emnlp emnlp2010 emnlp2010-35 knowledge-graph by maker-knowledge-mining
Source: pdf
Author: Sankaranarayanan Ananthakrishnan ; Rohit Prasad ; David Stallard ; Prem Natarajan
Abstract: Production of parallel training corpora for the development of statistical machine translation (SMT) systems for resource-poor languages usually requires extensive manual effort. Active sample selection aims to reduce the labor, time, and expense incurred in producing such resources, attaining a given performance benchmark with the smallest possible training corpus by choosing informative, nonredundant source sentences from an available candidate pool for manual translation. We present a novel, discriminative sample selection strategy that preferentially selects batches of candidate sentences with constructs that lead to erroneous translations on a held-out development set. The proposed strategy supports a built-in diversity mechanism that reduces redundancy in the selected batches. Simulation experiments on English-to-Pashto and Spanish-to-English translation tasks demon- strate the superiority of the proposed approach to a number of competing techniques, such as random selection, dissimilarity-based selection, as well as a recently proposed semisupervised active learning strategy.
Reference: text
sentIndex sentText sentNum sentScore
1 com , Abstract Production of parallel training corpora for the development of statistical machine translation (SMT) systems for resource-poor languages usually requires extensive manual effort. [sent-5, score-0.315]
2 We present a novel, discriminative sample selection strategy that preferentially selects batches of candidate sentences with constructs that lead to erroneous translations on a held-out development set. [sent-7, score-1.217]
3 The proposed strategy supports a built-in diversity mechanism that reduces redundancy in the selected batches. [sent-8, score-0.292]
4 1 Introduction Resource-poor language pairs present a significant challenge to the development of statistical machine translation (SMT) systems due to the latter’s dependence on large parallel texts for training. [sent-10, score-0.327]
5 Such a corpus may be constructed by selecting the most informative instances from a large collection of source sentences for translation by a human expert, a technique often referred to as active learning. [sent-13, score-0.516]
6 (2005) described a selection strategy that attempts to maximize coverage by choosing sentences with the highest proportion of previously unseen n-grams. [sent-16, score-0.617]
7 Depending on the composition of the candidate pool with respect to the domain, this strategy may select irrelevant outliers. [sent-17, score-0.544]
8 (2009) proposed a number of features, such as similarity to the seed corpus, translation probability, n-gram and phrase coverage, etc. [sent-22, score-0.3]
9 However, this approach requires that the pool have the same distributional characteristics as the development sets used to train the ranking model. [sent-28, score-0.377]
10 Since similar or identical sentences in the pool will typically meet the selection criteria simultaneously, this can have the undesired effect of choosing redundant batches with low diversity. [sent-30, score-0.849]
11 The semi-supervised active learning strategy proposed by Ananthakrishnan et al. [sent-31, score-0.367]
12 (2010) uses multilayer perceptrons (MLPs) to rank candidate sentences based on various features, including domain representativeness, translation difficulty, and batch diversity. [sent-32, score-0.567]
13 While this strategy was shown to be superior to random as well as n-gram based dissimilarity selection, its coarse granularity (reducing a candidate sentence to a lowdimensional feature vector for ranking) makes it un- suitable for many situations. [sent-34, score-0.388]
14 In particular, it is seen to have little or no benefit over random selection when there is no logical separation of the candidate pool into “in-domain” and “out-of-domain” subsets. [sent-35, score-0.674]
15 This paper introduces a novel, active sample selection technique that identifies translation errors on a held-out development set, and preferentially selects candidate sentences with constructs that are incorrectly translated in the former. [sent-36, score-1.135]
16 A discriminative pairwise comparator function, trained on the ranked development set, is used to order candidate sentences and pick sentences that provide maximum potential reduction in translation error. [sent-37, score-1.071]
17 The feature functions that power the comparator are updated after each selection to encourage batch diversity. [sent-38, score-0.819]
18 In the following sections, we provide details of the proposed sample selection approach, and describe simulation experiments that demonstrate its superiority over a number of competing strategies. [sent-39, score-0.712]
19 2 Error-Driven Active Learning Traditionally, unsupervised selection strategies have dominated the active learning literature for natural language processing (Hwa, 2004; Tang et al. [sent-40, score-0.474]
20 (2009) and the semi-supervised selection technique of Ananthakrishnan et al. [sent-48, score-0.277]
