emnlp emnlp2010 emnlp2010-3 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Shaojun Zhao ; Daniel Gildea
Abstract: A word in one language can be translated to zero, one, or several words in other languages. Using word fertility features has been shown to be useful in building word alignment models for statistical machine translation. We built a fertility hidden Markov model by adding fertility to the hidden Markov model. This model not only achieves lower alignment error rate than the hidden Markov model, but also runs faster. It is similar in some ways to IBM Model 4, but is much easier to understand. We use Gibbs sampling for parameter estimation, which is more principled than the neighborhood method used in IBM Model 4.
Reference: text
sentIndex sentText sentNum sentScore
1 Using word fertility features has been shown to be useful in building word alignment models for statistical machine translation. [sent-2, score-0.855]
2 We built a fertility hidden Markov model by adding fertility to the hidden Markov model. [sent-3, score-1.483]
3 This model not only achieves lower alignment error rate than the hidden Markov model, but also runs faster. [sent-4, score-0.247]
4 1 Introduction IBM models and the hidden Markov model (HMM) for word alignment are the most influential statistical word alignment models (Brown et al. [sent-7, score-0.422]
5 There are three kinds of important information for word alignment models: lexicality, locality and fertility. [sent-10, score-0.192]
6 IBM Model 1 uses only lexical information; IBM Model 2 and the hidden Markov model take advantage of both lexical and locality information; IBM Models 4 and 5 use all three kinds of information, and they remain the state of the art despite the fact that they were developed almost two decades ago. [sent-11, score-0.127]
7 Nevertheless, we believe that IBM Model 4 is essentially a better model because it exploits the fertility of words in the tar596 get language. [sent-13, score-0.694]
8 Most other researchers take either the HMM alignments (Liang et al. [sent-20, score-0.164]
9 , 2006) or IBM Model 4 alignments (Cherry and Lin, 2003) as input and perform post-processing, whereas our model is a potential replacement for the HMM and IBM Model 4. [sent-21, score-0.191]
10 Directly modeling fertility makes our model fundamentally different from others. [sent-22, score-0.694]
11 (2006) learn the alignment in both translation directions jointly, essentially pushing the fertility towards 1. [sent-25, score-0.825]
12 ITG models (Wu, 1997) assume the fertility to be either zero or one. [sent-26, score-0.681]
13 There have been works that try to simulate fertility using the hidden Markov model (Toutanova et al. [sent-28, score-0.773]
14 , 2002; Deng and Byrne, 2005), but we prefer to model fertility directly. [sent-29, score-0.694]
15 Our distortion parameters are similar to IBM Model 2 and the HMM, while IBM Model 4 uses inverse distortion (Brown et al. [sent-36, score-0.182]
16 Our model assumes that fertility follows a Poisson distribution, while IBM Model 4 assumes a multinomial distribution, and has to learn a much larger number of parameters, which makes it slower and less reliable. [sent-38, score-0.728]
17 In fact, we will show that it is also faster than the HMM, and has lower alignment error rate than the HMM. [sent-40, score-0.184]
18 Parameter estimation for word alignment models that model fertility is more difficult than for models without fertility. [sent-41, score-0.875]
19 (1993) and Och and Ney (2003) first compute the Viterbi alignments for simpler models, then consider only some neighbors of the Viterbi alignments for modeling fertility. [sent-43, score-0.342]
20 If the optimal alignment is not in those neighbors, this method will not be able find the optimal alignment. [sent-44, score-0.132]
21 (2008) applied the Markov Chain Monte Carlo method to word alignment for machine translation; they do not model word fertility. [sent-47, score-0.201]
22 , eI, we define the alignments between the two sentences as a subset of the Cartesian product of the word positions. [sent-55, score-0.185]
23 (1993), we assume that each source word is aligned to exactly one target word. [sent-57, score-0.147]
24 When a word fj is not aligned with any word e, aj is 0. [sent-62, score-0.609]
25 For convenience, we add an empty word ǫ to the target sentence at position 0 (i. [sent-63, score-0.228]
