| { |
| "paper_id": "W95-0103", |
| "header": { |
| "generated_with": "S2ORC 1.0.0", |
| "date_generated": "2023-01-19T04:37:00.502005Z" |
| }, |
| "title": "Prepositional Phrase Attachment through a Backed-Off Model", |
| "authors": [ |
| { |
| "first": "Michael", |
| "middle": [], |
| "last": "Collins", |
| "suffix": "", |
| "affiliation": { |
| "laboratory": "", |
| "institution": "University of Pennsylvania Philadelphia", |
| "location": { |
| "postCode": "19104", |
| "region": "PA" |
| } |
| }, |
| "email": "mcollins@gradient.cis.upenn.edu" |
| }, |
| { |
| "first": "James", |
| "middle": [], |
| "last": "Brooks", |
| "suffix": "", |
| "affiliation": { |
| "laboratory": "", |
| "institution": "University of Pennsylvania Philadelphia", |
| "location": { |
| "postCode": "19104", |
| "region": "PA" |
| } |
| }, |
| "email": "jbrooks@gradient.cis.upenn.edu" |
| } |
| ], |
| "year": "", |
| "venue": null, |
| "identifiers": {}, |
| "abstract": "Recent work has considered corpus-based or statistical approaches to the problem of prepositional phrase attachment ambiguity. Typically, ambiguous verb phrases of the form v rip1 p rip2 are resolved through a model which considers values of the four head words (v, nl, p and 77,2). This paper shows that the problem is analogous to n-gram language models in speech recognition, and that one of the most common methods for language modeling, the backed-off estimate, is applicable. Results on Wall Street Journal data of 84.5% accuracy are obtained using this method. A surprising result is the importance of low-count events-ignoring events which occur less than 5 times in training data reduces performance to 81.6%.", |
| "pdf_parse": { |
| "paper_id": "W95-0103", |
| "_pdf_hash": "", |
| "abstract": [ |
| { |
| "text": "Recent work has considered corpus-based or statistical approaches to the problem of prepositional phrase attachment ambiguity. Typically, ambiguous verb phrases of the form v rip1 p rip2 are resolved through a model which considers values of the four head words (v, nl, p and 77,2). This paper shows that the problem is analogous to n-gram language models in speech recognition, and that one of the most common methods for language modeling, the backed-off estimate, is applicable. Results on Wall Street Journal data of 84.5% accuracy are obtained using this method. A surprising result is the importance of low-count events-ignoring events which occur less than 5 times in training data reduces performance to 81.6%.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Abstract", |
| "sec_num": null |
| } |
| ], |
| "body_text": [ |
| { |
| "text": "Prepositional phrase attachment is a common cause of structural ambiguity in natural language. For example take the following sentence:", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Introduction", |
| "sec_num": "1" |
| }, |
| { |
| "text": "Pierre Vinken, 61 years old, joined the board as a nonexecutive director.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Introduction", |
| "sec_num": "1" |
| }, |
| { |
| "text": "The PP 'as a nonexecutive director' can either attach to the NP 'the board' or to the VP 'joined', giving two alternative structures. (In this case the VP attachment is correct): NP-attach: (joined ((the board) (as a nonexecutive director))) VP-attach: ((joined (the board)) (as a nonexecutive director)) Work by Ratnaparkhi, Reynar and Roukos [RRR94] and Brill and Resnik [BR94] has considered corpus-based approaches to this problem, using a set of examples to train a model which is then used to make attachment decisions on test data. Both papers describe methods which look at the four head words involved in the attachment -the VP head, the first NP head, the preposition and the second NP head (in this case joined, board, as and director respectively).", |
| "cite_spans": [ |
| { |
| "start": 313, |
| "end": 325, |
| "text": "Ratnaparkhi,", |
| "ref_id": null |
| }, |
| { |
| "start": 326, |
| "end": 351, |
| "text": "Reynar and Roukos [RRR94]", |
| "ref_id": null |
| }, |
| { |
| "start": 373, |
| "end": 379, |
| "text": "[BR94]", |
| "ref_id": "BIBREF0" |
| } |
| ], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Introduction", |
| "sec_num": "1" |
| }, |
| { |
| "text": "This paper proposes a new statistical method for PP-attachment disambiguation based on the four head words.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Introduction", |
| "sec_num": "1" |
| }, |
| { |
| "text": "The training and test data were supplied by IBM, being identical to that used in [RRR94] . Examples of verb phrases eontMning a (v np pp) sequence had been taken fl'om the Wall Street Journal Treebank [MSM93] . For each such VP the head verb, first head noun, preposition and second head noun were extracted, along with the attachment decision (1 for noun attachment, 0 for verb). For example the verb phrase:", |
