emnlp emnlp2010 emnlp2010-86 knowledge-graph by maker-knowledge-mining

86 emnlp-2010-Non-Isomorphic Forest Pair Translation


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Author: Hui Zhang ; Min Zhang ; Haizhou Li ; Eng Siong Chng

Abstract: This paper studies two issues, non-isomorphic structure translation and target syntactic structure usage, for statistical machine translation in the context of forest-based tree to tree sequence translation. For the first issue, we propose a novel non-isomorphic translation framework to capture more non-isomorphic structure mappings than traditional tree-based and tree-sequence-based translation methods. For the second issue, we propose a parallel space searching method to generate hypothesis using tree-to-string model and evaluate its syntactic goodness using tree-to-tree/tree sequence model. This not only reduces the search complexity by merging spurious-ambiguity translation paths and solves the data sparseness issue in training, but also serves as a syntax-based target language model for better grammatical generation. Experiment results on the benchmark data show our proposed two solutions are very effective, achieving significant performance improvement over baselines when applying to different translation models.

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Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 com Abstract This paper studies two issues, non-isomorphic structure translation and target syntactic structure usage, for statistical machine translation in the context of forest-based tree to tree sequence translation. [sent-3, score-1.249]

2 For the first issue, we propose a novel non-isomorphic translation framework to capture more non-isomorphic structure mappings than traditional tree-based and tree-sequence-based translation methods. [sent-4, score-0.471]

3 For the second issue, we propose a parallel space searching method to generate hypothesis using tree-to-string model and evaluate its syntactic goodness using tree-to-tree/tree sequence model. [sent-5, score-0.441]

4 This not only reduces the search complexity by merging spurious-ambiguity translation paths and solves the data sparseness issue in training, but also serves as a syntax-based target language model for better grammatical generation. [sent-6, score-0.491]

5 Therefore, from bilingual viewpoint, we face two fundamental problems: the mapping between bilingual structures and the way of carrying out the target structures combination. [sent-16, score-0.504]

6 For the first issue, a number of models have been proposed to model the structure mapping between tree and string (Galley et al. [sent-17, score-0.466]

7 , 2006; Yamada and Knight, 2001 ; DeNeefe and Knight, 2009) and between tree and tree (Eisner, 2003; Zhang et al. [sent-19, score-0.462]

8 However, one of the major challenges is that all the current models only allow one-to-one mapping from one source frontier non-terminal node (Galley et al. [sent-22, score-0.886]

9 , 2004) to one target frontier non-terminal node in a bilingual translation rule. [sent-23, score-1.079]

10 Therefore, all those translation equivalents with one-to-many frontier non-terminal node mapping cannot be covered by the current state-of-the-art models. [sent-24, score-1.01]

11 tc ho2d0s10 in A Nsastoucira tlio Lnan fogru Cagoem Ppruotcaetisosninagl, L pinag eusis 4t4ic0s–450, target side (string to tree model). [sent-28, score-0.47]

12 There is no well study in considering both the source side information and the compatibility between different target syntactic structures during combination. [sent-29, score-0.43]

13 In addition, it is well known that the traditional tree-to-tree models suffer heavily from the data sparseness issue in training and the spurious-ambiguity translation path issue (the same translation with different syntactic structures) in decoding. [sent-30, score-0.56]

14 In addition, because of the performance limitation of automatic syntactic parser, researchers propose using packed forest (Tomita, 1987; Klein and Manning, 2001 ; Huang, 2008)1 instead of 1-best parse tree to carry out training (Mi and Huang, 2008) and decoding (Mi et al. [sent-31, score-0.868]

15 However, when we apply the tree-to-tree model to the bilingual forest structures, both training and decoding become very complicated. [sent-33, score-0.547]

16 In this paper, to address the first issue, we propose a framework to model the non-isomorphic translation process from source tree fragment to target tree sequence, allowing any one source frontier non-terminal node to be translated into any number of target frontier non-terminal nodes. [sent-34, score-2.198]

17 We evaluate and integrate the two technologies into forest-based tree to tree sequence translation. [sent-36, score-0.643]

18 Experimental results on the NIST-2003 and NIST-2005 Chinese-English translation tasks show that our methods significantly outperform the forest-based tree to string and previous tree to tree models as well as the phrase-based model. [sent-37, score-0.942]

19 Yamada and Knight (2001) propose 1 A packed forest is a compact representation of a set of trees with sharing substructures; formally, it is defined as a triple a triple? [sent-43, score-0.561]

20 connect the father node to its children nodes as in a tree. [sent-56, score-0.459]

21 (2007) propose the tree sequence to string model to capture rules covered by continuous sequence of trees. [sent-64, score-0.857]

22 (2009a) propose the concept of virtual node to reform a tree sequence as a tree, and design efficient algorithms for tree sequence model in forest context. [sent-67, score-1.823]

23 All these works only consider either the source side or the target side syntax information. [sent-68, score-0.471]

24 One common limitation of the above works is they only allow the one-to-one mapping between each non-terminal frontier node, and thus they suffer from the issue of rule coverage. [sent-74, score-0.692]

25 , 2009) decoder has to rely solely on the span information or source side information to combine the target syntactic structures, without checking the compatibility of the merging nodes, in order not to fail many translation paths. [sent-77, score-0.819]

26 In addition, our proposed solution of using target syntax information enables our forest-based tree-to-tree sequence translation decoding algorithm to not only capture bilingual forest information but also have almost the same complexity as forest-based tree-to-string translation. [sent-84, score-1.128]