21 However, while the former uses the posterior translation probability and the latter, a sentence-level confidence score as part of the overall selection strategy, current active learning techniques for SMT do not explicitly target the sources of error. [sent-50, score-0.571]
22 Error-driven active learning attempts to choose candidate instances that potentially maximize error reduction on a reference set (Cohn et al. [sent-51, score-0.434]
23 The selection algorithm is then trained to choose, from the candidate pool, sentences containing constructs that give rise to translation errors on this set. [sent-54, score-0.635]
24 Assuming perfect reference translations and word alignment in subsequent SMT training, these sentences provide maximum potential reduction in translation error with respect to the seed SMT system. [sent-55, score-0.476]
25 • A candidate pool of monolingual source sentAen cceasn dPid fartoem p woohlic ohf samples nmguusalt b seo usrecleect seedn. [sent-59, score-0.471]
26 We further make the following reasonable assumptions: (a) the development set D and the test set T are drawn from the same distribution and (b) the candidate pool P consists of both in- and outof-domain source sentences, as well as an allowable level of redundancy (similar or identical sentences). [sent-62, score-0.647]
27 Using translation errors on the development set to drive sample selection has the following advantages over previously proposed active learning strategies for SMT. [sent-63, score-0.897]
28 This is the more intuitive, direct approach to sample selection for SMT. [sent-74, score-0.345]
29 The proposed implementation of error-driven active learning for SMT, discriminative sample selection, is described in the following section. [sent-78, score-0.435]
30 3 Discriminative Sample Selection The goal of active sample selection is to induce an ordering of the candidate instances that satisfies an objective criterion. [sent-79, score-0.71]
31 (2005) ordered candidate sentences based on the frequency of unseen n-grams. [sent-81, score-0.303]
32 (2010) attempted to order the candidate pool to incrementally maximize source ngram coverage on a held-out development set, subject to difficulty and diversity constraints. [sent-86, score-0.68]
33 In the case of error-driven active learning, we attempt to learn an ordering model based on errors observed on the held-out development set D. [sent-87, score-0.282]
34 This approach, inspired by Ailon and Mohri (2008), involves the construction of a binary classifier functioning as a relational operator that can be used to order the candidate sentences. [sent-89, score-0.339]
35 The pairwise comparator is trained on an ordering of D that ranks constituent sentences in decreasing order of the number of translation errors. [sent-90, score-0.685]
36 The comparator is then used to rank the candidate pool in decreasing order of potential translation error reduction. [sent-91, score-1.008]
37 As detailed in Ailon and Mohri (2008), the comparator must satisfy the constraint that h(u, v) and h(v, u) be complementary, i. [sent-94, score-0.332]
38 We implement h(u, v) as a combination of discriminative maximum entropy classifiers triggered by feature functions drawn from n-grams of u and v. [sent-98, score-0.244]
39 First, if we use constituent n-grams of u and v as feature functions to trigger the classifier, there is no way to distinguish between (u, v) and (v, u) as they will trigger the same feature functions. [sent-102, score-0.278]
40 i am* go ing :3y } * * Table 1: Standard and complementary trigram feature functions for a source pair (u, v). [sent-118, score-0.284]
41 Then, to evaluate p(u, v), for instance, we invoke the classifier with standard feature functions for u and complementary feature functions for v. [sent-120, score-0.428]
42 Similarly, p(v, u) is evaluated by triggering complementary feature functions for u and standard feature functions for v. [sent-121, score-0.352]
43 Thus, the binary pairwise comparator can be constructed from the permuted classifier outputs. [sent-129, score-0.46]
44 2 Training the Pairwise Comparator Training the maximum-entropy classifier for the pairwise comparator requires a set of target labels 629 and input feature functions, both of which are derived from the held-out development set D. [sent-131, score-0.576]
45 We begin by decoding the source sentences in D with the seed SMT system, followed by error analysis using the Translation Edit Rate (TER) measure (Snover et al. [sent-132, score-0.281]
46 TER measures translation quality by computing the number of edits (insertions, substitutions, and deletions) and shifts required to transform a translation hypothesis to its corresponding reference. [sent-134, score-0.312]
47 The first, signifying that u appears before v in D0, assigns the label true to a trigger list consisting of standard feature functions derived from u, and complementary feature functions derived from v. [sent-141, score-0.407]
48 The second, reinforcing this observation, assigns the label false to a trigger list consisting of complementary feature functions from u, and standard feature functions from v. [sent-142, score-0.407]
