emnlp emnlp2013 emnlp2013-25 knowledge-graph by maker-knowledge-mining

25 emnlp-2013-Appropriately Incorporating Statistical Significance in PMI


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Author: Om P. Damani ; Shweta Ghonge

Abstract: Two recent measures incorporate the notion of statistical significance in basic PMI formulation. In some tasks, we find that the new measures perform worse than the PMI. Our analysis shows that while the basic ideas in incorporating statistical significance in PMI are reasonable, they have been applied slightly inappropriately. By fixing this, we get new measures that improve performance over not just PMI but on other popular co-occurrence measures as well. In fact, the revised measures perform reasonably well compared with more resource intensive non co-occurrence based methods also.

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Summary: the most important sentenses genereted by tfidf model

sentIndex sentText sentNum sentScore

1 in Abstract Two recent measures incorporate the notion of statistical significance in basic PMI formulation. [sent-5, score-0.436]

2 In some tasks, we find that the new measures perform worse than the PMI. [sent-6, score-0.288]

3 Our analysis shows that while the basic ideas in incorporating statistical significance in PMI are reasonable, they have been applied slightly inappropriately. [sent-7, score-0.181]

4 By fixing this, we get new measures that improve performance over not just PMI but on other popular co-occurrence measures as well. [sent-8, score-0.593]

5 In fact, the revised measures perform reasonably well compared with more resource intensive non co-occurrence based methods also. [sent-9, score-0.592]

6 1 Introduction The notion of word association is used in many language processing and information retrieval applications and it is important to have low-cost, highquality association measures. [sent-10, score-0.103]

7 Lexical co-occurrence based word association measures are popular because they are computationally efficient and they can be applied to any language easily. [sent-11, score-0.339]

8 One of the most popular co-occurrence measure is Pointwise Mutual Information (PMI) (Church and Hanks, 1989). [sent-12, score-0.082]

9 To overcome this, recently two new measures have been proposed that incorporate the notion of statistical significance in basic PMI formulation. [sent-14, score-0.436]

10 In (Washtell and Markert, 2009), statistical significance is introduced in PMIsig by multiplying PMI value with the square root of the evidence. [sent-15, score-0.212]

11 In contrast, in (Damani, 2013), cPMId is 163 introduced by bounding the probability of observing a given deviation between a given word pair’s cooccurrence count and its expected value under a null model where with each word a global unigram generation probability is associated. [sent-16, score-0.224]

12 In Table 1, we give the definitions of PMI, PMIsig, and cPMId. [sent-17, score-0.042]

13 While these new measures perform better than PMI on some of the tasks, on many other tasks, we find that the new measures perform worse than the PMI. [sent-18, score-0.576]

14 In Table 3, we show how these measures perform compared to PMI on four different tasks. [sent-19, score-0.288]

15 We find that PMIsig degrades performance in three out of these four tasks while cPMId degrades performance in two out of these four tasks. [sent-20, score-0.068]

16 Our analysis shows that while the basic ideas in incorporating statistical significance are reasonable, they have been applied slightly inappropriately. [sent-23, score-0.181]

17 By fixing this, we get new measures that improve performance over not just PMI, but also on other popular co-occurrence measures on most of these tasks. [sent-24, score-0.593]

18 In fact, the revised measures perform reasonably well compared with more resource intensive non cooccurrence based methods also. [sent-25, score-0.667]

19 2 Adapting PMI for Statistical Significance In (Washtell and Markert, 2009), it is assumed that the statistical significance of a word pair association is proportional to the square root of the evidence. [sent-26, score-0.212]

20 The question of what constitutes the evidence is answered by taking the lesser of the frequencies of the two words in the word pair, since at most that many pairings are possible. [sent-27, score-0.052]

21 The sub-parts in bold represent the changes between the original formulas and the revised formulas. [sent-33, score-0.069]

22 f tT hite eth pisro way t om emphasize t(yhe) )tr ∗an msfionr(mda(txio),nd f(ryo)m) icnP MsPMIdI. [sent-35, score-0.04]

23 In (Dpamani, 2013), statistical significance is introduced by bounding the probability of observing a given number of word-pair occurrences in the corpus, just by chance, under a null model of independent unigram occurrences. [sent-37, score-0.384]

24 For this computation, one needs to decide what constitutes a random trial when looking for a word-pair occurrence. [sent-38, score-0.104]

25 Is it the occurrence of the first word (say x) in the pair, or the second (say y). [sent-39, score-0.059]

26 In (Damani, 2013), occurrences of x are arbitrarily chosen to represent the sites of the random trial. [sent-40, score-0.126]