27 3 Tree to Tree Sequence Rules The motivation of introducing tree to tree sequence rules is to add target syntax information to tree-to-string rules. [sent-86, score-0.993]

28 2 illustrates the examples of tree to string rules extracted from Fig. [sent-93, score-0.43]

29 Its source side is a sub-tree of source parse tree and its target side is a string with only one variable/non-terminal X. [sent-96, score-0.79]

30 The source side and the target side is translation of each other with the constraint of word alignments. [sent-97, score-0.573]

31 2 Tree to Tree Sequence Rules It is more challenging when extracting rules with target tree structure as constraint. [sent-100, score-0.549]

32 The problem is that, given a source tree node, we are able to find its target string translation, but these target string may not form a linguistic sub-tree. [sent-104, score-0.782]

33 3, the source tree node “ADVP” in solid eclipse is translated to “try hard to” in the target sentence, but there 442 is no corresponding sub-tree covering and only covering it in the target side. [sent-106, score-1.188]

34 The answer is that the previous tree or tree sequence-based models fail to model the Rule 1 and Rule 2 at Fig. [sent-109, score-0.462]

35 2, since at frontier node level they only allow one-to-one node mapping but the solution is one-to-many non-terminal frontier node mapping. [sent-110, score-1.85]

36 A restructured tree with a virtual span root • • Def. [sent-118, score-0.829]

37 The “root node sequence” of a span is such a node sequence that any node in this sequence could not be a child of a node in other node sequence of the span. [sent-124, score-2.551]

38 Intuitively, the “root node sequence” of a span is the node sequence with the highest topology level. [sent-125, score-1.109]

39 For example, “VBP ADVP TO” is the “root node sequence” of the span of “try hard to”. [sent-126, score-0.596]

40 The “span root” of a span is such a node that if the “root node sequence” contains only one tree node, then the “span root” is this tree node; otherwise, the “span root” is the virtual father node (Zhang et al. [sent-130, score-1.976]

41 3 by introducing the virtual node “VBP+ADVP+TO” as the “span root” of the span of “try hard to”. [sent-134, score-0.795]

42 For each such frontier node, we can find its corresponding target “span root”. [sent-137, score-0.515]

43 If the “span root” is a virtual node, then we add it into the target tree as a virtual segmentation joint point. [sent-138, score-0.787]

44 After adding the “span root” as joint point, we are able to ensure that each frontier source node has only one corresponding target node, then we can use any traditional rule extraction algorithm to extract rules, including those rules with one-to-many non-terminal frontier map- pings. [sent-139, score-1.612]

45 5 lists the corresponding rules with target structure information of the tree-to-string rules in Fig 2. [sent-143, score-0.472]

46 , 2009a) can extracted rule 3 since they allow one-to-many mapping in root node level. [sent-148, score-0.852]

47 As a result, our rule coverage is the same as tree-to-string framework while our rules contain more informative target syntax information. [sent-151, score-0.531]

48 3 Rule Extraction in Tree Context Given a word aligned tree pair, we first extract the set of minimum tree to string rules (Galley et al. [sent-155, score-0.661]

49 2004), then for each tree-to-string rule, we can easily extract its corresponding tree-to-tree sequence rule by introducing the virtual span root node. [sent-156, score-0.992]

50 Rule combination and virtual node removing Please note that in generating composite rules, if the joint node is a virtual node, we have to recover the original link and remove this virtual node to avoid unnecessary ambiguity. [sent-160, score-1.677]

51 4 Rule Extraction in Forest Context In forest pair context, we also first generate the minimum tree-to-string rule set as Mi et al. [sent-166, score-0.615]

52 In tree pair context, given a tree-to-string rule, there is one and only one corresponding tree-to-tree sequence rule. [sent-168, score-0.444]

53 But in forest pair context, given one such tree-to-string rule, there are many corresponding tree-to-tree sequence rules. [sent-169, score-0.621]

54 Given a source sub-tree, we can obtain the target root span where the target sub-forests start and the frontier spans where the target sub-forests stop. [sent-174, score-1.279]

55 To indentify all the hyper-edges in the sub-forests, we start from every node covering the root span, traverse from top to down, mark all the hyper-edges visited and stop at the node if its span is a sub-span of one of the forest frontier spans or if it is a word node. [sent-175, score-1.93]

56 The reason we stop at the node once it fell into a frontier span (i. [sent-176, score-0.893]

57 the span of the node is a sub-span of the frontier span) is to guarantee that given any frontier span, we could stop at the “root node sequence” of this span by Def. [sent-178, score-1.786]

58 Its corresponding target root span is [1,4] (corresponding to source root “VP” ) and its corresponding target frontier span is { [1,3], study[4,4] }. [sent-184, score-1.584]

59 Now given the target forest, we start from node VP[1,4] and traverse from top to down, finally stop at following nodes: VBP[1,1], ADVP[2,2], TO[3,3], study . [sent-185, score-0.548]

60 The root may be a virtual span root node in the case of the one-to-many frontier non-terminal node mappings. [sent-188, score-1.834]

61 444 Please note that the starting root node must be a single node, being either a normal forest node or a virtual “span root” node. [sent-189, score-1.518]

62 The virtual “span root” node serves as the frontier node of upper rules and root node of the currently being extracted rules. [sent-190, score-1.96]

63 Because we extract rules in a top-to-down manner, the necessary virtual “span root” node for current sub-forest has already been added into the global forest when extracting upper level rules. [sent-191, score-1.132]

