emnlp emnlp2010 emnlp2010-1 knowledge-graph by maker-knowledge-mining

1 emnlp-2010-"Poetic" Statistical Machine Translation: Rhyme and Meter

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Author: Dmitriy Genzel ; Jakob Uszkoreit ; Franz Och

Abstract: As a prerequisite to translation of poetry, we implement the ability to produce translations with meter and rhyme for phrase-based MT, examine whether the hypothesis space of such a system is flexible enough to accomodate such constraints, and investigate the impact of such constraints on translation quality.

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Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 1 Introduction Machine translation of poetry is probably one of the hardest possible tasks that can be considered in computational linguistics, MT, or even AI in general. [sent-4, score-0.547]

2 Robert Frost is reported to have said that poetry is that which gets lost in translation. [sent-6, score-0.442]

3 However, there are aspects of the problem that we can already tackle, namely the problem of the poetic form. [sent-9, score-0.374]

4 On the other hand, Douglas Hofstadter, who spends 600 pages describing 158 how to translate a 60 word poem in 80 different ways in Le Ton beau de Marot (1998), makes a strong case that a poem’s form must be preserved in translation, if at all possible. [sent-11, score-0.29]

5 Leaving the controversy to the professional translators, we investigate whether or not it is possible to produce translations that conform to certain metrical constraints common in poetry. [sent-12, score-0.178]

6 There has been some work where MT techniques were used to produce poetry (Jiang and Zhou, 2008). [sent-17, score-0.442]

7 In other computational poetry work, Ramakrishnan et al (2009) generate song lyrics from melody and various algorithms for poetry generation (Manurung et al. [sent-18, score-0.924]

8 There are books (Hartman, 1996) and articles (Bootz, 1996) on the subject of computer poetry from a literary point of view. [sent-21, score-0.442]

9 tc ho2d0s10 in A Nsastoucira tlio Lnan fogru Cagoem Ppruotcaetisosninagl, L pinag eusis 1t5ic8s–16 , 3 Statistical MT and Poetry We can treat any poetic form as a constraint on the potential outputs. [sent-25, score-0.483]

10 A naive approach to ensure that an output of the MT system is, say, a haiku, is to create a haiku detector and to examine a (very large) n-best list of translations. [sent-26, score-0.156]

11 This approach would not succeed very often, since the haikus that may be among the possible translations are a very small fraction of all translations, and the MT decoder is not actively looking for them, since it is not part of the cost it attempts to minimize. [sent-27, score-0.356]

12 Instead, we would want to recast “Haikuness” as a feature function, such that a real haiku has 0 cost, and those outputs that are not, have large cost. [sent-28, score-0.153]

13 For a phrase based system, a feature function is a function whose inputs are a partial hypothesis state sin, and a phrase pair p, and whose outputs are the hypothesis state after p is appended to the hypothesis: sout, and the cost incurred, c. [sent-31, score-0.746]

14 For hierarchical, tree-to-string and some other types of MT systems which combine two partial hypotheses and are not generating translations left-to-right, one instead has two partial hypotheses states sleft and sright as inputs, and the outputs are the same. [sent-32, score-0.324]

15 The feature function costs are multiplied by fixed weights and added together to obtain the total hypothesis cost. [sent-34, score-0.196]

16 Normally feature functions include the logarithm of probability of target phrase given source, source given target and other phrase-local features which require no state to be kept, as well as features like language model, which require nontrivial state. [sent-35, score-0.186]

17 We will now examine some different kinds of poetry and consider the properties of such feature functions, especially with regard to keeping necessary state. [sent-37, score-0.476]

18 1 Line-length constrained poetry Some poetic genres, like the above-mentioned haiku, require that a poem contain a certain number of lines (3 for haiku), each containing a certain number of syllables (5,7,5 for haiku). [sent-40, score-1.129]

19 This requires that each hypothesis state contain the current translation length (in syllables). [sent-44, score-0.301]

20 In addition, whenever a hypothesis is expanded, we must keep track of whether or not it would be possible to achieve the desired final length with such an expansion. [sent-45, score-0.334]