| "cite_spans": [ |
| { |
| "start": 81, |
| "end": 88, |
| "text": "[RRR94]", |
| "ref_id": null |
| }, |
| { |
| "start": 201, |
| "end": 208, |
| "text": "[MSM93]", |
| "ref_id": null |
| } |
| ], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Training and Test Data", |
| "sec_num": "2.1" |
| }, |
| { |
| "text": "((joined (the board)) (as a nonexecutive director))", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Training and Test Data", |
| "sec_num": "2.1" |
| }, |
| { |
| "text": "would give the quintuple: 0 joined board as director", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Training and Test Data", |
| "sec_num": "2.1" |
| }, |
| { |
| "text": "The elements of this quintuple will from here on be referred to as the random variables A, V, N1, P, and N2. In the above verb phrase A = 0, V = joined, N1 = board, P = as, and N2 = director.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Training and Test Data", |
| "sec_num": "2.1" |
| }, |
| { |
| "text": "The data consisted of training and test files of 20801 and 3097 quintuples respectively. In addition, a development set of 4039 quintuples was also supplied. This set was used during development of the attachment algorithm, ensuring that there was no implicit training of the method on the test set itself.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Training and Test Data", |
| "sec_num": "2.1" |
| }, |
| { |
| "text": "A PP-attachment algorithm must take each quadruple (V = v, N1 = nl, P = p, N2 = n2) in test data and decide whether the attachment variable A = 0 or 1. The accuracy of the algorithm is then the percentage of attachments it gets 'correct' on test data, using the A values taken from the treebank as the reference set.", |
| "cite_spans": [ |
| { |
| "start": 51, |
| "end": 83, |
| "text": "(V = v, N1 = nl, P = p, N2 = n2)", |
| "ref_id": null |
| } |
| ], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Outline of the Problem", |
| "sec_num": "2.2" |
| }, |
| { |
| "text": "The probability of the attachment variable A being 1 or 0 (signifying noun or verb attachment respectively) is a probability, p, which is conditional on the values of the words in the quadruple.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Outline of the Problem", |
| "sec_num": "2.2" |
| }, |
| { |
| "text": "In general a probabilistic algorithm will make an estimate, 15, of this probability:", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Outline of the Problem", |
| "sec_num": "2.2" |
| }, |
| { |
| "text": "15 (A= llV=v, Nl=nl, P=p, N2=n2) For brevity this estimate will be referred to from here on as:", |
| "cite_spans": [ |
| { |
| "start": 3, |
| "end": 13, |
| "text": "(A= llV=v,", |
| "ref_id": null |
| }, |
| { |
| "start": 14, |
| "end": 20, |
| "text": "Nl=nl,", |
| "ref_id": null |
| }, |
| { |
| "start": 21, |
| "end": 25, |
| "text": "P=p,", |
| "ref_id": null |
| }, |
| { |
| "start": 26, |
| "end": 32, |
| "text": "N2=n2)", |
| "ref_id": null |
| } |
| ], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Outline of the Problem", |
| "sec_num": "2.2" |
| }, |
| { |
| "text": "p(l[v, nl,p, n2)", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Outline of the Problem", |
| "sec_num": "2.2" |
| }, |
| { |
| "text": "The decision can then be made using the test:", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Outline of the Problem", |
| "sec_num": "2.2" |
| }, |
| { |
| "text": "~(llv, nl,p, n2 ) >= 0.5", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Outline of the Problem", |
| "sec_num": "2.2" |
| }, |
| { |
| "text": "If this is true the attachment is made to the noun, !f not then it is made to the verb.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Outline of the Problem", |
| "sec_num": "2.2" |
| }, |
| { |
| "text": "When evaluating an algorithm it is useful to have an idea of the lower and upper bounds on its performance. Some key results are summarised in the table below. All results in this section are on the IBM training and test data, with the exception of the two 'average human' results.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Lower and Upper Bounds on Performance", |
| "sec_num": "2.3" |
| }, |
| { |
| "text": "Always noun attachment 59.0 Most likely for each preposition 72.2 Average Human (4 head words only)", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Method Percentage Accuracy", |
| "sec_num": null |
| }, |
| { |
