emnlp emnlp2011 emnlp2011-73 knowledge-graph by maker-knowledge-mining

73 emnlp-2011-Improving Bilingual Projections via Sparse Covariance Matrices


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Author: Jagadeesh Jagarlamudi ; Raghavendra Udupa ; Hal Daume III ; Abhijit Bhole

Abstract: Mapping documents into an interlingual representation can help bridge the language barrier of cross-lingual corpora. Many existing approaches are based on word co-occurrences extracted from aligned training data, represented as a covariance matrix. In theory, such a covariance matrix should represent semantic equivalence, and should be highly sparse. Unfortunately, the presence of noise leads to dense covariance matrices which in turn leads to suboptimal document representations. In this paper, we explore techniques to recover the desired sparsity in covariance matrices in two ways. First, we explore word association measures and bilingual dictionaries to weigh the word pairs. Later, we explore different selection strategies to remove the noisy pairs based on the association scores. Our experimental results on the task of aligning comparable documents shows the efficacy of sparse covariance matrices on two data sets from two different language pairs.

Reference: text


Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 Many existing approaches are based on word co-occurrences extracted from aligned training data, represented as a covariance matrix. [sent-6, score-0.725]

2 In theory, such a covariance matrix should represent semantic equivalence, and should be highly sparse. [sent-7, score-0.721]

3 Unfortunately, the presence of noise leads to dense covariance matrices which in turn leads to suboptimal document representations. [sent-8, score-1.009]

4 In this paper, we explore techniques to recover the desired sparsity in covariance matrices in two ways. [sent-9, score-1.063]

5 First, we explore word association measures and bilingual dictionaries to weigh the word pairs. [sent-10, score-0.345]

6 Later, we explore different selection strategies to remove the noisy pairs based on the association scores. [sent-11, score-0.287]

7 Our experimental results on the task of aligning comparable documents shows the efficacy of sparse covariance matrices on two data sets from two different language pairs. [sent-12, score-1.093]

8 Most of the existing approaches use manually aligned document pairs to find a common subspace in which the aligned document pairs are maximally correlated. [sent-19, score-0.384]

9 The discriminative approaches capture essential word co-occurrences in terms of two monolingual covariance matrices and a cross-covariance matrix. [sent-29, score-1.044]

10 Subsequently, they use these covariance matrices to find projection directions in each language such that aligned documents lie close to each other (Sec. [sent-30, score-1.133]

11 The strong reliance of these approaches on the covariance matrices leads to problems, especially with the noisy data caused either by the noisy words in a document or the noisy document alignments. [sent-32, score-1.198]

12 In this paper, we address the problem of identifying and removing noisy entries in the covariance matrices. [sent-39, score-0.723]

13 In the first stage, we explore the use of word association measures such as Mutual Information (MI) and Yule’s ω (Reis and Judd, 2000) in computing the strength of a word pair (Sec. [sent-41, score-0.183]

14 We also explore the use of bilingual dictionaries developed from cleaner resources such as parallel data. [sent-44, score-0.232]

15 In the second stage, we use the association strengths in filtering out the noisy word pairs from the covariance matrices. [sent-45, score-0.809]

16 We evaluate the utility of sparse covariance matrices in improving the bilingual projections incrementally (Sec. [sent-49, score-1.073]

17 We found that sparsifying the covariance matrices helps in general, but using cleaner resource such bilingual dictionaries performed best. [sent-55, score-1.204]

18 We mainly focus on representing the solution of CCA in terms of covariance matrices. [sent-57, score-0.629]

19 Given a training data of n aligned document pairs, CCA finds projection directions for each language, so that the documents when projected along these directions are maximally correlated (Hotelling, 1936). [sent-59, score-0.355]

20 (1) where Cxx = XXT, Cyy = Y YT are the monolingual covariance matrices, Cxy = XYT is the crosscovariance matrix and λ is the regularization parameter. [sent-73, score-0.887]

21 Using these eigenvectors as columns, we form the projection matrices A and B. [sent-74, score-0.397]

22 These projection matrices are used to map documents in both the languages into interlingual representation. [sent-75, score-0.49]

23 So, every non-zero entry of the crosscovariance matrix restricts the choice of the projection directions. [sent-85, score-0.217]

24 Every occurrence of a noisy word will have a non-zero contribution towards the covariance matrix making it dense, which in turn prevents the selection of appropriate projection directions. [sent-88, score-0.973]

25 In this section, we describe some techniques to recover the sparsity by removing the noisy entries from the covariance matrices. [sent-89, score-0.878]

26 We break this task into two sub problems: computing an association score for every word pair and then using an appropriate strategy to identify the noisy pairs based on their weights. [sent-90, score-0.18]

27 This measure uses information about the occurrence of a word pair in aligned documents and doesn’t use other statistics such as ‘how often this pair doesn ’t co-occur together’ and so on. [sent-105, score-0.195]

28 2 Mutual Information Association measures like covariance and Pointwise Mutual Information, which only use the frequency with which a word pair co-occurs, often overestimate the strength of low frequent words (Moore, 2004). [sent-108, score-0.697]