27 Using Hoeffdings Inequality: + P[f(x, y) ≥ f(x) ∗ f(y)/W f(x) ∗ t] ≤ exp(−2 ∗ f(x) ∗ t2) δ By setting t = plnδ/(−2 ∗ f(x)), we get as an upper bound on pprobability ∗of f observing more tsh aann f(x) ∗ f(y)/W + f(x) ∗ t bigram occurrences in the corpus, just by +chfan(cxe). [sent-41, score-0.131]

28 Bta bsiegdr on othccisu Corpus i Lne vtheel Significant PMI(cPMI) is defined as: cPMI(x,y) = logf(x) ∗ f(yf)(/xW,y) + f(x) ∗ t = logf(x) ∗ f(y)/W +f(px,fy()x) ∗plnδ/(−2) In (Damani, 2013), severapl variantsp of cPMI are introduced that incorporate different notions of statistical significance. [sent-42, score-0.067]

29 1 Choice of Random Trial While considering statistical significance, one has to decide what constitutes a random trial. [sent-45, score-0.084]

30 When looking for a word-pair (x, y)’s occurrences, y can potentially occur near each occurrence of x, or x can potentially occur near each occurrence of y. [sent-46, score-0.194]

31 Which of these two set of occurrences should be considered the sites of random trial. [sent-47, score-0.126]

32 We believe that the occurrences of the more frequent of x and y should be considered, since near each ofthese occurrences the other word could have occurred. [sent-48, score-0.248]

33 Similarly, d(x) and d(y) in cPMId formula should be replaced with max(d(x) , d(y)) and min(d(x) , d(y)) respectively to give a new measure Significant PMI based on Documpent count(sPMId). [sent-50, score-0.069]

34 Using the same logic, pmin(f(x),f(y)) ipn PMIsig formula should bpe replaced with pmax(f(x),f(y)) to give the formula for a new pmeasure PMI-significant(PMIs). [sent-51, score-0.072]

35 The definitions of sPMId and PMIs are also given in Table 1. [sent-52, score-0.042]

36 3 Related Work There are three main types of word association measures: Knowledge based, Distributional Similarity based, and Lexical Co-occurrence based. [sent-53, score-0.035]

37 co-occurrence measures for each data-set is shown in bold and underline respectively. [sent-55, score-0.255]

38 Except GoogleDistance and LLR, all results for all co-occurrence measures are statistically significant at p = . [sent-56, score-0.255]

39 For each task, the best known result for different non co-occurrence based methods is also shown. [sent-58, score-0.102]

40 165 two words for distributional similarity (Agirre et al. [sent-59, score-0.126]

41 Knowledge-based measures use knowledgesources like thesauri, semantic networks, or taxonomies (Milne and Witten, 2008; Hughes and Ramage, 2007; Gabrilovich and Markovitch, 2007; Yeh et al. [sent-67, score-0.305]

42 Co-occurrence based measures (Pecina and Schlesinger, 2006) simply rely on unigram and bigram frequencies of the words in a pair. [sent-70, score-0.291]

43 1 Co-occurrence Measures being Compared Co-occurrence based measures of association be- tween two entities are used in several domains like ecology, psychology, medicine, language processing, etc. [sent-73, score-0.29]

44 To compare the performance of our newly introduced measures with other co-occurrence measures, we have selected a number of popular co-occurrence measures like ChiSquare (χ2), Dice (Dice, 1945), GoogleDistance (L. [sent-74, score-0.594]

45 In addition to these popular measures, we also experiment with other known variations of PMI like nPMI (Bouma, 2009), PMI2 (Daille, 1994), Ochiai (Janson and Vegelius, 1981), and SCI (Washtell and Markert, 2009). [sent-76, score-0.049]

46 In Table 2, we present the definitions of these measures. [sent-78, score-0.042]

47 1, we can assume that SCI is PMI adapted for statistical significance (multiplied by √f(y)), where the site of random trial is taken to be the occurrences of the second word y, instead of the less frequent word, as in the case of PMIsig. [sent-80, score-0.287]

48 The span of a word-pair’s occurrence is the direction-independent distance between the occurrences of the members of the pair. [sent-82, score-0.175]

49 We consider only those co-occurrences where span is less than a given threshold. [sent-83, score-0.029]

50 Therefore, span threshold is a parameter for all the co-occurrence measures being considered. [sent-84, score-0.284]

51 4 Performance Evaluation Having introduced the revised measures PMIs and sPMId, we need to evaluate the performance ofthese measures compared to PMI and the original measures introducing significance. [sent-85, score-0.905]

52 In addition, we also wish to compare the performance of these measures with other co-occurrence measures. [sent-86, score-0.255]

53 To compare the performance of these measures with more resource heavy non co-occurrence based measures, we have chosen those tasks and datasets on which published results exist for distributional similarity and knowl- edge based word association measures. [sent-87, score-0.554]

54 1 Task Details We evaluate these measures on three tasks: Sentence Similarity(65 sentence-pairs from (Li et al. [sent-89, score-0.255]