| "text": "88.2 Average Human (whole sentence) 93.2 'Always noun attachment' means attach to the noun regardless of (v,nl,p,n2). 'Most likely for each preposition' means use the attachment seen most often in training data for the preposition seen in the test quadruple. The human performance results are taken from [RRR94], and are the average performance of 3 treebanking experts on a set of 300 randomly selected test events from the WSJ corpus, first looking at the four head words alone, then using the whole sentence.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Method Percentage Accuracy", |
| "sec_num": null |
| }, |
| { |
| "text": "A reasonable lower bound seems to be 72.2% as scored by the 'Most likely for each preposition' method. An approximate upper bound is 88.2% -it seems unreasonable to expect an algorithm to perform much better than a human.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Method Percentage Accuracy", |
| "sec_num": null |
| }, |
| { |
| "text": "3.1", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Estimation based on Training Data Counts", |
| "sec_num": "3" |
| }, |
| { |
| "text": "We will use the symbol f to denote the number of times a particular tuple is seen in training data. For example f(1, is, revenue, from, research) is the number of times the quadruple (is, revenue, from, research) is seen with a noun attachment. Counts of lower order tuples can also be made-for example f(1, P = from) is the number of times (P = from) is seen with noun attachment in training data, f(V = is, N2 = research) is the number of times (V = is, N2 = research)", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Notation", |
| "sec_num": null |
| }, |
| { |
| "text": "is seen with either attachment and any value of N1 and P.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Notation", |
| "sec_num": null |
| }, |
| { |
| "text": "A maximum likelihood method would use the training data to give the following estimation for the conditional probability:", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Maximum Likelihood Estimation", |
| "sec_num": null |
| }, |
| { |
| "text": "l~ (l[v, nl,p, n2)= f(1,v, nl,p, n2) f (v, nl, p, n2) Unfortunately sparse data problems make this estimate useless. A quadruple may appear in test data which has never been seen in training data. ie. f (v, nl,p, n2) = 0. The above estimate is undefined in this situation, which happens extremely frequently in a large vocabulary domain such as WSJ. (In this experiment about 95% of those quadruples appearing in test data had not been seen in training data).", |
| "cite_spans": [ |
| { |
| "start": 3, |
| "end": 36, |
| "text": "(l[v, nl,p, n2)= f(1,v, nl,p, n2)", |
| "ref_id": null |
| }, |
| { |
| "start": 39, |
| "end": 53, |
| "text": "(v, nl, p, n2)", |
| "ref_id": null |
| }, |
| { |
| "start": 203, |
| "end": 216, |
| "text": "(v, nl,p, n2)", |
| "ref_id": null |
| } |
| ], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Maximum Likelihood Estimation", |
| "sec_num": null |
| }, |
| { |
| "text": "Even if f(v, nl,p, n2) > 0, it may still be very low, and this may make the above MLE estimate inaccurate. Unsmoothed MLE estimates based on low counts are notoriously bad in similar problems such as n-gram language modeling [GC90]. However later in this paper it is shown that estimates based on low counts are surprisingly useful in the PP-attachment problem.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Maximum Likelihood Estimation", |
| "sec_num": null |
| }, |
| { |
| "text": "Hindle and Rooth [HR93] describe one of the first statistical approaches to the prepositional phrase attachment problem. Over 200,000 (v, nl,p) triples were extracted from 13 million words of AP news stories. The attachment decisions for these triples were unknown, so an unsupervised training method was used (section 5.2 describes the algorithm in more detail). Two human judges annotated the attachment decision for 880 test examples, and the method performed at 80% accuracy on these cases. Note that it is difficult to compare this result to results on Wall Street Journal, as the two corpora may be quite different.", |
| "cite_spans": [ |
| { |
| "start": 134, |
| "end": 143, |
| "text": "(v, nl,p)", |
| "ref_id": null |
| } |
| ], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Previous Work", |
| "sec_num": "3.3" |
| }, |
| { |
| "text": "The Wall Street Journal Treebank [MSM93] enabled both [RRR94] and [BR94] to extract a large amount of supervised training material for the problem. Both of these methods consider the second noun, n2, as well as v, nl and p, with the hope that this additional information will improve results.", |
| "cite_spans": [ |
| { |
| "start": 66, |
| "end": 72, |
| "text": "[BR94]", |
| "ref_id": "BIBREF0" |
| } |
| ], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Previous Work", |
| "sec_num": "3.3" |
| }, |
| { |
