. Following the latter reference, we introduce the following variables: fi,j (resp. ek,l) is a binary indicator variable that is true when the phrase contains all spans from betweenword position i to j (resp. k to l) of the source (resp. target) sentence. We also introduce a binary variable, denoted ai,j,k,l, to describe a possible link between source phrase fi,j and target phrase ek,l. These variables are built from the entries of the phrase table according to selection strategies introduced in Section 2.4. In the following, index variables are so that: 0 ≤ i< j ≤ n, in the source sentence and 0 ≤ k < l ≤ m, in the target sentence, where n (resp. m) is the length of the source (resp. target) sentence. Solving the oracle decoding problem then amounts to optimizing the following objective function: mi,j,akx,li,Xj,k,lai,j,k,l· (l − k), (1) under the constraints: X ∀x ∈ J1,mK : ek,l ≤ 1 (2) = (3) 1∀,kn,lK : Xai,j,k,l = fk,l (4) ∀i,j : Xai,j,k,l (5) k,l s.tX. Xk≤x≤l ∀∀xy ∈∈ J11,,mnKK : X i,j s.tX. Xi≤y≤j fi,j 1 Xi,j = ei,j Xk,l The objective function (1) corresponds to the number of target words that are generated. The first set of constraints (2) ensures that each word in the reference e ap- pears in no more than one phrase. Maximizing the objective under these constraints amounts to maximizing the unigram recall. The second set of constraints (3) ensures that each word in the source f is translated exactly once, which guarantees that the search space of the ILP problem is the same as the search space of a phrase-based system. Constraints (4) bind the fk,l and ai,j,k,l variables, ensuring that whenever a link ai,j,k,l is active, the corresponding phrase fk,l is also active. Constraints (5) play a similar role for the reference. The Relaxed Problem Even though it accurately models the search space of a phrase-based decoder, this programs is not really useful as is: due to out-ofvocabulary words or missing entries in the phrase table, the constraint that all source words should be translated yields infeasible problems8. We propose to relax this problem and allow some source words to remain untranslated. This is done by replacing constraints (3) by: ∀y ∈ J1,nK : X i,j s.tX. Xi≤y≤j fi,j ≤ 1 To better ref∀lyec ∈t th J1e, bneKh :avior of phrase-based decoders, which attempt to translate all source words, we also need to modify the objective function as follows: X i,Xj,k,l ai,j,k,l · (l − k) +Xfi,j · (j − i) Xi,j (6) The second term in this new objective ensures that optimal solutions translate as many source words as possible. 8An ILP problem is said to be infeasible when tion violates at least one constraint. every possible solu- 936 The Relaxed-Distortion Problem A last caveat with the Relaxed optimization program is caused by frequently occurring source tokens, such as function words or punctuation signs, which can often align with more than one target word. For lack of taking distortion information into account in our objective function, all these alignments are deemed equivalent, even if some of them are clearly more satisfactory than others. This situation is illustrated on Figure 1. le chat et the cat and le the chien dog Figure 1: Equivalent alignments between “le” and “the”. The dashed lines corresponds to a less interpretable solution. To overcome this difficulty, we propose a last change to the objective function: X i,Xj,k,l ai,j,k,l · (l − k) +Xfi,j · (j − i) X ai,j,k,l|k − i| Xi,j −α (7) i Xk ,l X,j, Compared to the objective function of the relaxed problem (6), we introduce here a supplementary penalty factor which favors monotonous alignments. For each phrase pair, the higher the difference between source and target positions, the higher this penalty. If α is small enough, this extra term allows us to select, among all the optimal alignments of the re l axed problem, the one with the lowest distortion. In our experiments, we set α to min {n, m} to ensure that the penalty factor is always smminall{enr, ,tmha}n tthoe e rneswuarred t fhoart aligning atwltyo single iwso ardlwsa. 2.4 Selecting Indicator Variables In the approach introduced in the previous sections, the oracle decoding problem is solved by selecting, among a set of possible translation links, the ones that yield the solution with the highest unigram recall. We propose two strategies to build this set of possible translation links. In the first one, denoted exact match, an indicator ai,j,k,l is created if there is an entry (f, e) so that f spans from word position ito j in the source and e from word position k to l in the target. In this strategy, the ILP program considers exactly the same ruleset as conventional phrase-based decoders. We also consider an alternative strategy, which could help us to identify errors made during the phrase extraction process. In this strategy, denoted inside match, an indicator ai,j,k,l is created when the following three criteria are met: i) f spans from position ito j of the source; ii) a substring of e, denoted e, spans from position k to l of the reference; iii) (f, e¯) is not an entry of the phrase table. The resulting set of indicator variables thus contains, at least, all the variables used in the exact match strategy. In addition, we license here the use of phrases containing words that do not occur in the reference. In fact, using such solutions can yield higher BLEU scores when the reward for additional correct matches exceeds the cost incurred by wrong predictions. These cases are symptoms of situations where the extraction heuristic failed to extract potentially useful subphrases. 