21 For example, if in the initial state, we have a choice between two phrases, and picking the longer of the two would make it impossible to have a 17-syllable translation later on, we must impose a high cost on it, so as to avoid going down a garden path. [sent-46, score-0.445]

22 For either constraint, however, the sentence has to be assembled strictly left-to-right, which makes it impossible to build partial hypotheses that do not start the sentence, which hierarchical and tree-to-string decoders require. [sent-50, score-0.191]

23 2 Rhythmic poetry Some famous Western poetry, notably Shakespeare, is written in rhythmic poetry, also known as blank verse. [sent-52, score-0.554]

24 This poetry imposes a constraint on the pattern of stressed and unstressed syllables. [sent-53, score-0.714]

25 For example, ifwe use 0 to indicate no stress, and 1to indicate stress, blank verse with iambic foot obeys the regular expression (01)∗, while one with a dactylic foot l aorok exs plirekess (100)∗. [sent-54, score-0.49]

26 s Tnhoits require csu trhreen eta position, banutonly its value modulo foot length (e. [sent-56, score-0.314]

27 3 Rhythmic and rhyming poetry The majority of English poetry that was written until recently has both rhythm and rhyme. [sent-61, score-1.182]

28 Generally speaking, a poetic genre of this form can be described by two properties. [sent-62, score-0.505]

29 A rhyming scheme is a string of letters, each corresponding to a line of a poem, such that the same letter is used for the lines that rhyme. [sent-64, score-0.435]

30 aa is a scheme for a couplet, a 2-line poem whose lines rhyme. [sent-67, score-0.221]

31 We can describe a genre completely by its rhyming scheme and a meter for each letter used in the rhyming scheme. [sent-76, score-0.903]

32 Nithote t tihmaett ethre i omthbeirc tawnod kinds of poetry can also be fit by this structure, if one permits another symbol (we use *) to stand for the syllables whose stress is not important, e. [sent-83, score-0.886]

33 Fhoairk tuh:is { type oaf : genre, we n :e ∗e∗d to obey ,thce : same two constraints as in the line-based poetry, but also to ensure that rhyming constraints hold. [sent-86, score-0.453]

34 It is not sufficient to include just the syllable that must rhyme, because we wish to avoid self-rhymes (word rhyming with an identical word). [sent-88, score-0.446]

35 4 Stress pattern feature function We will first discuss an easier special case, namely a feature function for blank verse, which we will refer to as stress pattern feature function. [sent-89, score-0.734]

36 This can be done with a pronunciation module of a text-to-speech system, or a freely available pronunciation dictio- nary, such as CMUDict (Rudnicky, 2010). [sent-93, score-0.16]

37 1 Stress pattern for a phrase-based system In a phrase based system, the feature function state consists of the current hypothesis length modulo foot length. [sent-96, score-0.699]

38 The proposed target phrase is converted into a stress pattern using the pronunciation module, and the desired stress pattern is left shifted by the current offset. [sent-98, score-0.932]

39 The cost is the number of mismatches of the target phrase vs. [sent-99, score-0.265]

40 For example, if the desired pattern is 010, current offset is 1, and the proposed new phrase has pattern 10011, we shift the desired pattern by 1, obtaining 100 and extend it to length 5, obtaining 10010, matching it against the proposal. [sent-101, score-0.683]

41 There is one mismatch, at the fifth position, and we report a cost of 1. [sent-102, score-0.193]

42 The new state is simply the old state plus phrase length, modulo foot length, 0 in this example. [sent-103, score-0.432]

43 2 Stress pattern for a hierarchical system In a hierarchical system, we in general do not know how a partial hypothesis might be combined on the left. [sent-105, score-0.315]

44 A hypothesis that is a perfect fit for pattern 010 would be horrible if it is placed at an offset that is not divisible by 3, and vice versa, an apparently bad hypothesis might be perfectly good if placed at such an offset. [sent-106, score-0.412]

45 To solve this problem, we create states that track how well a partial hypothesis fits not only the desired pattern, but all patterns obtained by placing this pattern at any offset, and also the hypothesis length (modulo foot length, as usual). [sent-107, score-0.75]