| "text": "[BR94] use 12,000 training and 500 test examples. A greedy search is used to learn a sequence of 'transformations' which minimise the error rate on training data. A transformation is a rule which makes an attachment decision depending on up to 3 elements of the (v, nl,p, n2) quadruple. (Typical examples would be 'If P=ofthen choose noun attachment' or 'If V=buy and P=for choose verb attachment'). A further experiment incorporated word-class information from WordNet into the model, by allowing the transformations to look at classes as well as the words. (An example would be 'If N2 is in the time semantic class, choose verb attachment'). The method gave 80.8%", |
| "cite_spans": [ |
| { |
| "start": 262, |
| "end": 275, |
| "text": "(v, nl,p, n2)", |
| "ref_id": null |
| } |
| ], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Previous Work", |
| "sec_num": "3.3" |
| }, |
| { |
| "text": "accuracy with words only, 81.8% with words and semantic classes, and they also report an accuracy of 75.8% for the metric of [HR93] on this data. Transformations (using words only) score 81.9% 1 on the IBM data used in this paper.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Previous Work", |
| "sec_num": "3.3" |
| }, |
| { |
| "text": "[RRR94] use the data described in section 2.1 of this paper -20801 training and 3097 test examples from Wall Street Journal. They use a maximum entropy model which also considers subsets of the quadruple. Each sub-tuple predicts noun or verb attachment with a weight indicating its strength of prediction -the weights are trained to maximise the likelihood of training data. For example (P = of) might have a strong weight for noun attachment, while (V = buy, P = for) would have a strong weight for verb attachment.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Previous Work", |
| "sec_num": "3.3" |
| }, |
| { |
| "text": "[RRR94] also allow the model to look a.t class inlbrmation, this time the classes were learned automatically from a corpus. Results of 77.7% (words only) and 81.6% (words and classes) are reported. Crucially they ignore low-count events in training data by imposing a frequency cut-off somewhere between 3 and 5.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Previous Work", |
| "sec_num": "3.3" |
| }, |
| { |
| "text": "[KATZ87] describes backed-off n-gram word models for speech recognition. There the task is to estimate the probability of the next word in a text given the (n-l) preceding words. The MLE estimate of this probability would be:", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "The Backed-Off Estimate", |
| "sec_num": "4" |
| }, |
| { |
| "text": "f(Wl,W2 .... Wn) p(WnlWl, W2 .... Wn-1) = f'~li~U2....~Vn_l)", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "The Backed-Off Estimate", |
| "sec_num": "4" |
| }, |
| { |
| "text": "But again the denominator f(Wl, W2 .... Wn_l) will frequently be zero, especially for large n. The backed-off estimate is a method of combating the sparse data problem. It is defined recursively as follows:", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "The Backed-Off Estimate", |
| "sec_num": "4" |
| }, |
| { |
| "text": "If f(wl, w2 .... Wn-1) > Cl f(Wl, W2 .... ten) /5(W~lWl,W2 .... W~-l) = S-~l;tV2...~W~-l) Else if f(w2, w3 .... Wn-1) > C2 P(WnIWl,W2 .... Wn--1) = ~1 X Else if f(w3, w4 .... Wn--1) > C3 iG(w~lwl,w2 .... W~-l) = al X as X", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "The Backed-Off Estimate", |
| "sec_num": "4" |
| }, |
| { |
| "text": "Else backing-off continues in the same way.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "The Backed-Off Estimate", |
| "sec_num": "4" |
| }, |
| { |
| "text": "f(w2, w3 .... Wn) f(w~, W 3 .... Wn-1 ) f(w3, W4 .... ten) f(w3, w4 .... w~_~)", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "The Backed-Off Estimate", |
| "sec_num": "4" |
| }, |
| { |
| "text": "The idea here is to use MLE estimates based on lower order n-grams if counts are not high enough to make an accurate estimate at the current level. The cut off frequencies (O, c2 .... ) are thresholds determining whether to back-off or not at each level -counts lower than ci at stage i are deemed to be too low to give an accurate estimate, so in this case backing-off continues. (~1, ~2, .... ) are normalisation constants which ensure that conditional probabilities sum to one.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "The Backed-Off Estimate", |
| "sec_num": "4" |
| }, |
| { |
| "text": "Note that the estimation of 15(wn[w~, w2 .... Wn-1) is analogous to the estimation of 15(1]v, nl, p, n2), and the above method can therefore also be applied to the PP-attachment problem. For example a simple method for estimation of 15(1[v, nl,p, n2) nl,p) , (v,p, n2) , (nl,p, n2) and (v, nl, n2)) and six possible pairs when backing off from triples ((v,p) ", |