64 (2009), we assign a fractional count to a rule to measure how likely it appears given the context of the forest pair. [sent-196, score-0.633]

65 In following equation, “S” means source sub-tree, “T” means target sub-tree, “SF” is source forest and “TF” is the target forest. [sent-197, score-0.886]

66 The above equation means the fractional count of a source-target tree pair is just the product of each of their fractional count in corresponding forest context in following equation. [sent-239, score-0.759]

67 In addition, if a sub-tree root is a virtual node (formed by a root node sequence), then we use following equation to approximate the outside probability of the virtual node. [sent-350, score-1.5]

68 1 Decoding Traditional Forest-based Decoding A typical translation process of a forest-based system is to first convert the source packed forest into a target translation forest, and then apply search algorithm to find the best translation result from this target translation forest (Mi et al. [sent-391, score-2.022]

69 For the tree-to-string model, the forest conversion process is as following: given an input packed forest, we do pattern matching (Zhang et al. [sent-393, score-0.533]

70 A forest conversion step in a tree to string model Fig. [sent-398, score-0.747]

71 The node “X-VP[4,4]” 445 in the target forest means that its syntactic label in target forest is “X” and it is translated from the source node “VP[4,4]” in the source forest. [sent-401, score-2.086]

72 In this target hyper-edge, “X-ADVP[3,3] X-ADVP[2,2]” means the translation from source node “ADVP[3,3]” is put before the translation from “ADVP[2,2]”, representing a structure reordering. [sent-402, score-0.981]

73 For example, a source node may be translated into a “NP” (noun phrase) in target side. [sent-407, score-0.643]

74 In this case, the target tree does not well model the translation syntactically. [sent-409, score-0.561]

75 One natural solution to the above issue is to use the tree to tree/tree sequence model, which have richer target syntax structures for more discriminative probability and finer labels to guide the combination process. [sent-411, score-0.876]

76 We restructure the tree-to-tree sequence rule set by grouping all the rules according to their corresponding tree-to-string rules. [sent-416, score-0.516]

77 With the re-constructed rule set, during decoding, we generate two target translation hypothesis spaces (in the form of packed forests) synchronously by the tree-to-string rules and tree-to-tree sequence rules, and maintain the projection between them. [sent-419, score-1.02]

78 In other words, we generate hypothesis (searching) from the tree-to-string forest and calculate the probability (evaluating syntax goodness) for each hypothesis by the hyper-edges in the tree-to-tree sequence forest. [sent-420, score-0.755]

79 10, given a tree-to-tree sequence rule, it is easy to find its corresponding tree-to-string rule by simply ignoring the target inside structure and renaming the root and leaves non-terminal labels into “X”. [sent-426, score-0.822]

80 We iterate through the tree-to-tree sequence rule set, find its corresponding tree-to-string rule and then group those rules with the same tree-to-string projection. [sent-427, score-0.697]

81 After that, the original tree-to-tree sequence rule set becomes a set of smaller rule sets. [sent-428, score-0.543]

82 We apply the tree-to-string rules to generate an explicit target translation forest to represent the target sentences space. [sent-430, score-1.044]

83 At the same time, whenever a tree-to-string rule is applied, we also retrieve its corresponding tree-to-tree sequence rule set and generate a set of latent hyper-edges with fine-grained syntax information. [sent-431, score-0.696]

84 We can view the latent fine forest as imbedded inside the explicit coarse forest. [sent-435, score-0.605]

85 Derivation path and derivation forest In this subsection, we show exactly how our decoder finds the best result from the parallel spaces. [sent-443, score-0.557]

86 We generate hypothesis by traversing the coarse forest in the parallel spaces with cube-pruning (Huang and Chiang, 2007). [sent-444, score-0.671]

87 Given a newly generated hypothesis, it is affiliated with a derivation path (tree) in the coarse forest and a group of derivation paths (sub-forest) in the finer forest. [sent-445, score-0.762]

88 In this paper, we use the sum of probabilities of all the derivation paths in the finer forest to measure the quality of the candidate translation suggested by the hypothesis. [sent-448, score-0.795]

89 11, we can see there may be more than one corresponding finer forests, it is easy to understand that the sum of all the trees’ probabilities in these finer forests is equal to the sum of the inside probability of all these root nodes of these finer forests. [sent-450, score-0.754]

90 While for the finer hyper-edges, we only link the root nodes of sub-forests to upper hyper-edges with the same linking node label. [sent-453, score-0.787]

91 , 2008) to 8 on both source and target forests for rule extraction. [sent-481, score-0.475]

92 4) FT2TS (1to1): our forest-based tree-to-tree sequence system, where 1to1 means only one-to-one frontier non-terminal node mapping is allowed, thus the system does not follow our non-isomorphic mapping framework. [sent-489, score-1.106]

93 Statistics of rule coverage, where “T2S covered” means the percentage of tree-to-string rules that can be covered by the model Table 2 studies the node isomorphism between bilingual forest pair. [sent-523, score-1.168]

94 We can see that the non-isomorphic node translation mapping (1toN) 448 accounts for 57. [sent-524, score-0.652]

95 36)) of all the forest non-terminal nodes with target translation. [sent-527, score-0.638]

96 This means that the one-to-many node mapping is a major issue in structure transformation. [sent-528, score-0.584]

97 FT2TS (1to1) does not allow one-to-many frontier node mapping, so it could only recover the non-isomorphic node mapping in the root level, while FT2TS (1toN) could make it at both root and leaf levels. [sent-533, score-1.598]