26 However, as we will see, we have to add more than one empty word for the HMM. [sent-66, score-0.129]
27 In order to compute the “jump probability” in the HMM model, we need to know the position of the aligned target word for the previous source word. [sent-67, score-0.184]
28 If the previous source word aligns to an empty word, we could use the position of the empty word to indi- f1J cate the nearest previous source word that does not align to an empty word. [sent-68, score-0.543]
29 For this reason, we use a 597 total of I 1 empty words for the HMM model1 . [sent-69, score-0.108]
30 + Moore (2004) also suggested adding multiple empty words to the target sentence for IBM Model 1. [sent-70, score-0.184]
31 After we add I 1empty words to the target sentence, the + alignment is a mapping from source to target word positions: a :j → i,i= aj where j = 1, 2, . [sent-71, score-0.66]
32 Words from position I 1 to 2I + 1 in the target + sentence are all empty words. [sent-78, score-0.207]
33 We allow each source word to align with exactly one target word, but each target word may align with multiple source words. [sent-79, score-0.284]
34 The fertility φi of a word ei at position iis defined as the number of aligned source words: = XJ φi Xδ(aj,i) Xj=1 where δ is the Kronecker delta function: δ(x,y) =? [sent-80, score-0.871]
35 01 oift hxe=r wi yse In particular, the fePrtility of all empty words in the target sentence is φi. [sent-81, score-0.184]
36 pair e21I+1 and The invertPed alignments for position iin the target sentence are a set Bi, such that each element in Bi is aligned with i, and all alignments of iare in Bi. [sent-84, score-0.466]
37 Inverted alignments are explicitly used in IBM Models 3, 4 and 5, but not in our model, which is one reason that our model is easier to understand. [sent-85, score-0.211]
38 There are I 1possibilities: fj is + the first word in the source sentence, or fj−1 aligns with one of the target word. [sent-88, score-0.309]
39 The absolute position in the HMM is not important, because we re-parametrize the distortion probability in terms of the distance between adjacent alignment points (Vogel et al. [sent-96, score-0.283]
40 The HMM is more likely to align a source word to a target word that is adjacent to the previous aligned target word, which is more suitable than IBM Model 1 because adjacent words tend to form phrases. [sent-99, score-0.296]
41 For these two models, in theory, the fertility for a target word can be as large as the length of the source sentence. [sent-100, score-0.795]
42 In practice, the fertility for a target word in IBM Model 1is not very big except for rare target words, which can become a garbage collector, and align to many source words (Brown et al. [sent-101, score-0.892]
43 The HMM is less likely to have this garbage collector problem because of the alignment probability constraint. [sent-103, score-0.215]
44 However, fertility is an inherent cross-language property and these two models cannot assign consistent fertility to words. [sent-104, score-1.348]
45 This is our motivation for adding fertility to these two models, and we expect that the resulting models will perform better than the baseline models. [sent-105, score-0.681]
46 Because the HMM performs much better than IBM Model 1, we expect that the fertility hidden Markov model will perform much better than the fertility IBM Model 1. [sent-106, score-1.422]
47 Throughout the paper, “our model” refers to the fertility hidden Markov model. [sent-107, score-0.728]
48 , 1993; Och and Ney, 2003) from IBM Model 4, but it is computationally very expensive due to the larger number of parameters than IBM Model 4, and IBM Model 5 often provides no improvement on alignment accuracy. [sent-112, score-0.154]
49 Th|ee fertility foPr a non-empty word ei is a erandom variable φi, and we assume φi follows a Poisson distribution Poisson(φi; λ(ei)). [sent-114, score-0.778]
50 The sum of the fertilities of all the empty words (φǫ) grows with the × length of the target sentence. [sent-115, score-0.257]
51 However, we also enforce the fertility for the same target word across the corpus to be consistent. [sent-122, score-0.744]
52 The expected fertility for a non-empty word ei is λ(ei), and the expected fertility for all empty words is Iλ(ǫ). [sent-123, score-1.593]