| "cite_spans": [ |
| { |
| "start": 259, |
| "end": 268, |
| "text": "(v,p, n2)", |
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| { |
| "start": 271, |
| "end": 281, |
| "text": "(nl,p, n2)", |
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| { |
| "start": 352, |
| "end": 358, |
| "text": "((v,p)", |
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| { |
| "start": 233, |
| "end": 250, |
| "text": "15(1[v, nl,p, n2)", |
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| }, |
| { |
| "start": 251, |
| "end": 256, |
| "text": "nl,p)", |
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| ], |
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| "section": "The Backed-Off Estimate", |
| "sec_num": "4" |
| }, |
| { |
| "text": ", (nl,p), (p, n2), (v, nl), (v", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "The Backed-Off Estimate", |
| "sec_num": "4" |
| }, |
| { |
| "text": "A key observation in choosing between these tuples is that the preposition is particularly important to the attachment decision. For this reason only tuples which contained the preposition were used in backed off estimates -this reduces the problem to a choice between 3 triples and 3 pairs at each respective stage. Section 6.2 describes experiments which show that tuples containing the preposition are much better indicators of attachment.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": ", n2) and", |
| "sec_num": null |
| }, |
| { |
| "text": "The following method of combining the counts was found to work best in practice:", |
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| "eq_spans": [], |
| "section": ", n2) and", |
| "sec_num": null |
| }, |
| { |
| "text": "15t,ipl~(11v , nl,p, n2) = f(1, v, nl,p) + f(1, v,p, n2) + f(1, nl,p, n2) f(v, nl,p) + f(v,p, n2) + f(nl,p, n2) and iSp~ir(l[v, nl,p, n2) = f(1, v,p) + f(1, nl,p) + f(1,p, n2) f(v,p) + f(nl,p) + f(p, n2)", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": ", n2) and", |
| "sec_num": null |
| }, |
| { |
| "text": "Note that this method effectively gives more weight to tuples with high overall counts. Another obvious method of combination, a simple average 2, gives equal weight to the three tuples regardless of their total counts and does not perform as well.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": ", n2) and", |
| "sec_num": null |
| }, |
| { |
| "text": "The cut-off frequencies must then be chosen. A surprising difference fi'om language modeling is that a cut-off frequency of 0 is found to be optimum at all stages. This effectively means however low a count is, still use it rather than backing off a level. f (1,v,p,n2) f (1,nl,p,n2) 15t,.ipee(l[v, nl,p, n2) ", |
| "cite_spans": [ |
| { |
| "start": 259, |
| "end": 269, |
| "text": "(1,v,p,n2)", |
| "ref_id": null |
| }, |
| { |
| "start": 272, |
| "end": 308, |
| "text": "(1,nl,p,n2) 15t,.ipee(l[v, nl,p, n2)", |
| "ref_id": null |
| } |
| ], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": ", n2) and", |
| "sec_num": null |
| }, |
| { |
| "text": "= f(v,nl,p) --k f(v,v,n2) \"-I-f(nl,p,~2) 3 4.1", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": ", n2) and", |
| "sec_num": null |
| }, |
| { |
| "text": "The algorithm is then as follows:", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Description of the Algorithm", |
| "sec_num": null |
| }, |
| { |
| "text": "1. If 3 f (v, nl,p, n2) > 0 l~ (llv, nl,p, n2)= f(1,v, nl,p, n2) f (v, nl, p, n2) 2. Else if f (v, nl,p) ", |
| "cite_spans": [ |
| { |
| "start": 10, |
| "end": 23, |
| "text": "(v, nl,p, n2)", |
| "ref_id": null |
| }, |
| { |
| "start": 31, |
| "end": 64, |
| "text": "(llv, nl,p, n2)= f(1,v, nl,p, n2)", |
| "ref_id": null |
| }, |
| { |
| "start": 67, |
| "end": 81, |
| "text": "(v, nl, p, n2)", |
| "ref_id": null |
| }, |
| { |
| "start": 95, |
| "end": 104, |
| "text": "(v, nl,p)", |
| "ref_id": null |
| } |
| ], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Description of the Algorithm", |
| "sec_num": null |
| }, |
| { |
| "text": "+ f(v,p, n2) + f(nl,p, n2) > 0 fi(11 v, nl, p, n2) = f( 1, v, nl, p) + f( 1, v, p, n2) + .f( 1, nl, p, n2) f(v, nl, p) + f(v, p, n2) + f(nl, p, n2) 3. Else if f(v,p) + f(nl,p) + f(p, n2) > 0", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Description of the Algorithm", |
| "sec_num": null |
| }, |
| { |
| "text": "15 (11v, nl,p, n2 ) ", |
| "cite_spans": [ |
| { |
| "start": 3, |
| "end": 19, |
| "text": "(11v, nl,p, n2 )", |
| "ref_id": null |
| } |
| ], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Description of the Algorithm", |
| "sec_num": null |
| }, |
| { |