46 m Ifin biomthum co scotsst a raen dg immediately output it as cost: this is the unavoidable cost of this combination. [sent-113, score-0.227]

47 For this example we get cost of 1, and a new state: {length: 1, 01 cost: 4, 10 cost: 0}. [sent-114, score-0.193]

48 For tahe n fwin salta state, we output t1h ceo remaining cost 0f}o. [sent-115, score-0.193]

49 We simply track all foot patterns (length 2 and length 3 are the only ones used in poetry) as in the above algorithm, taking care to combine the right pattern scores based on length offset. [sent-121, score-0.521]

50 The length offset now has to be tracked modulo 2*3. [sent-122, score-0.275]

51 This feature function can now be used to translate arbitrary text into blank verse, picking whatever meter fits best. [sent-123, score-0.312]

52 If no meters can fit completely, it will produce translations with the fewest violations (assuming the weight for this feature function is set high). [sent-124, score-0.184]

53 5 General poetic form feature function In this section we discuss a framework for tracking any poetic genre, specified as a genre description object (Section 3. [sent-125, score-1.004]

54 As in the case of the stress pattern function, we use a statistical MT system, which is now required to be phrase-based only. [sent-127, score-0.385]

55 We also use a pronunciation dictionary, but in addition to tracking the number and stress of syllables, we must now be able to provide a function that classifies a pair of words as rhyming or nonrhyming. [sent-128, score-0.76]

56 In fact rhyming is a continuum, from very strong rhymes to weak ones. [sent-130, score-0.349]

57 We use a very weak definition which is limited to a single syllable: if the final syllables of both words have the same nucleus and coda1 , we say that the words rhyme. [sent-131, score-0.176]

58 1 Tracking the target length The hardest constraint to track efficiently is the range of lengths of the resulting sentence. [sent-134, score-0.343]

59 To avoid this problem, we need to have a set of possible sentence lengths available at any point in the search, and to impose a high cost if the desired length is not in that set. [sent-138, score-0.474]

60 This is unacceptably slow to be done for each hypothesis (even noting that hypotheses with the same set of already covered source position can share this computation). [sent-141, score-0.154]

61 This is due to phrase extraction constraints, which normally ensure that the lengths of target phrases form a complete range. [sent-144, score-0.185]

62 Second, we can note that whenever a source range is interrupted by a covered phrase and split into two ranges, the minimal and maximal sentence length is simply the sum of the corresponding lengths over the two uncovered subranges, plus the current hypothesis length. [sent-146, score-0.335]

63 3 The combination algorithm To combine the hypothesis state sin with a phrase pair p, do the following 1. [sent-151, score-0.242]

64 Update sout: increment sentence length by target phrase length (in syllables), update coverage range 3. [sent-153, score-0.256]

65 Compute minimum and maximum achievable sentence length; if desired length not in range, increment cost by a penalty 4. [sent-154, score-0.425]

66 For each word in the target phrase (a) If the word’s syllable pattern does not match against desired pattern, add number of mismatches to cost (b) If at the end of a line: i. [sent-155, score-0.517]

67 If the line would end mid-word, increment cost by a penalty ii. [sent-156, score-0.289]

68 If x is present in the state sout, check if the word associated with x rhymes with the current word, if not, increment cost by a penalty iv. [sent-158, score-0.417]

69 Remove x with associated word from the state sout v. [sent-159, score-0.196]

70 If letter x occurs further in the rhyming scheme, add x with the current word to the state sout 5. [sent-160, score-0.546]

71 4 Tracking multiple patterns The above algorithm will allow to efficiently search the hypothesis space for a single genre description object. [sent-161, score-0.217]

72 As a result, a pattern that 162 matches one pattern, but not another, will still have high cost, perhaps as high as a pattern that partially matches both. [sent-164, score-0.232]

73 As long as at least one function has zero cost (i. [sent-167, score-0.228]

74 can potentially match), no cost is reported to the decoder. [sent-169, score-0.193]

75 As soon as all costs become positive, the minimum over all costs is reported to the decoder as unavoidable cost, and should be subtracted from each feature function cost, bringing the minimum stored in the output state back to 0. [sent-170, score-0.311]