53 Any fertility value has a non-zero probability, but fertility values that 599 are further away from the mean have low probability. [sent-124, score-1.334]
54 In the fertility IBM Model 1, we assume that the distortion probability is uniform, and the lexical probability depends only on the aligned target word: P(φ1I, = a1J, f1J|e21I+1) Yi=I1λ(ei)φφiei! [sent-127, score-0.924]
55 We can remove the deficiency for fertility IBM Model 1by assuming a different distortion probability: the distortion probability is 0 if fertility is not consistent with alignments, and uniform otherwise. [sent-134, score-1.563]
56 The total number of consistent fertility and alignments is φǫ! [sent-135, score-0.831]
57 jYJ=1P(fj|eaj) In our experiments, we did not find a noticeable change in terms of alignment accuracy by removing the deficiency. [sent-143, score-0.15]
58 For the fertility IBM Model 1, we do not need to estimate the distortion probability. [sent-147, score-0.763]
59 5 Gibbs Sampling for Fertility HMM Although we can estimate the parameters by using the EM algorithm, in order to compute the expected counts, we have to sum over all possible alignments a1J, which is, unfortunately, exponential. [sent-148, score-0.25]
60 For each target sentence and source sen- e21I+1 tence f1J, we initialize the alignment aj for each source word fj using the Viterbi alignments from IBM Model 1. [sent-150, score-1.0]
61 During the training stage, we try all 2I + 1 possible alignments for aj but fix all other alignments. [sent-151, score-0.562]
62 2 We choose alignment aj with probability P(aj|a1, · · ·aj−1, aj+1 · ·· aJ, f1J, which can be computed in the following way: e12I+1), P(aj|a1, · · · , aj−1, aj+1, · · · , aJ, f1J, e21I+1) =PPaj(Pa(J1a,1Jf1J,f|e1J21|Ie+12I1)+1) (7) For each alignment vaPriable aj, we choose t samples. [sent-152, score-0.657]
63 However, this sampling method needs a large amount of communication between machines in order to keep the parameters up to date ifwe compute the expected counts in parallel. [sent-155, score-0.14]
64 Instead, we do “batch learning”: we fix the parameters, scan through the entire corpus and compute expected counts in parallel (E-step); then combine all the counts together and update the parameters (Mstep). [sent-156, score-0.122]
65 For the fertility hidden Markov model, updating P(a1J, wheneverwe change the alignment aj can be| edone in constant time, so the complexity of choosing t samples for all aj (j = 1, 2, . [sent-159, score-1.623]
66 Surprisingly, we can achieve better results than the HMM by computing as few as 1 sample for each alignment, so the fertility hidden Markov model is much faster than the HMM. [sent-164, score-0.807]
67 2For fertility IBM Model 1, we only need to compute I 1 + values because e2II++11 are identical empty words. [sent-166, score-0.789]
68 601 Algorithm 1: One iteration of E-step:draw t samples for each aj for each sentence pair (f1J, in the corpus e21I+1) for (f1J, e21I+1) in the corpus do We also consider initializing the alignments using the HMM Viterbi algorithm in the E-step. [sent-167, score-0.6]
69 In this case, the fertility hidden Markov model is not faster than the HMM. [sent-168, score-0.807]
70 Fortunately, initializing using IBM Model 1 Viterbi does not decrease the accuracy in any noticeable way, and reduces the complexity of the Gibbs sampling algorithm. [sent-169, score-0.102]
71 In the testing stage, the sampling algorithm is the same as above except that we keep the alignments f1J|e21I+1). [sent-170, score-0.231]
72 a1J that maximize P(a1J, We need more samples in the testing stage because it is unlikely to get to the optimal alignments by sampling a few times for each alignment. [sent-171, score-0.317]
73 On the contrary, in the above training stage, although the samples are not accurate enough to represent the distribution defined by Equation 7 for each alignment aj, it is accurate enough for computing the expected counts, which are defined at the corpus level. [sent-172, score-0.187]
74 Interestingly, we found that throwing away the fertility and using the HMM Viterbi decoding achieves same results as the sampling approach (we can ignore the difference because it is tiny), but is faster. [sent-173, score-0.734]
75 Gibbs sampling for the fertility IBM Model 1 is similar but simpler. [sent-175, score-0.734]
76 IBM1F refers to the fertility IBM1 and HMMF refers to the fertility HMM. [sent-184, score-1.334]