| "text": "= f(1,v,p) + f(1, nl,p) + f(1,p, n2) f(v,p) + f(nl,p) + f(p, n2)", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Description of the Algorithm", |
| "sec_num": null |
| }, |
| { |
| "text": "15 (llv, nl,p, n2 ) ", |
| "cite_spans": [ |
| { |
| "start": 3, |
| "end": 19, |
| "text": "(llv, nl,p, n2 )", |
| "ref_id": null |
| } |
| ], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Else if f(p) > 0", |
| "sec_num": "4." |
| }, |
| { |
| "text": "_ f(1,p) f(P)", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Else if f(p) > 0", |
| "sec_num": "4." |
| }, |
| { |
| "text": "5. Else/}(1Iv, nl,p, n2) = 1.0 (default is noun attachment).", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Else if f(p) > 0", |
| "sec_num": "4." |
| }, |
| { |
| "text": "The decision is then:", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Else if f(p) > 0", |
| "sec_num": "4." |
| }, |
| { |
| "text": "If 15(11v , nl,p, n2) >= 0.5 choose noun attachment.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Else if f(p) > 0", |
| "sec_num": "4." |
| }, |
| { |
| "text": "Otherwise choose verb attachment", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Else if f(p) > 0", |
| "sec_num": "4." |
| }, |
| { |
| "text": "The figure below shows the results for the method on the 3097 test sentences, also giving the total count and accuracy at each of the backed-off stages. ", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Results", |
| "sec_num": "5" |
| }, |
| { |
| "text": "In an effort to reduce sparse data problems the following processing was run over both test and training data:", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Results with Morphological Analysis", |
| "sec_num": "5.1" |
| }, |
| { |
| "text": "\u2022 All 4-digit numbers were replaced with the string 'YEAR'.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Results with Morphological Analysis", |
| "sec_num": "5.1" |
| }, |
| { |
| "text": "\u2022 All other strings of numbers (including those which had commas or decimal points) were replaced with the token 'NUM'.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Results with Morphological Analysis", |
| "sec_num": "5.1" |
| }, |
| { |
| "text": "\u2022 The verb and preposition fields were converted entirely to lower case.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Results with Morphological Analysis", |
| "sec_num": "5.1" |
| }, |
| { |
| "text": "\u2022 In the nl and n2 fields M1 words starting with a capital letter followed by one or more lower case letters were replaced with 'NAME'.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Results with Morphological Analysis", |
| "sec_num": "5.1" |
| }, |
| { |
| "text": "\u2022 All strings 'NAME-NAME' were then replaced by 'NAME'.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Results with Morphological Analysis", |
| "sec_num": "5.1" |
| }, |
| { |
| "text": "\u2022 All verbs were reduced to their morphological stem using the morphological analyser described in [KSZE94].", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Results with Morphological Analysis", |
| "sec_num": "5.1" |
| }, |
| { |
| "text": "These modifications are similar to those performed on the corpus used by [BR94] .", |
| "cite_spans": [ |
| { |
| "start": 73, |
| "end": 79, |
| "text": "[BR94]", |
| "ref_id": "BIBREF0" |
| } |
| ], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Results with Morphological Analysis", |
| "sec_num": "5.1" |
| }, |
| { |
| "text": "The result using this modified corpus was 84.5%, an improvement of 0.4~0 on the previous result. ", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Results with Morphological Analysis", |
| "sec_num": "5.1" |
| }, |
| { |
| "text": "f(1,nl,p) f(O,v,p) >= /(1, nl) f(O,v)", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Stage", |
| "sec_num": null |
| }, |
| { |
| "text": "then choose noun attachment, else choose verb attachment. This is effectively a comparison of the maximum likelihood estimates of/)(pll, nl ) and P(PI(}, v), a different measure from the backed-off estimate which gives i5(lIv,p , nl).", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Stage", |
| "sec_num": null |
| }, |
| { |
| "text": "The backed-off method based on just the f (v,p) and f(nl,p) counts would be: If 15(llv , nl,p) >= 0.5 then choose noun attachment, else choose verb attachment, where l~ (lIv, nl, p) = f(1, v, p)+ f(1, nl, p) f (v,p) + f(nl,p) 5This ignores refinements to the test such ~ smoothing of the estimate, and a measure of the confidence of the decision. However the measure given is at the core of the algorithm.", |
| "cite_spans": [ |
| { |
| "start": 42, |
| "end": 47, |
| "text": "(v,p)", |
| "ref_id": null |
| }, |
| { |
| "start": 169, |
| "end": 174, |
| "text": "(lIv,", |