76 It is also possible to prune the set of functions that are still viable, based on their cost, to avoid keeping track of patterns that cannot possibly match. [sent-171, score-0.178]

77 Using this approach we can translate arbitrary text, provide a large number of poetic patterns and expect to get some sort of poem at the end. [sent-172, score-0.588]

78 Given a wide variety of poetic genres, it is not unreasonable to expect that for most inputs, some pattern will apply. [sent-173, score-0.49]

79 We are instead interested in two metrics: percentage of sentences that can be translated while obeying a stress pattern constraint, and the impact of this constraint on BLEU score (Papineni et al. [sent-180, score-0.501]

80 33, and stress Table 1: Stress pattern distribution INTaramomcbheee01P10attern97%. [sent-185, score-0.385]

81 The proportion of sentences successfully matched is 85% , and if we permit a single stress error, it is 93% , which suggests that the constraint can be satisfied in the great majority of cases. [sent-190, score-0.392]

82 The distribution of stress patterns among the perfect matches is given in Table 1. [sent-191, score-0.306]

83 Some of the more interesting example translations with stress pattern enforcement enabled are given in table 2. [sent-192, score-0.467]

84 2 Poetic Form Feature Function For poetic form feature function, we perform the same evaluation as above, to estimate the impact of forcing prose into an arbitrary poetic form, but to get more relevant results we also translate a poetic work with a specific genre requirement. [sent-194, score-1.328]

85 Our poetic form feature function is given a list of some 210 genre descriptions which vary from Haikus to Shakespearean sonnets. [sent-195, score-0.574]

86 The proportion of sentences that satisfied one of the poetic constraints is 87% . [sent-200, score-0.48]

87 For a proper poetic evaluation, we use a French translation of Oscar Wilde’s Ballad of Reading Gaol by Jean Guiloineau as input, and the original Wilde’s text as reference. [sent-203, score-0.439]

88 The poem consists of 109 stanzas of 6 lines each, with a genre description of {abcbdb, aof/c 6/d li: 01010101, tbh: 010101}. [sent-204, score-0.337]

89 We evaluate our system with a poetic constraint given above. [sent-211, score-0.45]

90 Out of 109 stanzas, we found 12 translations that satisfy the genre constraint (If we allow any poetic form, 108 out of 109 stanzas match some form). [sent-217, score-0.698]

91 Two sample stanzas that satisfied the constraints are given in Table 4. [sent-218, score-0.174]

92 7 Discussion and Future Work In this work we demonstrate how modern-day statistical MT system can be constrained to search for translations obeying particular length, meter, and rhyming constraints, whether a single constraint, or any one of a set. [sent-219, score-0.42]

93 In the present form, however, we can already find good translations, as a sort of found poetry (Drury, 2006), by translating a large quantity of text, whether poetic or not. [sent-223, score-0.816]

94 This is the first attempt to deal with poetry translation, and the great majority of work to achieve reasonable quality in form and meaning still remains to be done. [sent-224, score-0.475]

95 One major problem with the current feature function is that while it can avoid the areas of the search space where length constraints cannot be Table 2: Example translations. [sent-225, score-0.236]

96 Stressed syllables are italicized ReferenceA police spokesman said three people had been arrested and the BaselinemAa pteolri acelm waasn b saeiidng th eaxta thmreineed p. [sent-226, score-0.182]

97 a satisfied, it cannot avoid the areas where rhyming constraints are impossible to satisfy. [sent-241, score-0.424]

98 As a result, we need to allow a very wide hypothesis beam (5000 per each source phrase coverage), to ensure that enough hypotheses are considered, so that there are some that lead to correct solutions later. [sent-242, score-0.264]

99 A more radical solution is to create an entirely different decoding algorithm which places words not left-to-right, or in a hierarchical fashion, but first placing words that must rhyme, and building hypotheses around them, like human translators of poetry do. [sent-244, score-0.672]

100 Using an on-line dictionary to find rhyming words and pronunciations for unknown words. [sent-259, score-0.298]

similar papers computed by tfidf model

tfidf for this paper:

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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. 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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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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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