49 The labeled training set (feature:label pairs) for the comparator can be expressed as follows: ∀(u, v) ∈ D0 : u < v, {f(u) f0(v) } : true {f0(u) f(v)} : false Thus, if there are d sentences in D0, we obtain a total of d(d − 1) labeled examples to train the comparator. [sent-143, score-0.358]
50 3 Greedy Discriminative Selection The discriminatively-trained pairwise comparator can be used as a relational operator to sort the candidate pool P in decreasing order of potential translation error reduction. [sent-146, score-1.238]
51 Assuming the pool contains N candidate sentences, and given a fast sorting algorithm such as Quicksort, the complexity of this strategy is O(N log N). [sent-148, score-0.544]
52 A potential downside of this approach reveals it- self when there is redundancy in the candidate pool. [sent-150, score-0.249]
53 Since the batch is selected in a single atomic operation from the sorted candidates, and because similar or identical sentences will typically occupy the same range in the ordered list, it is likely that this approach will result in batches with low diversity. [sent-151, score-0.519]
54 Whereas we desire diverse batches for better coverage and efficient use of manual translation resources. [sent-152, score-0.453]
55 (2010) used a greedy, incremental batch construction strategy with an integrated, explicit batch diversity feature as part of the ranking model. [sent-156, score-0.658]
56 Based on these ideas, we design a greedy selection strategy using the discriminative relational operator. [sent-157, score-0.593]
57 The subscript indicates that our implementation of this function utilizes the discriminative relational operator trained on the development set D. [sent-159, score-0.303]
58 We then remove the standard and complementary feature functions f(s) and f0(s) triggered by s from the global pool of feature functions obtained from D, so that they do not play a role in the selection of subsequent sentences for the batch. [sent-161, score-0.924]
59 4 Experiments and Results We conduct a variety of simulation experiments with multiple language pairs (English-Pashto and Spanish-English) and different data configurations in order to demonstrate the utility of discriminative sample selection in the context of resource-poor SMT. [sent-165, score-0.696]
60 We also compare the performance of the proposed strategy to numerous competing active and passive selection methods as follows: • Random: Source sentences are uniformly sampled foromm: tShoeu rcacned siednatteen pool Pre. [sent-166, score-1.047]
61 Longest: Pick the longest sentences from the cLaonndgiedsat:te pool P th. [sent-171, score-0.351]
62 • Semi-supervised: Semi-supervised active learning iw-siuthp greedy iSnecmreim-seunptearlv siseeledc atciotniv (Ananthakrishnan et al. [sent-172, score-0.285]
63 • Discriminative: Choose sentences that potentially amtiivniem:ize translation error using a maximum-entropy pairwise comparator (proposed method). [sent-174, score-0.652]
64 Identical low-resource initial conditions are applied to each selection strategy so that they may be objectively compared. [sent-175, score-0.359]
65 A very small seed corpus S is sampled from the available parallel training data; the remainder serves as the candidate pool. [sent-176, score-0.421]
66 Following the literature on active learning for SMT, our simulation experiments are iterative. [sent-177, score-0.429]
67 A fixed-size batch of source sentences is constructed from the candidate pool using one of the above selection strategies. [sent-178, score-0.924]
68 We then look up the corresponding translations from the candidate targets (simulating an expert human translator), augment the seed corpus with the selected data, and update the SMT system with the expanded training corpus. [sent-179, score-0.372]
69 At each iteration, we decode the unseen test set T with the most current SMT configuration and evaluate translation performance in terms of BLEU as well as coverage (defined as the fraction of untranslatable source words in the target hypotheses). [sent-182, score-0.391]
70 1 English-Pashto Simulation Our English-Pashto (E2P) data originates from a two-way collection of spoken dialogues, and consists of two parallel sub-corpora: a directional E2P corpus and a directional Pashto-English (P2E) corpus. [sent-186, score-0.356]
71 We obtained a seed training corpus by randomly sampling 1,000 sentence pairs from the directional E2P training partition. [sent-201, score-0.324]
72 The remainder ofthis set, and the entire reversed P2E training partition were combined to create the pool (109. [sent-202, score-0.289]
73 In the past, we have observed that the reversed directional P2E data gives very little performance gain in the E2P direction even though its vocabulary is 631 similar, and can be considered “out-of-domain” as far as the E2P translation task is concerned. [sent-204, score-0.321]
74 Thus, our pool consists of 30% in-domain and 70% outof-domain sentence pairs, making for a challenging active learning problem. [sent-205, score-0.458]
75 A pool training set of 10k source sentences is sampled from this collection for the semi-supervised selection strategy, leaving us with 99. [sent-206, score-0.628]
