| { |
| "paper_id": "W96-0114", |
| "header": { |
| "generated_with": "S2ORC 1.0.0", |
| "date_generated": "2023-01-19T04:59:09.878602Z" |
| }, |
| "title": "Towards Automatic Grammar Acquisition from a Bracketed Corpus", |
| "authors": [ |
| { |
| "first": "Thanaruk", |
| "middle": [], |
| "last": "Theeramunkong", |
| "suffix": "", |
| "affiliation": {}, |
| "email": "" |
| }, |
| { |
| "first": "Manabu", |
| "middle": [], |
| "last": "Okumura", |
| "suffix": "", |
| "affiliation": {}, |
| "email": "" |
| } |
| ], |
| "year": "", |
| "venue": null, |
| "identifiers": {}, |
| "abstract": "In this paper, we propose a method to group brackets in a bracketed corpus (with lexical tags), according to their local contextual information, as a first step towards the automatic acquisition of a context-free grammar. Using a bracketed corpus, the learning task is reduced to the problem of how to determine the nonterminal label of each bracket in the corpus. In a grouping process, a single nonterminai label is assigned to each group of brackets which are similar. Two techniques, distributional analysis and hierarchical Bayesian clustering, are applied to exploit local contextual information for computing similarity between two brackets. We also show a technique developed for determining the appropriate number of bracket groups based on the concept of entropy analysis. Finally, we present a set of experimental results and evaluate the obtained results with a model solution given by humans.", |
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| "paper_id": "W96-0114", |
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| "abstract": [ |
| { |
| "text": "In this paper, we propose a method to group brackets in a bracketed corpus (with lexical tags), according to their local contextual information, as a first step towards the automatic acquisition of a context-free grammar. Using a bracketed corpus, the learning task is reduced to the problem of how to determine the nonterminal label of each bracket in the corpus. In a grouping process, a single nonterminai label is assigned to each group of brackets which are similar. Two techniques, distributional analysis and hierarchical Bayesian clustering, are applied to exploit local contextual information for computing similarity between two brackets. We also show a technique developed for determining the appropriate number of bracket groups based on the concept of entropy analysis. Finally, we present a set of experimental results and evaluate the obtained results with a model solution given by humans.", |
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| "section": "Abstract", |
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| "text": "Designing and refining a natural language grammar is a diiBcult and time-consuming task and requires a large amount of skilled effort. A hand-crafted grammar is usually not completely satisfactory and frequently fails to cover many unseen sentences. Automatic acquisition of grammars is a solution to this problem. Recently, with the increasing availability of large, machine-readable, parsed corpora, there have been numerous attempts to automatically acquire a CFG grammar through the application of enormous existing corporaILar90][Mi194][Per92][Shi95 ]. Lari and Young[Lar90] proposed so-called inside-outside algorithm, which constructs a grammar from an unbracketed corpus based on probability theory. The grammar acquired by this method is assumed to be in Chomsky normal form and a large amount of computation is required. Later, Pereira[Per92] applied this algorithm to a partially bracketed corpus to improve the computation time. Kiyono[Kiy94b] [Kiy94a] combined symbolic and statistical approaches to extract useful grammar rules from a partially bracketed corpus. To avoid generating a large number of grammar rules, some basic grammatical constraints, local boundaries constraints and X bar-theory were applied. Kiyono's approach performed a refinement of an original grammar by adding some additional rules while the inside-outside algorithm tries to construct a whole grammar from a corpus based on Maximum Likelihood. However, it is costly to obtain a suitable grammar from an unbracketed corpus and hard to evaluate results of these approaches. As the increase of the construction of bracketed corpora, an attempt to use a bracketed (tagged) corpus for grammar inference was made by Shiral[Shi95]. Shirai constructed a Japanese grammar based on some simple rules to give a name (a label) to each bracket in the corpus. To reduce the grammar size and ambiguity, some hand-encoded knowledge is applied in this approach.", |
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| "text": "Lari and Young[Lar90]", |
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| "section": "Introduction", |
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| "text": "In our work, like Shirai's approach, we make use of a bracketed corpus with lexical tags, but instead of using a set of human-encoded predefined rules to give a name (a label) to each bracket, we introduce some statistical techniques to acquire such label automatically. Using a bracketed corpus, the grammar learning task is reduced to the problem of how to determine the nonterminal label of each bracket in the corpus. More precisely, this task is concerned with the way to classify brackets to some certain groups and give each group a label. We propose a method to group brackets in a bracketed corpus (with lexical tags), according to their local contextual information, as a first step towards the automatic acquisition of a context-free grammar. In the grouping process, a single nontermina] label is assigned to each group of brackets which are similar. To do this, we apply and compare two types of techniques called distributional analysis [HarSl] and hierarchical Bayesian clustering [Iwa95] for setting a measure representing similarity among the bracket groups. We also propose a method to determine the appropriate number of bracket groups based on the concept of entropy analysis. Finally, we present a set of experimental results and evaluate our methods with a model solution given by humans.", |
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| "text": "[HarSl]", |
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| "section": "Introduction", |
| "sec_num": "1" |
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| "text": "In this section, we give a brief explanation of grammar acquisition using a bracketed corpus. In this work, the grammar acquisition utilizes a lexical-tagged corpus with bracketings. An example of the parse structures of two sentences in the corpus is shown graphically in Figure 1 .", |
| "cite_spans": [], |