98 Based on this framework, we design an efficient algorithm to extract tree-to-tree sequence translation rules from word aligned bilingual forest pairs. [sent-561, score-0.947]

99 We also elaborate the parallel searching space-based decoding algorithm and the node label checking scheme, which leads to very efficient decoding speed as fast as the forest-based tree-to-string model does, at the same time is able to utilize informative target structure knowledge. [sent-562, score-0.886]

100 In the future, we are interested in testing our algorithm at forest-based tree sequence to tree sequence translation. [sent-565, score-0.824]


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Abstract: Extant Statistical Machine Translation (SMT) systems are very complex softwares, which embed multiple layers of heuristics and embark very large numbers of numerical parameters. As a result, it is difficult to analyze output translations and there is a real need for tools that could help developers to better understand the various causes of errors. In this study, we make a step in that direction and present an attempt to evaluate the quality of the phrase-based translation model. In order to identify those translation errors that stem from deficiencies in the phrase table (PT), we propose to compute the oracle BLEU-4 score, that is the best score that a system based on this PT can achieve on a reference corpus. By casting the computation of the oracle BLEU-1 as an Integer Linear Programming (ILP) problem, we show that it is possible to efficiently compute accurate lower-bounds of this score, and report measures performed on several standard benchmarks. Various other applications of these oracle decoding techniques are also reported and discussed. 1 Phrase-Based Machine Translation 1.1 Principle A Phrase-Based Translation System (PBTS) consists of a ruleset and a scoring function (Lopez, 2009). The ruleset, represented in the phrase table, is a set of phrase1pairs {(f, e) }, each pair expressing that the source phrase f can ,bee) r}e,w earicthten p (atirra enxslparteedss)i inngto t a target phrase e. Trarsaens flation hypotheses are generated by iteratively rewriting portions of the source sentence as prescribed by the ruleset, until each source word has been consumed by exactly one rule. The order of target words in an hypothesis is uniquely determined by the order in which the rewrite operation are performed. The search space ofthe translation model corresponds to the set of all possible sequences of 1Following the usage in statistical machine translation literature, use “phrase” to denote a subsequence of consecutive words. we 933 rules applications. The scoring function aims to rank all possible translation hypotheses in such a way that the best one has the highest score. A PBTS is learned from a parallel corpus in two independent steps. In a first step, the corpus is aligned at the word level, by using alignment tools such as Gi z a++ (Och and Ney, 2003) and some symmetrisation heuristics; phrases are then extracted by other heuristics (Koehn et al., 2003) and assigned numerical weights. In the second step, the parameters of the scoring function are estimated, typically through Minimum Error Rate training (Och, 2003). Translating a sentence amounts to finding the best scoring translation hypothesis in the search space. Because of the combinatorial nature of this problem, translation has to rely on heuristic search techniques such as greedy hill-climbing (Germann, 2003) or variants of best-first search like multi-stack decoding (Koehn, 2004). Moreover, to reduce the overall complexity of decoding, the search space is typically pruned using simple heuristics. For instance, the state-of-the-art phrase-based decoder Moses (Koehn et al., 2007) considers only a restricted number of translations for each source sequence2 and enforces a distortion limit3 over which phrases can be reordered. As a consequence, the best translation hypothesis returned by the decoder is not always the one with the highest score. 1.2 Typology of PBTS Errors Analyzing the errors of a SMT system is not an easy task, because of the number of models that are combined, the size of these models, and the high complexity of the various decision making processes. For a SMT system, three different kinds of errors can be distinguished (Germann et al., 2004; Auli et al., 2009): search errors, induction errors and model errors. The former corresponds to cases where the hypothesis with the best score is missed by the search procedure, either because of the use of an ap2the 3the option of Moses, defaulting to 20. dl option of Moses, whose default value is 7. tt l ProceMedITin,g Ms oasfs thaceh 2u0se1t0ts C,o UnSfAer,e n9c-e11 on O Ectmobpeir ic 2a0l1 M0.e ?tc ho2d0s10 in A Nsastouciraatlio Lnan fogru Cagoem Ppruotcaetisosninagl, L pinaggeusis 9t3ic3s–943, proximate search method or because of the restrictions of the search space. Induction errors correspond to cases where, given the model, the search space does not contain the reference. Finally, model errors correspond to cases where the hypothesis with the highest score is not the best translation according to the evaluation metric. Model errors encompass several types oferrors that occur during learning (Bottou and Bousquet, 2008)4. Approximation errors are errors caused by the use of a restricted and oversimplistic class of functions (here, finitestate transducers to model the generation of hypotheses and a linear scoring function to discriminate them) to model the translation process. Estimation errors correspond to the use of sub-optimal values for both the phrase pairs weights and the parameters of the scoring function. The reasons behind these errors are twofold: first, training only considers a finite sample of data; second, it relies on error prone alignments. As a result, some “good” phrases are extracted with a small weight, or, in the limit, are not extracted at all; and conversely that some “poor” phrases are inserted into the phrase table, sometimes with a really optimistic score. Sorting out and assessing the impact of these various causes of errors is of primary interest for SMT system developers: for lack of such diagnoses, it is difficult to figure out which components of the system require the most urgent attention. Diagnoses are however, given the tight intertwining among the various component of a system, very difficult to obtain: most evaluations are limited to the computation of global scores and usually do not imply any kind of failure analysis. 