2.5 Oracle Decoding with Reordering Constraints The ILP problem introduced in the previous section can be extended in several ways to describe and test various improvements to phrase-based systems or to evaluate the impact of different parameter settings. This flexibility mainly stems from the possibility offered by our framework to express arbitrary constraints over variables. In this section, we illustrate these possibilities by describing how reordering constraints can easily be considered. As a first example, the Moses decoder uses a distortion limit to constrain the set of possible reorderings. This constraint “enforces (...) that the last word of a phrase chosen for translation cannot be more than d9 words from the leftmost untranslated word in the source” (Lopez, 2009) and is expressed as: ∀aijkl , ai0j0k0l0 s.t. k > k0, aijkl · ai0j0k0l0 · |j − i0 + 1| ≤ d, The maximum distortion limit strategy (Lopez, 2009) is also easily expressed and take the following form (assuming this constraint is parameterized by d): ∀l < m − 1, ai,j,k,l·ai0,j0,l+1,l0 · |i0 − j − 1| 71is%t e6hs.a distortion greater that Moses default distortion limit. alignment decisions enabled by the use of larger training corpora and phrase table. To evaluate the impact ofthe second heuristic, we computed the number of phrases discarded by Moses (be- cause of the default ttl limit) but used in the oracle hypotheses. In the English to French NEWSCO setting, they account for 34.11% of the total number of phrases used in the oracle hypotheses. When the oracle decoder is constrained to use the same phrase table as Moses, its BLEU-4 score drops to 42.78. This shows that filtering the phrase table prior to decoding discards many useful phrase pairs and is seriously limiting the best achievable performance, a conclusion shared with (Auli et al., 2009). Search Errors Search errors can be identified by comparing the score of the best hypothesis found by Moses and the score of the oracle hypothesis. If the score of the oracle hypothesis is higher, then there has been a search error; on the contrary, there has been an estimation error when the score of the oracle hypothesis is lower than the score of the best hypothesis found by Moses. 940 Based on the comparison of the score of Moses hypotheses and of oracle hypotheses for the English to French NEWSCO setting, our preliminary conclusion is that the number of search errors is quite limited: only about 5% of the hypotheses of our oracle decoder are actually getting a better score than Moses solutions. Again, this shows that the scoring function (model error) is one of the main bottleneck of current PBTS. Comparing these hypotheses is nonetheless quite revealing: while Moses mostly selects phrase pairs with high translation scores and generates monotonous alignments, our ILP decoder uses larger reorderings and less probable phrases to achieve better solutions: on average, the reordering score of oracle solutions is −5.74, compared to −76.78 fscoro rMeo osfe osr outputs. iGonivsen is −the5 weight assigned through MERT training to the distortion score, no wonder that these hypotheses are severely penalized. The Impact of Phrase Length The observed outputs do not only depend on decisions made during the search, but also on decisions made during training. One such decision is the specification of maximal length for the source and target phrases. In our framework, evaluating the impact of this decision is simple: it suffices to change the definition of indicator variables so as to consider only alignments between phrases of a given length. In the English-French NEWSCO setting, the most restrictive choice, when only alignments between single words are authorized, yields an oracle BLEU-4 of 48.68; however, authorizing phrases up to length 2 allows to achieve an oracle value of 66.57, very close to the score achieved when considering all extracted phrases (67.77). This is corroborated with a further analysis of our oracle alignments, which use phrases whose average source length is 1.21 words (respectively 1.31 for target words). If many studies have already acknowledged the predomi- nance of “small” phrases in actual translations, our oracle scores suggest that, for this language pair, increasing the phrase length limit beyond 2 or 3 might be a waste of computational resources. 