| "ref_id": null |
| }, |
| { |
| "start": 175, |
| "end": 178, |
| "text": "nl,", |
| "ref_id": null |
| }, |
| { |
| "start": 179, |
| "end": 188, |
| "text": "p) = f(1,", |
| "ref_id": null |
| }, |
| { |
| "start": 189, |
| "end": 191, |
| "text": "v,", |
| "ref_id": null |
| }, |
| { |
| "start": 192, |
| "end": 200, |
| "text": "p)+ f(1,", |
| "ref_id": null |
| }, |
| { |
| "start": 201, |
| "end": 204, |
| "text": "nl,", |
| "ref_id": null |
| }, |
| { |
| "start": 205, |
| "end": 207, |
| "text": "p)", |
| "ref_id": null |
| }, |
| { |
| "start": 210, |
| "end": 225, |
| "text": "(v,p) + f(nl,p)", |
| "ref_id": null |
| } |
| ], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Stage", |
| "sec_num": null |
| }, |
| { |
| "text": "On the surface the method described in [HR93] looks very similar to the backed-off estimate. For this reason the two methods deserve closer comparison. Itindle and Rooth used a partial paxser to extract head nouns from a corpus, together with a preceding verb and a followillg preposition, giving a table of (v, nl,p) triples. An iterative, unsupervised method was thell used to decide between noun and verb attachment for each triple. The decision was made as followsZ:", |
| "cite_spans": [ |
| { |
| "start": 308, |
| "end": 317, |
| "text": "(v, nl,p)", |
| "ref_id": null |
| } |
| ], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "/ ,", |
| "sec_num": null |
| }, |
| { |
| "text": "An experiment was implemented to investigate the difference in performance between these two methods. The test set was restricted to those cases where f(1,nl) > 0, .f(0, v) > 0, and Hindle and Rooth's method gave a definite decision. (ie. the above inequality is strictly less-than or greater-than). This gave 1924 test cases. Hindle and Rooth's method scored 82.1% accuracy (1580 correct) on this set, whereas the backed-off measure scored 86.5% (1665 correct).", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "/ ,", |
| "sec_num": null |
| }, |
| { |
| "text": "A possible criticism of the backed-off estimate is that it uses low count events without any smoothing, which has been shown to be a mistake in similar problems such as n-gram language models. In particular, quadruples and triples seen in test data will frequently be seen only once or twice in trMning data.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Low Counts are Important", |
| "sec_num": "6.1" |
| }, |
| { |
| "text": "An experiment was made with all counts less than 5 being put to zero, 6 effectively making the algorithm ignore low count events. In [RRR94] a cut-off 'between 3 and 5' is used for all events. The training and test data were both the unprocessed, original data sets. The decrease in accuracy from 84.1% to 81.6% is clear evidence for the importance of low counts.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Low Counts are Important", |
| "sec_num": "6.1" |
| }, |
| { |
| "text": "We have excluded tuples which do not contain a preposition from the model. This section gives results which justify this.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Tuples with Prepositions are Better", |
| "sec_num": "6.2" |
| }, |
| { |
| "text": "The table below gives accuracies for the sub-tuples at each stage of backing-off. The accuracy figure for a particular tuple is obtained by modifying the algorithm in section 4.1 to use only information from that tuple at the appropriate stage. For example for (v, nl, n2), stage 2 would be modified to read 6Specifically: if for a subset x of the quadruple f(x) < 5, then make f(x) = f(1, x) = f(0, x) = 0.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Tuples with Prepositions are Better", |
| "sec_num": "6.2" |
| }, |
| { |
| "text": "If f(v, nl,n2) > 0, 15(llv, nl,p, n2) = f (1, v, nl, n2) .f ( v, ' /~, 1, n2) All other stages in the algorithm would be unchanged. The accuracy figure is then the percentage accuracy on the test cases where the (v, nl, n2) counts were used. The development set with no morphologicM processing was used for these tests. At each stage there is a sharp difference in accuracy between tuples with and without a preposition. Moreover, if the 14 tuples in the above table were ranked by accuracy, the top 7 tuples wouhl be the 7 tuples which contain a preposition.", |
| "cite_spans": [ |
| { |
| "start": 42, |
| "end": 56, |
| "text": "(1, v, nl, n2)", |
| "ref_id": null |
| }, |
| { |
| "start": 60, |
| "end": 77, |
| "text": "( v, ' /~, 1, n2)", |
| "ref_id": null |
| } |
| ], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Tuples with Prepositions are Better", |
| "sec_num": "6.2" |
| }, |
| { |