1.3 Contribution and organization To systematically assess the impact of the multiple heuristic decisions made during training and decoding, we propose, following (Dreyer et al., 2007; Auli et al., 2009), to work out oracle scores, that is to evaluate the best achievable performances of a PBTS. We aim at both studying the expressive power of PBTS and at providing tools for identifying and quantifying causes of failure. Under standard metrics such as BLEU (Papineni et al., 2002), oracle scores are difficult (if not impossible) to compute, but, by casting the computation of the oracle unigram recall and precision as an Integer Linear Programming (ILP) problem, we show that it is possible to efficiently compute accurate lower-bounds of the oracle BLEU-4 scores and report measurements performed on several standard benchmarks. The main contributions of this paper are twofold. We first introduce an ILP program able to efficiently find the best hypothesis a PBTS can achieve. This program can be easily extended to test various improvements to 4We omit here optimization errors. 934 phrase-base systems or to evaluate the impact of different parameter settings. Second, we present a number of complementary results illustrating the usage of our oracle decoder for identifying and analyzing PBTS errors. Our experimental results confirm the main conclusions of (Turchi et al., 2008), showing that extant PBTs have the potential to generate hypotheses having very high BLEU4 score and that their main bottleneck is their scoring function. The rest of this paper is organized as follows: in Section 2, we introduce and formalize the oracle decoding problem, and present a series of ILP problems of increasing complexity designed so as to deliver accurate lowerbounds of oracle score. This section closes with various extensions allowing to model supplementary constraints, most notably reordering constraints (Section 2.5). Our experiments are reported in Section 3, where we first introduce the training and test corpora, along with a description of our system building pipeline (Section 3. 1). We then discuss the baseline oracle BLEU scores (Section 3.2), analyze the non-reachable parts of the reference translations, and comment several complementary results which allow to identify causes of failures. Section 4 discuss our approach and findings with respect to the existing literature on error analysis and oracle decoding. We conclude and discuss further prospects in Section 5. 2 Oracle Decoder 2.1 The Oracle Decoding Problem Definition To get some insights on the errors of phrasebased systems and better understand their limits, we propose to consider the oracle decoding problem defined as follows: given a source sentence, its reference translation5 and a phrase table, what is the “best” translation hypothesis a system can generate? As usual, the quality of an hypothesis is evaluated by the similarity between the reference and the hypothesis. Note that in the oracle decoding problem, we are only assessing the ability of PBT systems to generate good candidate translations, irrespective of their ability to score them properly. We believe that studying this problem is interesting for various reasons. First, as described in Section 3.4, comparing the best hypothesis a system could have generated and the hypothesis it actually generates allows us to carry on both quantitative and qualitative failure analysis. The oracle decoding problem can also be used to assess the expressive power of phrase-based systems (Auli et al., 2009). Other applications include computing acceptable pseudo-references for discriminative training (Tillmann and Zhang, 2006; Liang et al., 2006; Arun and 5The oracle decoding problem can be extended to the case of multiple references. For the sake of simplicity, we only describe the case of a single reference. Koehn, 2007) or combining machine translation systems in a multi-source setting (Li and Khudanpur, 2009). We have also used oracle decoding to identify erroneous or difficult to translate references (Section 3.3). Evaluation Measure To fully define the oracle decoding problem, a measure of the similarity between a translation hypothesis and its reference translation has to be chosen. The most obvious choice is the BLEU-4 score (Papineni et al., 2002) used in most machine translation evaluations. However, using this metric in the oracle decoding problem raises several issues. First, BLEU-4 is a metric defined at the corpus level and is hard to interpret at the sentence level. More importantly, BLEU-4 is not decomposable6: as it relies on 4-grams statistics, the contribution of each phrase pair to the global score depends on the translation of the previous and following phrases and can not be evaluated in isolation. Because of its nondecomposability, maximizing BLEU-4 is hard; in particular, the phrase-level decomposability of the evaluation × metric is necessary in our approach. To circumvent this difficulty, we propose to evaluate the similarity between a translation hypothesis and a reference by the number of their common words. This amounts to evaluating translation quality in terms of unigram precision and recall, which are highly correlated with human judgements (Lavie et al., ). This measure is closely related to the BLEU-1 evaluation metric and the Meteor (Banerjee and Lavie, 2005) metric (when it is evaluated without considering near-matches and the distortion penalty). We also believe that hypotheses that maximize the unigram precision and recall at the sentence level yield corpus level BLEU-4 scores close the maximal achievable. Indeed, in the setting we will introduce in the next section, BLEU-1 and BLEU-4 are highly correlated: as all correct words of the hypothesis will be compelled to be at their correct position, any hypothesis with a high 1-gram precision is also bound to have a high 2-gram precision, etc. 2.2 Formalizing the Oracle Decoding Problem The oracle decoding problem has already been considered in the case of word-based models, in which all translation units are bound to contain only one word. The problem can then be solved by a bipartite graph matching algorithm (Leusch et al., 2008): given a n m binary matarligxo describing possible t 2r0an08sl)a:ti goinv elinn aks n b×emtw beeinna source words and target words7, this algorithm finds the subset of links maximizing the number of words of the reference that have been translated, while ensuring that each word 6Neither at the sentence (Chiang et al., 2008), nor at the phrase level. 7The (i, j) entry of the matrix is 1if the ith word of the source can be translated by the jth word of the reference, 0 otherwise. 