4 Related Work To the best of our knowledge, there are only a few works that try to study the expressive power ofphrase-based machine translation systems or to provide tools for analyzing potential causes of failure. The approach described in (Auli et al., 2009) is very similar to ours: in this study, the authors propose to find and analyze the limits of machine translation systems by studying the reference reachability. A reference is reachable for a given system if it can be exactly generated by this system. Reference reachability is assessed using Moses in forced decoding mode: during search, all hypotheses that deviate from the reference are simply discarded. Even though the main goal of this study was to compare the search space of phrase-based and hierarchical systems, it also provides some insights on the impact of various search parameters in Moses, delivering conclusions that are consistent with our main results. As described in Section 1.2, these authors also propose a typology of the errors of a statistical translation systems, but do not attempt to provide methods for identifying them. The authors of (Turchi et al., 2008) study the learn- ing capabilities of Moses by extensively analyzing learning curves representing the translation performances as a function of the number of examples, and by corrupting the model parameters. Even though their focus is more on assessing the scoring function, they reach conclusions similar to ours: the current bottleneck of translation performances is not the representation power of the PBTS but rather in their scoring functions. Oracle decoding is useful to compute reachable pseudo-references in the context of discriminative training. This is the main motivation of (Tillmann and Zhang, 2006), where the authors compute high BLEU hypotheses by running a conventional decoder so as to maximize a per-sentence approximation of BLEU-4, under a simple (local) reordering model. Oracle decoding has also been used to assess the limitations induced by various reordering constraints in (Dreyer et al., 2007). To this end, the authors propose to use a beam-search based oracle decoder, which computes lower bounds of the best achievable BLEU-4 using dynamic programming techniques over finite-state (for so-called local and IBM constraints) or hierarchically structured (for ITG constraints) sets of hypotheses. Even 941 though the numbers reported in this study are not directly comparable with ours17, it seems that our decoder is not only conceptually much simpler, but also achieves much more optimistic lower-bounds of the oracle BLEU score. The approach described in (Li and Khudanpur, 2009) employs a similar technique, which is to guide a heuristic search in an hypergraph representing possible translation hypotheses with n-gram counts matches, which amounts to decoding with a n-gram model trained on the sole reference translation. Additional tricks are presented in this article to speed-up decoding. Computing oracle BLEU scores is also the subject of (Zens and Ney, 2005; Leusch et al., 2008), yet with a different emphasis. These studies are concerned with finding the best hypotheses in a word graph or in a consensus network, a problem that has various implications for multi-pass decoding and/or system combination techniques. The former reference describes an exponential approximate algorithm, while the latter proves the NPcompleteness of this problem and discuss various heuristic approaches. Our problem is somewhat more complex and using their techniques would require us to built word graphs containing all the translations induced by arbitrary segmentations and permutations of the source sentence. 5 Conclusions In this paper, we have presented a methodology for analyzing the errors of PBTS, based on the computation of an approximation of the BLEU-4 oracle score. We have shown that this approximation could be computed fairly accurately and efficiently using Integer Linear Programming techniques. Our main result is a confirmation of the fact that extant PBTS systems are expressive enough to achieve very high translation performance with respect to conventional quality measurements. The main efforts should therefore strive to improve on the way phrases and hypotheses are scored during training. This gives further support to attempts aimed at designing context-dependent scoring functions as in (Stroppa et al., 2007; Gimpel and Smith, 2008), or at attempts to perform discriminative training of feature-rich models. (Bangalore et al., 2007). We have shown that the examination of difficult-totranslate sentences was an effective way to detect errors or inconsistencies in the reference translations, making our approach a potential aid for controlling the quality or assessing the difficulty of test data. Our experiments have also highlighted the impact of various parameters. Various extensions of the baseline ILP program have been suggested and/or evaluated. In particular, the ILP formalism lends itself well to expressing various constraints that are typically used in conventional PBTS. In 17The best BLEU-4 oracle they achieve on Europarl German to English is approximately 48; but they considered a smaller version of the training corpus and the WMT’06 test set. our future work, we aim at using this ILP framework to systematically assess various search configurations. We plan to explore how replacing non-reachable references with high-score pseudo-references can improve discrim- inative training of PBTS. We are also concerned by determining how tight is our approximation of the BLEU4 score is: to this end, we intend to compute the best BLEU-4 score within the n-best solutions of the oracle decoding problem. 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