| "text": "The backed-off estimate scores appreciably better than other methods which have been tested on the Wall Street Journal corpus. The accuracy of 84.5% is close to the hmna.n peribrnlance figure of 88% using the 4 head words alone. A particularly surprising result is the significance of low count events in training data. The Mgorithm has the additional advantages of being conceptually simple, and computationMly inexpensive to implement.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Conclusions", |
| "sec_num": "7" |
| }, |
| { |
| "text": "There are a few possible improvements which may raise performance further. Firstly, while we have shown the importance of low-count events, some kind of smoothing 1nay improve peribrmance further -this needs to be investigated. Word-classes of semantically similar words may be used to help the sparse data problem -both [RRR94] and [BR94] report significant improvements through the use of word-classes. Finally, more training data is almost certain to improve results.", |
| "cite_spans": [ |
| { |
| "start": 333, |
| "end": 339, |
| "text": "[BR94]", |
| "ref_id": "BIBREF0" |
| } |
| ], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Conclusions", |
| "sec_num": "7" |
| }, |
| { |
| "text": "1Personal communication fromBrill.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "", |
| "sec_num": null |
| } |
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| "back_matter": [ |
| { |
| "text": "f (nl,p) f (v,p) f (nl) f (v) then choose noun attachment, else choose verb attachment.Here f(w,p) is the number of times preposition p is seen attached to word w in the table. ~tnd f(w) = Ep f(w, p).If we ignore n2 then the IBM data is equivalent to Hindle and Rooth's (v, hi, p} triples, with the advantage of the attachment decision being known, allowing a supervised algorithm. The test used in [HR93] can then be stated as follows in our notation:", |
| "cite_spans": [ |
| { |
| "start": 2, |
| "end": 8, |
| "text": "(nl,p)", |
| "ref_id": null |
| }, |
| { |
| "start": 11, |
| "end": 16, |
| "text": "(v,p)", |
| "ref_id": null |
| }, |
| { |
| "start": 19, |
| "end": 23, |
| "text": "(nl)", |
| "ref_id": null |
| }, |
| { |
| "start": 26, |
| "end": 29, |
| "text": "(v)", |
| "ref_id": null |
| } |
| ], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "If", |
| "sec_num": null |
| } |
| ], |
| "bib_entries": { |
| "BIBREF0": { |
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| "title": "A Rule-Based Approach to Prepositional Phrase Attachment Disambiguation", |
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| "FIGREF0": { |
| "num": null, |
| "uris": null, |
| "type_str": "figure", |
| "text": "2eg. A simple average for triples would be defined as f(1 ..... 1,p)" |
| }, |
| "TABREF0": { |
| "num": null, |
| "html": null, |
| "content": "<table/>", |
| "type_str": "table", |
| "text": "would go from MLE estimates ofiS(llv, nl,p, n2) to ~5(11v , nl,p) to ~5(1[v, nl) to 15(1[v) to 15(1). However a crucial difference between the two problems is that in the n-gram task the words Wl to wn are sequentiM, giving a natural order in which backing off takes place -from p(Wn[Wl, W 2 .... Wn_l) to 15(WnIW2, W3 .... Wn-1) to 15(W~[W3, W4 .... Wn_l) and soon. There is no such sequence in the PP-attachment problem, and because of this there are four possible triples when backing off from quadruples((v," |
| }, |
| "TABREF2": { |
| "num": null, |
| "html": null, |
| "content": "<table><tr><td/><td/><td/><td colspan=\"2\">TotM Number Number Correct Percent Correct</td></tr><tr><td/><td colspan=\"2\">Quadruples</td><td>242</td><td>224</td><td>92.6</td></tr><tr><td/><td/><td>Triples</td><td>977</td><td>858</td><td>87.8</td></tr><tr><td/><td colspan=\"2\">Doubles</td><td>1739</td><td>1433</td><td>82.4</td></tr><tr><td/><td/><td>Singles</td><td>136</td><td>99</td><td>72.8</td></tr><tr><td/><td colspan=\"2\">Default</td><td>3</td><td>3</td><td>100.0</td></tr><tr><td/><td/><td>Totals</td><td>3097</td><td>2617</td><td>84.5</td></tr><tr><td>5.2</td><td>Comparison</td><td colspan=\"2\">with Other Work</td></tr><tr><td colspan=\"4\">Results from [RRR94], [Method</td><td>Percentage Accuracy</td></tr><tr><td/><td/><td colspan=\"2\">[RRR94] (words only)</td><td>77.7</td></tr><tr><td/><td/><td colspan=\"2\">[RRR94] (words and classes)</td><td>81.6</td></tr><tr><td/><td/><td/><td>[BR94] (words only)</td><td>81.9</td></tr><tr><td/><td/><td colspan=\"2\">Backed-off (no processing)</td><td>84.1</td></tr><tr><td/><td colspan=\"4\">Backed-off (morphological processing)</td><td>84.5</td></tr></table>", |
| "type_str": "table", |
| "text": "BR94] and the backed-off method are shown in the table below 4. All results are for the IBM data. These figures should be taken in the context of the lower and upper bounds of 72.2%-88.2% proposed in section 2.3." |
| } |
| } |
| } |
| } |