29 We treat the occurrence of a word in a document slightly different from others, we treat a word as occurring in a document if it has occurred more than its average frequency in the corpus. [sent-112, score-0.208]

30 4 Bilingual Dictionary The above three association measures use the same training data that is available to compute the covariance matrices in CCA. [sent-122, score-0.969]

31 Thus, their utility in bringing additional information, which is not captured by the covariance matrices, is arguable (our experiments show that they are indeed helpful). [sent-123, score-0.629]

32 Moreover, they use document level co-occurrence information which is coarse compared to the cooccurrence at sentence level or the translational information provided by a bilingual dictionary. [sent-124, score-0.195]

33 So, we use bilingual dictionaries as our final resource to weigh the word co-occurrences. [sent-125, score-0.193]

34 While the first three association measures can also be applied to monolingual data, bilingual dictionary can’t be used for weighting monolingual word pairs. [sent-132, score-0.619]

35 So in this case, we use either of the above mentioned techniques for weighting monolingual word pairs. [sent-133, score-0.206]

36 1 Thresholding A straight forward way to remove the noisy word co-occurrences is to zero out the entries of the cross-covariance matrix that are lower than a threshold. [sent-139, score-0.217]

37 So, iPf we want to remove some of the entries of the covariance matrix with minimal change in the value of the objective function, then the optimal choice is to sort the entries of the covariance matrix and filter out the less confident word pairs. [sent-142, score-1.545]

38 4 Monolingual Augmentation The above three selection strategies operate on the covariance matrices independently. [sent-176, score-0.986]

39 Specifically, we propose to augment the set of selected bilingual word pairs using the monolingual word pairs. [sent-178, score-0.356]

40 We first use any of the above mentioned strategies to select bilingual and monolingual word pairs. [sent-179, score-0.327]

41 Let Ixy, Ixx and Iyy be the binary matrices that indicate the selected word pairs based on the bilingual and monolingual association scores. [sent-180, score-0.628]

42 Then the monolingual augmentation strategy updates Ixy in the following way: Ixy ← Binarize(IxxIxyIyy) i. [sent-181, score-0.242]

43 , we multiply Ixy with the monolingual selection matrices and then binarize the resulting matrix. [sent-183, score-0.453]

44 Our monolingual augmentation is motivated by the following probabilistic interpretation: P(x,y) = XP(x|x′)P(y|y′)P(x′,y′) xX′ X,y′ which can be rewritten as P ← TxP(Ty)T where wTxh acnhd c Tany are monolingual Psta ←te t Transition matrices. [sent-184, score-0.415]

45 3 Our Approach In this section we summarize our approach for the task of finding aligned documents from a crosslingual comparable corpora. [sent-186, score-0.176]

46 The training phase involves finding projection directions for documents of both the languages. [sent-187, score-0.19]

47 We compute the covariance matrices using the training data. [sent-188, score-0.878]

48 2) to recover the sparseness in either only the cross-covariance or all of the covariance matrices. [sent-193, score-0.677]

49 Let Ixy, Ixx and Iyy be the binary matrices which represent the word pairs that are selected based on the chosen sparsification technique. [sent-194, score-0.379]

50 Let A and B be the matrices formed with top eigenvectors of Eq. [sent-199, score-0.303]

51 These projection matrices are used to map documents into the interlingual representation. [sent-201, score-0.49]

52 During the testing, given an English document x, finding an aligned Spanish document involves solv- ing: argmyaxrxT? [sent-205, score-0.211]

53 1 Experimental Setup We experiment with the task of finding aligned documents from a cross-lingual comparable corpora. [sent-213, score-0.176]

54 As the corpora are comparable, some documents in one collection have a comparable document in the other collection. [sent-215, score-0.184]

55 We evaluate our idea of sparsifying the covariance matrices incrementally. [sent-218, score-1.002]

56 That leaves us 12 different ways for sparsifying the covariance matrices, with each method having parameters to control the amount of sparseness. [sent-222, score-0.753]

57 We use the true feature correspondences to form the cross-covariance selection matrix Ixy (Sec. [sent-237, score-0.208]

58 For this experiment, we use the full monolingual covariance matrices. [sent-240, score-0.764]

59 We tokenize the documents, retain only the most frequent 2000 words in each language and convert the docu- Figure 2: Comparison of the word association measures along with different selection criteria. [sent-254, score-0.191]

60 The x-axis plots the number of non-zero entries in the covariance matrices and the y-axis plots the accuracy oftop-ranked document. [sent-255, score-1.002]

61 2 shows the performance of these different combinations with varying levels of sparsity in the covariance matrices. [sent-263, score-0.764]

62 We start with 2000 non-zero entries in the covariance matrices and experiment up to 20,000 non-zero entries. [sent-265, score-0.914]

63 Since our data set has 2000 words in each language, 2000 non-zero entries in a covariance matrix implies that, on an average, every word is associated with only one word. [sent-266, score-0.788]

64 selecting more number of elements in the covariance matrices, increases the performance slightly and then decreases again. [sent-270, score-0.629]