935 is translated only once. Generalizing this approach to phrase-based systems amounts to solving the following problem: given a set of possible translation links between potential phrases of the source and of the target, find the subset of links so that the unigram precision and recall are the highest possible. The corresponding oracle hypothesis can then be easily generated by selecting the target phrases that are aligned with one source phrase, disregarding the others. In addition, to mimic the way OOVs are usually handled, we match identical OOV tokens appearing both in the source and target sentences. In this approach, the unigram precision is always one (every word generated in the oracle hypothesis matches exactly one word in the reference). As a consequence, to find the oracle hypothesis, we just have to maximize the recall, that is the number of words appearing both in the hypothesis and in the reference. Considering phrases instead of isolated words has a major impact on the computational complexity: in this new setting, the optimal segmentations in phrases of both the source and of the target have to be worked out in addition to links selection. Moreover, constraints have to be taken into account so as to enforce a proper segmentation of the source and target sentences. These constraints make it impossible to use the approach of (Leusch et al., 2008) and concur in making the oracle decoding problem for phrase-based models more complex than it is for word-based models: it can be proven, using arguments borrowed from (De Nero and Klein, 2008), that this problem is NP-hard even for the simple unigram precision measure. 2.3 An Integer Program for Oracle Decoding To solve the combinatorial problem introduced in the previous section, we propose to cast it into an Integer Linear Programming (ILP) problem, for which many generic solvers exist. ILP has already been used in SMT to find the optimal translation for word-based (Germann et al., 2001) and to study the complexity of learning phrase alignments (De Nero and Klein, 2008) models. Following the latter reference, we introduce the following variables: fi,j (resp. ek,l) is a binary indicator variable that is true when the phrase contains all spans from betweenword position i to j (resp. k to l) of the source (resp. target) sentence. We also introduce a binary variable, denoted ai,j,k,l, to describe a possible link between source phrase fi,j and target phrase ek,l. These variables are built from the entries of the phrase table according to selection strategies introduced in Section 2.4. In the following, index variables are so that: 0 ≤ i< j ≤ n, in the source sentence and 0 ≤ k < l ≤ m, in the target sentence, where n (resp. m) is the length of the source (resp. target) sentence. Solving the oracle decoding problem then amounts to optimizing the following objective function: mi,j,akx,li,Xj,k,lai,j,k,l· (l − k), (1) under the constraints: X ∀x ∈ J1,mK : ek,l ≤ 1 (2) = (3) 1∀,kn,lK : Xai,j,k,l = fk,l (4) ∀i,j : Xai,j,k,l (5) k,l s.tX. Xk≤x≤l ∀∀xy ∈∈ J11,,mnKK : X i,j s.tX. Xi≤y≤j fi,j 1 Xi,j = ei,j Xk,l The objective function (1) corresponds to the number of target words that are generated. The first set of constraints (2) ensures that each word in the reference e ap- pears in no more than one phrase. Maximizing the objective under these constraints amounts to maximizing the unigram recall. The second set of constraints (3) ensures that each word in the source f is translated exactly once, which guarantees that the search space of the ILP problem is the same as the search space of a phrase-based system. Constraints (4) bind the fk,l and ai,j,k,l variables, ensuring that whenever a link ai,j,k,l is active, the corresponding phrase fk,l is also active. Constraints (5) play a similar role for the reference. The Relaxed Problem Even though it accurately models the search space of a phrase-based decoder, this programs is not really useful as is: due to out-ofvocabulary words or missing entries in the phrase table, the constraint that all source words should be translated yields infeasible problems8. We propose to relax this problem and allow some source words to remain untranslated. This is done by replacing constraints (3) by: ∀y ∈ J1,nK : X i,j s.tX. Xi≤y≤j fi,j ≤ 1 To better ref∀lyec ∈t th J1e, bneKh :avior of phrase-based decoders, which attempt to translate all source words, we also need to modify the objective function as follows: X i,Xj,k,l ai,j,k,l · (l − k) +Xfi,j · (j − i) Xi,j (6) The second term in this new objective ensures that optimal solutions translate as many source words as possible. 8An ILP problem is said to be infeasible when tion violates at least one constraint. every possible solu- 936 The Relaxed-Distortion Problem A last caveat with the Relaxed optimization program is caused by frequently occurring source tokens, such as function words or punctuation signs, which can often align with more than one target word. For lack of taking distortion information into account in our objective function, all these alignments are deemed equivalent, even if some of them are clearly more satisfactory than others. This situation is illustrated on Figure 1. le chat et the cat and le the chien dog Figure 1: Equivalent alignments between “le” and “the”. The dashed lines corresponds to a less interpretable solution. To overcome this difficulty, we propose a last change to the objective function: X i,Xj,k,l ai,j,k,l · (l − k) +Xfi,j · (j − i) X ai,j,k,l|k − i| Xi,j −α (7) i Xk ,l X,j, Compared to the objective function of the relaxed problem (6), we introduce here a supplementary penalty factor which favors monotonous alignments. For each phrase pair, the higher the difference between source and target positions, the higher this penalty. If α is small enough, this extra term allows us to select, among all the optimal alignments of the re l axed problem, the one with the lowest distortion. In our experiments, we set α to min {n, m} to ensure that the penalty factor is always smminall{enr, ,tmha}n tthoe e rneswuarred t fhoart aligning atwltyo single iwso ardlwsa. 