77 We choose t = 1, 5, and 30 for the fertility HMM. [sent-185, score-0.667]
78 603 6 Experiments We evaluated our model by computing the word alignment and machine translation quality. [sent-189, score-0.206]
79 We use the alignment error rate (AER) as the word alignment evaluation criterion. [sent-190, score-0.285]
80 Let A be the alignments output by word alignment system, P be a set of possible alignments, and S be a set of sure alignments both labeled by human beings. [sent-191, score-0.481]
81 We evaluate our fertility models on a ChineseEnglish corpus. [sent-195, score-0.681]
82 We initialize IBM Model 1 and the fertility IBM Model 1 with a uniform distribution. [sent-199, score-0.701]
83 AER results are computed using the IBM Model 1 Viterbi alignments, and the Viterbi alignments obtained from the Gibbs sampling algorithm. [sent-202, score-0.231]
84 We initialize the HMM and the fertility HMM with the parameters learned in the 5th iteration of IBM Model 1. [sent-203, score-0.706]
85 However, both fertility models achieve better results than their baseline models using a small amount of samples. [sent-208, score-0.695]
86 For the fertility IBM Model 1, we sample 10 times for each aj, and restart 3 times in the training stage; 604 we sample 100 times and restart 12 times in the testing stage. [sent-209, score-0.793]
87 For the fertility HMM, we sample 30 times for each aj with no restarting in the training stage; no sampling in the testing stage because we use traditional HMM Viterbi decoding for testing. [sent-210, score-1.149]
88 Initially, the fertility IBM Model 1 and fertility HMM did not perform well. [sent-212, score-1.334]
89 If a target word e only appeared a few times in the training corpus, our model cannot reliably estimate the parameter λ(e). [sent-213, score-0.14]
90 Unfortunately, this does not solve the problem because all infrequent words tend to have larger fertility than they should. [sent-216, score-0.689]
91 We can see that the fer- tility IBM Model 1 consistently outperforms IBM Model 1, and the fertility HMM consistently outperforms the HMM. [sent-220, score-0.667]
92 The fertility HMM not only has lower AER than the HMM, it also runs faster than the HMM. [sent-221, score-0.746]
93 In fact, with just 1 sample for each alignment, our model archives lower AER than the HMM, and runs more than 5 times faster than the HMM. [sent-223, score-0.126]
94 We conclude that the fertility HMM not only has better AER results, but also runs faster than the hidden Markov model. [sent-225, score-0.807]
95 The training data is the same as the above word alignment evaluation bitexts, with alignments for each model symmetrized using the grow-diag-final heuristic. [sent-229, score-0.344]
96 Results are shown in Table 2; we see that better word alignment results do not lead to better translations. [sent-231, score-0.153]
97 77 Table 2: BLEU results 7 Conclusion We developed a fertility hidden Markov model that runs faster and has lower AER than the HMM. [sent-235, score-0.834]
98 While better word alignment results do not necessarily correspond to better translation quality, our translation results are comparable in translation quality to both the HMM and IBM Model 4. [sent-239, score-0.231]
99 HMM word and phrase alignment for statistical machine translation. [sent-270, score-0.153]
100 Extensions to HMM-based statis- tical word alignment models. [sent-305, score-0.153]
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Abstract: A word in one language can be translated to zero, one, or several words in other languages. Using word fertility features has been shown to be useful in building word alignment models for statistical machine translation. We built a fertility hidden Markov model by adding fertility to the hidden Markov model. This model not only achieves lower alignment error rate than the hidden Markov model, but also runs faster. It is similar in some ways to IBM Model 4, but is much easier to understand. We use Gibbs sampling for parameter estimation, which is more principled than the neighborhood method used in IBM Model 4.
2 0.68956852 18 emnlp-2010-Assessing Phrase-Based Translation Models with Oracle Decoding
Author: Guillaume Wisniewski ; Alexandre Allauzen ; Francois Yvon
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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