65 From the figure, it 936 seems that sparsifying the covariance matrices might help in improving the performance of the task. [sent-271, score-1.002]

66 This suggests that, apart from the weighting of the word pairs, appropriate selection of the word pairs is also equally important. [sent-274, score-0.208]

67 From this figure, we observe that Mutual Information and Yule’s ω perform competitively but they consistently outperform models that use covariance as the association measure. [sent-276, score-0.714]

68 2 Amount of Sparsity In the previous experiment, we used same level of sparsity for all the covariance matrices, i. [sent-280, score-0.736]

69 same number of associations were selected for each word in all the three covariance matrices. [sent-282, score-0.66]

70 In the following experiment, we use different levels of sparsity for the individual covariance matrices. [sent-283, score-0.764]

71 In the Yule+Match combination, we use Yule’s ω association measure for weighting the word pairs and use matching for selection. [sent-286, score-0.203]

72 In the Dictionary+Match combination, we use bilingual dictionary for sparsifying cross-covariance matrix, i. [sent-287, score-0.311]

73 And for monolingual word pairs, we use MI for weighting and matching for word pair selection. [sent-290, score-0.278]

74 For each level of sparsity of the cross-covariance matrix, we experiment with different levels of sparsity on the monolingual covariance matrices. [sent-291, score-1.006]

75 ‘Only XY’ indicates we use the full monolingual covariance matrices. [sent-292, score-0.764]

76 ‘Aug’ indicates that we use monolingual augmentation to refine the sparsity of the cross-covariance matrix (Sec. [sent-295, score-0.441]

77 From both the figures 3(a) and 3(b), we observe that ‘Only XY’ run (dark blue) performs poorly compared to the other runs, indicating that sparsifying all the covariance matrices is better than spar- sifying only the cross-covariance matrix. [sent-299, score-1.002]

78 Matching is used as selection criteria for all the covariance matrices. [sent-303, score-0.698]

79 The x-axis plots the threshold on bilingual translation probability and it determines the sparsity of Cxy. [sent-305, score-0.3]

80 Figure 3: Comparison of Yule+Match and Dictionary+Match combination with different levels of sparsity for the covariance matrices. [sent-307, score-0.764]

81 In both the figures, the x-axis plots the sparsity of the cross-covariance matrix and for each value we try different levels of sparsity on the monolingual covariance matrices (which are grouped together). [sent-308, score-1.391]

82 In both the above experiments, the performance bars are very similar when we use MI instead of Yule and vice versa for weighting monolingual word pairs. [sent-322, score-0.249]

83 Yule(l)+Match(k), where l ∈ {2, 3} is the number Yofu Spanish wcho(rkd)s, wallhoewreed l f∈or { e2a,3ch} English wmoberdr and vice versa and k=2 is the number of monolingual word associations for each word. [sent-327, score-0.209]

84 Again, we run these combinatainodns t wyi kth monolingual augmentation eidseen ctoimfiebdi by Dictionary+Match(k)+Aug. [sent-331, score-0.242]

85 of English document and the second half of its aligned foreign language document (Mimno et al. [sent-377, score-0.211]

86 From the results, it is clear that sparsifying the covariance matrices helps improving the accuracies significantly. [sent-400, score-1.002]

87 This indicates that using fine granular information such as a bilingual dictionary gleaned from an external source is very helpful in improving the accuracies. [sent-402, score-0.234]

88 Among the models that rely solely on the training data, models that use monolingual augmentation performed better on Wikipedia data set, while models that do not use augmentation performed better on Europarl data sets. [sent-403, score-0.349]

89 As the documents become comparable, we need to use monolingual statistics to refine the bilingual statistics. [sent-405, score-0.326]

90 This conforms with our initial hunch that, when the training data is clean the covariance matrices tend to be less noisy. [sent-407, score-0.906]

91 5 Discussion In this paper, we have proposed the idea of sparsifyng covariance matrices to improve bilingual projection directions. [sent-408, score-1.094]

92 We are not aware of any NLP research that attempts to recover the sparseness of the covariance matrices to improve the projection directions. [sent-409, score-1.02]

93 Their objective is to find projection directions such that the original documents are represented as a sparse vectors in the common sub-space. [sent-411, score-0.263]

94 Another seemingly relevant but different direction is the sparse covariance matrix selection research (Banerjee et al. [sent-412, score-0.863]

95 The objective in this work is to find matrices such that the inverse of the covariance matrix is sparse which has applications in Gaussian processes. [sent-414, score-1.043]

96 Our experimental results show that using external information such as bilingual dictionaries which is gleaned from cleaner resources brings significant improvements. [sent-416, score-0.249]

97 Moreover, we also observe that computing word pair association measures from the same training data along with an appropriate selection criteria can also yield significant improvements. [sent-417, score-0.191]

98 This is certainly encouraging and in future we would like to explore more sophisticated techniques to recover the sparsity based on the training data itself. [sent-418, score-0.185]

99 Sparse covariance selection 939 CoRR, via robust maximum likelihood estimation. [sent-436, score-0.698]

100 From bilingual dictionaries to interlin- gual document representations. [sent-504, score-0.235]


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