2.4 Selecting Indicator Variables In the approach introduced in the previous sections, the oracle decoding problem is solved by selecting, among a set of possible translation links, the ones that yield the solution with the highest unigram recall. We propose two strategies to build this set of possible translation links. In the first one, denoted exact match, an indicator ai,j,k,l is created if there is an entry (f, e) so that f spans from word position ito j in the source and e from word position k to l in the target. In this strategy, the ILP program considers exactly the same ruleset as conventional phrase-based decoders. We also consider an alternative strategy, which could help us to identify errors made during the phrase extraction process. In this strategy, denoted inside match, an indicator ai,j,k,l is created when the following three criteria are met: i) f spans from position ito j of the source; ii) a substring of e, denoted e, spans from position k to l of the reference; iii) (f, e¯) is not an entry of the phrase table. The resulting set of indicator variables thus contains, at least, all the variables used in the exact match strategy. In addition, we license here the use of phrases containing words that do not occur in the reference. In fact, using such solutions can yield higher BLEU scores when the reward for additional correct matches exceeds the cost incurred by wrong predictions. These cases are symptoms of situations where the extraction heuristic failed to extract potentially useful subphrases. 2.5 Oracle Decoding with Reordering Constraints The ILP problem introduced in the previous section can be extended in several ways to describe and test various improvements to phrase-based systems or to evaluate the impact of different parameter settings. This flexibility mainly stems from the possibility offered by our framework to express arbitrary constraints over variables. In this section, we illustrate these possibilities by describing how reordering constraints can easily be considered. As a first example, the Moses decoder uses a distortion limit to constrain the set of possible reorderings. This constraint “enforces (...) that the last word of a phrase chosen for translation cannot be more than d9 words from the leftmost untranslated word in the source” (Lopez, 2009) and is expressed as: ∀aijkl , ai0j0k0l0 s.t. k > k0, aijkl · ai0j0k0l0 · |j − i0 + 1| ≤ d, The maximum distortion limit strategy (Lopez, 2009) is also easily expressed and take the following form (assuming this constraint is parameterized by d): ∀l < m − 1, ai,j,k,l·ai0,j0,l+1,l0 · |i0 − j − 1| 71is%t e6hs.a distortion greater that Moses default distortion limit. alignment decisions enabled by the use of larger training corpora and phrase table. To evaluate the impact ofthe second heuristic, we computed the number of phrases discarded by Moses (be- cause of the default ttl limit) but used in the oracle hypotheses. In the English to French NEWSCO setting, they account for 34.11% of the total number of phrases used in the oracle hypotheses. When the oracle decoder is constrained to use the same phrase table as Moses, its BLEU-4 score drops to 42.78. This shows that filtering the phrase table prior to decoding discards many useful phrase pairs and is seriously limiting the best achievable performance, a conclusion shared with (Auli et al., 2009). Search Errors Search errors can be identified by comparing the score of the best hypothesis found by Moses and the score of the oracle hypothesis. If the score of the oracle hypothesis is higher, then there has been a search error; on the contrary, there has been an estimation error when the score of the oracle hypothesis is lower than the score of the best hypothesis found by Moses. 940 Based on the comparison of the score of Moses hypotheses and of oracle hypotheses for the English to French NEWSCO setting, our preliminary conclusion is that the number of search errors is quite limited: only about 5% of the hypotheses of our oracle decoder are actually getting a better score than Moses solutions. Again, this shows that the scoring function (model error) is one of the main bottleneck of current PBTS. Comparing these hypotheses is nonetheless quite revealing: while Moses mostly selects phrase pairs with high translation scores and generates monotonous alignments, our ILP decoder uses larger reorderings and less probable phrases to achieve better solutions: on average, the reordering score of oracle solutions is −5.74, compared to −76.78 fscoro rMeo osfe osr outputs. iGonivsen is −the5 weight assigned through MERT training to the distortion score, no wonder that these hypotheses are severely penalized. The Impact of Phrase Length The observed outputs do not only depend on decisions made during the search, but also on decisions made during training. One such decision is the specification of maximal length for the source and target phrases. In our framework, evaluating the impact of this decision is simple: it suffices to change the definition of indicator variables so as to consider only alignments between phrases of a given length. In the English-French NEWSCO setting, the most restrictive choice, when only alignments between single words are authorized, yields an oracle BLEU-4 of 48.68; however, authorizing phrases up to length 2 allows to achieve an oracle value of 66.57, very close to the score achieved when considering all extracted phrases (67.77). This is corroborated with a further analysis of our oracle alignments, which use phrases whose average source length is 1.21 words (respectively 1.31 for target words). If many studies have already acknowledged the predomi- nance of “small” phrases in actual translations, our oracle scores suggest that, for this language pair, increasing the phrase length limit beyond 2 or 3 might be a waste of computational resources. 4 Related Work To the best of our knowledge, there are only a few works that try to study the expressive power ofphrase-based machine translation systems or to provide tools for analyzing potential causes of failure. The approach described in (Auli et al., 2009) is very similar to ours: in this study, the authors propose to find and analyze the limits of machine translation systems by studying the reference reachability. A reference is reachable for a given system if it can be exactly generated by this system. Reference reachability is assessed using Moses in forced decoding mode: during search, all hypotheses that deviate from the reference are simply discarded. Even though the main goal of this study was to compare the search space of phrase-based and hierarchical systems, it also provides some insights on the impact of various search parameters in Moses, delivering conclusions that are consistent with our main results. As described in Section 1.2, these authors also propose a typology of the errors of a statistical translation systems, but do not attempt to provide methods for identifying them. The authors of (Turchi et al., 2008) study the