76 4k candidate sentences, which we use for all competing techniques. [sent-207, score-0.241]
77 The data configuration used in this simulation is identical to Ananthakrishnan et al. [sent-208, score-0.295]
78 We simulated a total of 20 iterations with batches of 200 sentences each; the original 1,000 sample seed corpus grows to 5,000 sentence pairs and the end of our simulation. [sent-210, score-0.661]
79 Figure 1(a) illustrates the variation in BLEU scores across iterations for each selection strategy. [sent-211, score-0.337]
80 The proposed discriminative sample selection technique performs significantly better at every iteration than random, similarity, dissimilarity, longest, and semi-supervised active selection. [sent-212, score-0.712]
81 Figure 1(b) shows the variation in coverage (percentage of untranslatable source words in target hypotheses) for each selection technique. [sent-221, score-0.454]
82 Here, discriminative sample selection was better than all other approaches except longest-sentence selection. [sent-222, score-0.427]
83 E26309Uare Table 2: Source corpus size (in words) and BLEUarea after 20 sample selection iterations. [sent-234, score-0.345]
84 Note that this data configuration is different from that of the E2P simulation in that there is no logical separation of the training data into “in-domain” and “out-of-domain” sets. [sent-237, score-0.293]
85 The remainder, after setting aside another 10k source sentences for training the semisupervised strategy, serves as the candidate pool. [sent-241, score-0.347]
86 We again simulated a total of 20 iterations, except in this case, we used batches of 100 sentences in an attempt to obtain smoother performance trajectories. [sent-242, score-0.309]
87 The training corpus grows from 500 sentence pairs to 2,500 as the simulation progresses. [sent-243, score-0.269]
88 Variation in BLEU scores and coverage for the S2E simulation are illustrated in Figures 2(a) and 2(b), respectively. [sent-244, score-0.286]
89 Discriminative sample selection outperformed all other selection techniques across all iterations of the simulation. [sent-245, score-0.625]
90 The proposed method also outperformed other selection strategies in improving coverage, with significantly better results especially in the early iterations. [sent-252, score-0.296]
91 We proposed a novel, discriminative sample selection strategy that can help lower these costs by choosing batches of source sentences from a large candidate pool. [sent-255, score-1.139]
92 The chosen sentences, in conjunction with their manual translations, provide significantly better SMT performance than numerous competing active and passive selection techniques. [sent-256, score-0.618]
93 Our approach hinges on a maximum-entropy pairwise comparator that serves as a relational operator for comparing two source sentences. [sent-257, score-0.663]
94 This allows us to rank the candidate pool in decreasing order of potential reduction in translation error with respect to an existing seed SMT system. [sent-258, score-0.884]
95 The discriminative comparator is coupled with a greedy, incremental selection technique that discourages redundancy in the chosen batches. [sent-259, score-0.79]
96 The proposed technique diverges from existing work on active sample selection for SMT in that it uses machine learning techniques in an attempt to explicitly reduce translation error by choosing sentences whose constituents were incorrectly translated in a held-out development set. [sent-260, score-0.988]
97 While the performance of competing strategies varied across language pairs and data configurations, discriminative sample selection proved consistently superior under all test conditions. [sent-261, score-0.597]
98 It provides a powerful, flexible, data selection front-end for rapid development of SMT systems. [sent-262, score-0.302]
99 We are now actively exploring the possibility of linking the sample selection front-end to a crowd-sourcing backend, in order to obtain “non-expert” translations using a platform such as the Amazon Mechanical Turk. [sent-265, score-0.391]
100 A semisupervised batch-mode active learning strategy for improved statistical machine translation. [sent-272, score-0.374]
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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. Acknowledgments Warm thanks to Houda Bouamor for helping us with the annotation tool. This work has been partly financed by OSEO, the French State Agency for Innovation, under the Quaero program. References Tobias Achterberg. 2007. Constraint Integer Programming. Ph.D. thesis, Technische Universit a¨t Berlin. http : / / opus .kobv .de /tuberl in/vol ltexte / 2 0 0 7 / 16 11/ . Abhishek Arun and Philipp Koehn. 2007. Online learning methods for discriminative training of phrase based statistical machine translation. In Proc. of MT Summit XI, Copenhagen, Denmark. Michael Auli, Adam Lopez, Hieu Hoang, and Philipp Koehn. 2009. A systematic analysis of translation model search spaces. In Proc. of WMT, pages 224–232, Athens, Greece. Satanjeev Banerjee and Alon Lavie. 2005. METEOR: An automatic metric for MT evaluation with improved correlation with human judgments. 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