55 For each of these tasks, gold standard human judgment results exist. [sent-92, score-0.032]

56 , 2006), we evaluate a measure by the Pearsons correlation between the ranking produced by the measure and the human ranking. [sent-94, score-0.066]

57 For synonym selection, we compute the percentage of correct answers, since there is a unique answer for each challenge word in the datasets. [sent-95, score-0.03]

58 Semantic relatedness has been evaluated by Spearman’s rank correlation with human judgment instead of Pearsons correlation in literature and we follow the same practice to make results comparable. [sent-96, score-0.117]

59 For sentence similarity detection, the algorithm used by us (Li et al. [sent-97, score-0.053]

60 Hence we normalize the value produced by each measure using gray-row, for all other questions, incorrect answers becomes correct on using PMIs instead of PMIsig, and vice-versa for the gray-row. [sent-99, score-0.15]

61 The association values have been suitably scaled for readability. [sent-100, score-0.035]

62 max-min normalization: 0 v0 v − min = max − min mvax − − m minin where max and min are computed over all association scores for the entire task for a given measure. [sent-103, score-0.289]

63 In Table 3, we present the performance of all the co-occurrence measures considered on all the tasks. [sent-109, score-0.255]

64 Note that, except GoogleDistance and LLR, all re- sults for all co-occurrence measures are statistically significant at p = . [sent-110, score-0.255]

65 For completeness of comparison, we also include the best known results from literature for different non co-occurrence based word association measures on these tasks. [sent-112, score-0.392]

66 3 Performance Analysis and Conclusions We find that on average, PMIsig and cPMId, the recently introduced measures that incorporate significance in PMI, do not perform better than PMI on the given datasets. [sent-114, score-0.439]

67 Both of them perform worse than PMI on three out of four datasets. [sent-115, score-0.033]

68 By appropriately incorporating significance, we get new measures PMIs and sPMId that perform better than PMI(also PMIsig and cPMId respectively) on most datasets. [sent-116, score-0.354]

69 For example, on the ESL dataset, while the percentage of correct answers increases from 58 to 66 from PMIsig to PMIs, it is not the case that on moving from PMIsig to PMIs, several correct answers become incorrect and an even larger number of incorrect answers become correct. [sent-119, score-0.337]

70 As shown in Table 4, only one correct answers become incorrect while seven incorrect answers get corrected. [sent-120, score-0.234]

71 The same trend holds for most parameters values, and for moving from cPMId to sPMId. [sent-121, score-0.029]

72 PMIs and sPMId perform better than not just PMI, but they perform better than all popular cooccurrence measures on most of these tasks. [sent-124, score-0.445]

73 When compared with any other co-occurrence measure, on three out of four datasets each, both PMIs and sPMId perform better than that measure. [sent-125, score-0.033]

74 In fact, PMIs and sPMId perform reasonably well compared with more resource intensive non co-occurrence based methods as well. [sent-126, score-0.268]

75 Note that different non cooccurrence based measures perform well on different tasks. [sent-127, score-0.465]

76 We are comparing the performance of a single measure (say sPMId or PMIs) against the best measure for each task. [sent-128, score-0.066]

77 A study on similarity and relatedness using distributional and wordnet-based approaches. [sent-132, score-0.211]

78 Measuring semantic similarity between words using web search engines. [sent-136, score-0.103]

79 Normalized (pointwise) mutual information in collocation extraction, from form to meaning: Processing texts automatically. [sent-140, score-0.094]

80 Novel association measures using web search with double checking. [sent-144, score-0.29]

81 Improving pointwise mutual information (pmi) by incorporating significant cooccurrence. [sent-160, score-0.139]

82 Measures of the amount of ecological association between species. [sent-166, score-0.092]

83 General estimation and evaluation of compositional distributional semantic models. [sent-187, score-0.123]

84 Experimental support for a categorical compositional distributional model of meaning. [sent-195, score-0.073]

85 A solution to platos problem: The latent semantic analysis theory of acquisition, induction, and representation of knowledge. [sent-217, score-0.05]

86 Sentence similarity based on semantic nets and corpus statistics. [sent-230, score-0.103]

87 An effective, lowcost measure of semantic relatedness obtained from wikipedia links. [sent-239, score-0.168]

88 More data trumps smarter algorithms: Comparing pointwise mutual information with latent semantic analysis. [sent-254, score-0.156]

89 Hsh: Estimating semantic similarity of words and short phrases with frequency normalized distance measures. [sent-280, score-0.103]

90 A comparison of windowless and window-based computational association measures as predictors of syntagmatic human associations. [sent-284, score-0.29]


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[(3, 0.021), (6, 0.013), (18, 0.02), (22, 0.59), (30, 0.032), (50, 0.01), (51, 0.133), (66, 0.034), (71, 0.018), (75, 0.02), (96, 0.026)]

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