learn- ing capabilities of Moses by extensively analyzing learning curves representing the translation performances as a function of the number of examples, and by corrupting the model parameters. Even though their focus is more on assessing the scoring function, they reach conclusions similar to ours: the current bottleneck of translation performances is not the representation power of the PBTS but rather in their scoring functions. Oracle decoding is useful to compute reachable pseudo-references in the context of discriminative training. This is the main motivation of (Tillmann and Zhang, 2006), where the authors compute high BLEU hypotheses by running a conventional decoder so as to maximize a per-sentence approximation of BLEU-4, under a simple (local) reordering model. Oracle decoding has also been used to assess the limitations induced by various reordering constraints in (Dreyer et al., 2007). To this end, the authors propose to use a beam-search based oracle decoder, which computes lower bounds of the best achievable BLEU-4 using dynamic programming techniques over finite-state (for so-called local and IBM constraints) or hierarchically structured (for ITG constraints) sets of hypotheses. Even 941 though the numbers reported in this study are not directly comparable with ours17, it seems that our decoder is not only conceptually much simpler, but also achieves much more optimistic lower-bounds of the oracle BLEU score. The approach described in (Li and Khudanpur, 2009) employs a similar technique, which is to guide a heuristic search in an hypergraph representing possible translation hypotheses with n-gram counts matches, which amounts to decoding with a n-gram model trained on the sole reference translation. Additional tricks are presented in this article to speed-up decoding. Computing oracle BLEU scores is also the subject of (Zens and Ney, 2005; Leusch et al., 2008), yet with a different emphasis. These studies are concerned with finding the best hypotheses in a word graph or in a consensus network, a problem that has various implications for multi-pass decoding and/or system combination techniques. The former reference describes an exponential approximate algorithm, while the latter proves the NPcompleteness of this problem and discuss various heuristic approaches. Our problem is somewhat more complex and using their techniques would require us to built word graphs containing all the translations induced by arbitrary segmentations and permutations of the source sentence. 5 Conclusions In this paper, we have presented a methodology for analyzing the errors of PBTS, based on the computation of an approximation of the BLEU-4 oracle score. We have shown that this approximation could be computed fairly accurately and efficiently using Integer Linear Programming techniques. Our main result is a confirmation of the fact that extant PBTS systems are expressive enough to achieve very high translation performance with respect to conventional quality measurements. The main efforts should therefore strive to improve on the way phrases and hypotheses are scored during training. This gives further support to attempts aimed at designing context-dependent scoring functions as in (Stroppa et al., 2007; Gimpel and Smith, 2008), or at attempts to perform discriminative training of feature-rich models. (Bangalore et al., 2007). We have shown that the examination of difficult-totranslate sentences was an effective way to detect errors or inconsistencies in the reference translations, making our approach a potential aid for controlling the quality or assessing the difficulty of test data. Our experiments have also highlighted the impact of various parameters. Various extensions of the baseline ILP program have been suggested and/or evaluated. In particular, the ILP formalism lends itself well to expressing various constraints that are typically used in conventional PBTS. In 17The best BLEU-4 oracle they achieve on Europarl German to English is approximately 48; but they considered a smaller version of the training corpus and the WMT’06 test set. our future work, we aim at using this ILP framework to systematically assess various search configurations. We plan to explore how replacing non-reachable references with high-score pseudo-references can improve discrim- inative training of PBTS. We are also concerned by determining how tight is our approximation of the BLEU4 score is: to this end, we intend to compute the best BLEU-4 score within the n-best solutions of the oracle decoding problem. 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In Proc. of ACL: HLT, Short Papers, pages 25–28, Columbus, Ohio. Markus Dreyer, Keith B. Hall, and Sanjeev P. Khudanpur. 2007. Comparing reordering constraints for smt using efficient bleu oracle computation. In NAACL-HLT/AMTA Workshop on Syntax and Structure in Statistical Translation, pages 103– 110, Rochester, New York. 942 Ulrich Germann, Michael Jahr, Kevin Knight, Daniel Marcu, and Kenji Yamada. 2001 . Fast decoding and optimal decoding for machine translation. In Proc. of ACL, pages 228–235, Toulouse, France. Ulrich Germann, Michael Jahr, Kevin Knight, Daniel Marcu, and Kenji Yamada. 2004. Fast and optimal decoding for machine translation. Artificial Intelligence, 154(1-2): 127– 143. Ulrich Germann. 2003. Greedy decoding for statistical machine translation in almost linear time. In Proc. of NAACL, pages 1–8, Edmonton, Canada. Kevin Gimpel and Noah A. Smith. 2008. Rich source-side context for statistical machine translation. In Proc. of WMT, pages 9–17, Columbus, Ohio. Philipp Koehn, Franz Josef Och, and Daniel Marcu. 2003. Statistical phrase-based translation. In Proc. of NAACL, pages 48–54, Edmonton, Canada. Philipp Koehn, Hieu Hoang, Alexandra Birch, Chris CallisonBurch, Marcello Federico, Nicola Bertoldi, Brooke Cowan, Wade Shen, Christine Moran, Richard Zens, Chris Dyer, Ondrej Bojar, Alexandra Constantin, and Evan Herbst. 2007. Moses: Open source toolkit for statistical machine translation. In Proc. of ACL, demonstration session. Philipp Koehn. 2004. Pharaoh: A beam search decoder for phrase-based statistical machine translation models. In Proc. of AMTA, pages 115–124, Washington DC. Shankar Kumar and William Byrne. 2005. Local phrase reordering models for statistical machine translation. In Proc. of HLT, pages 161–168, Vancouver, Canada. Alon Lavie, Kenji Sagae, and Shyamsundar Jayaraman. The significance of recall in automatic metrics for MT evaluation. In In Proc. of AMTA, pages 134–143, Washington DC. 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