| "ref_spans": [ |
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| "start": 273, |
| "end": 281, |
| "text": "Figure 1", |
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| "section": "Grammar Acquisition with a Bracketed Corpus", |
| "sec_num": "2" |
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| { |
| "text": "(1) Parse Tree (1)", |
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| "section": "Sentence", |
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| "text": "(2) Parse Tree 2: A big man slipped on the ice. : (((ART,\"a\") ((ADJ,\" big') (NOUN,\" man\"))) ((VI,\" slipped\")((PREP,\"on\") ((ART,\"the\") (NOUN,\" ice')))))", |
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| "section": "Sentence", |
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| "text": ": The boy dropped his wallet somewhere. : (((ART,\"the\") (NOUN,\"boy')) (((VT,\"dropped\") ((PROg,\"his\") (NOUN,\"wallet'))) (AVV,\"somewhere\")))", |
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| "section": "Sentence", |
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| { |
| "text": "m m \u2022 | | t i |", |
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| "section": "Sentence", |
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| "text": "A big man slipped on the ice The boy dropped his wallet somewhere Figure 1 : The graphical representation of the parse structures of a big man slipped on the ice and the boy dropped his wallet somewhere", |
| "cite_spans": [], |
| "ref_spans": [ |
| { |
| "start": 66, |
| "end": 74, |
| "text": "Figure 1", |
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| "eq_spans": [], |
| "section": "ART ADJ NOUN Vl PREP ART NOUN ART NOUN VT PRON NOUN ADV", |
| "sec_num": null |
| }, |
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| "text": "In the parse structures, each terminal category (leaf node) is given a name (tag) while there is no label for each nonterminal category (intermediate node). With this corpus, the grammar learning task corresponds to a process to determine the nonterminal label of each bracket in the corpus. More precisely, this task is concerned with the way to classify the brackets into some certain groups and give each group a label. For instance, in Figure 1 , it is reasonable to classify the brackets 1 (c2),(c4) and (c5) into a same group and give them a same label (e.g., NP(noun phrase)). As the result, we obtain three grammar rules: NP ~ (ART)(NOUN), NP ~ (PRON)(NOUN) and NP ~ (ART)(el). To perform this task, our grammar acquisition algorithm operates in five stages as follows.", |
| "cite_spans": [], |
| "ref_spans": [ |
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| "start": 440, |
| "end": 448, |
| "text": "Figure 1", |
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| "eq_spans": [], |
| "section": "ART ADJ NOUN Vl PREP ART NOUN ART NOUN VT PRON NOUN ADV", |
| "sec_num": null |
| }, |
| { |
| "text": "1. Assign a unique label to each node of which lower nodes are assigned labels. At the initial step, such node is one whose lower nodes are lexical categories 2. This process is performed throughout all parse trees in the corpus.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "ART ADJ NOUN Vl PREP ART NOUN ART NOUN VT PRON NOUN ADV", |
| "sec_num": null |
| }, |
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| "text": "1A bracket corresponds to a node in In this paper, as a first step of our grammar acquisition, we focus on step (1)-(4), that is how to group nodes of which lower nodes are lexical categories. To compute the similarity of a pair of labels(in step 2), we propose two types of techniques called distributional analysis and hierarchical Bayesian cbtstering as shown in section 3. In section 4, we introduce the concept of differential entropy as the termination condition used in step (4).", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "ART ADJ NOUN Vl PREP ART NOUN ART NOUN VT PRON NOUN ADV", |
| "sec_num": null |
| }, |
| { |
| "text": "In this section, we describe two techniques which utilize \"local context information\" to calculate similarity between two labels. The term \"local contextual information\" considered here is represented by a pair of words immediately before and after a label. In the rest of this section, we first describe distributional analysis in subsection 3.1. Next, we give the concept of Bayesian clustering in subsection 3.2.", |
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| "eq_spans": [], |
| "section": "Local Contextual Information as Similarity Measure", |
| "sec_num": "3" |
| }, |
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| "text": "Distributional analysis is a statistical method originally proposed by Harris[Harbl] to uncover regularities in the distributional relations among the features of speech. Applications of this technique are varied [Bri92] [Per93]. In this paper, we apply this technique to group similar brackets in a bracketed corpus. The detail of this technique is illustrated below. Let P1 and P2 be two probability distributions over environments. The relative entropy between P1 and P2 is:", |
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| { |
| "start": 213, |
| "end": 220, |
| "text": "[Bri92]", |
| "ref_id": "BIBREF1" |
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| "section": "Distributional Analysis", |
| "sec_num": "3.1" |
| }, |
| { |
| "text": "Pl(e) D(PIlIP2) = ~ Pz(e) x log P~(e) \u2022 E Env~iro~m\u00a2~'ts", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Distributional Analysis", |
| "sec_num": "3.1" |
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| "text": "Relative entropy D(PIlIP2 ) is a measure of the amount of extra information beyond P2 needed to describe Pl. The divergence between Pz and P= is defined as D(PIlIP2 ) + D(P2IIP1), and is a measure of how difficult it is to distinguish between the two distributions. The environment is a pair of words immediately before and after a label(bracket). A pair of labels is considered to be identical when they are distributionaliy similar, i.e., the divergence of their probability distributions over environments is low.", |
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| "eq_spans": [], |
| "section": "Distributional Analysis", |
| "sec_num": "3.1" |
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| "text": "The probability distribution can be simply calculated by counting the occurrence of (c~) and", |
| "cite_spans": [], |
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| "section": "Distributional Analysis", |
| "sec_num": "3.1" |
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| "text": "(word1 c~ words). For the example in Figure 1 , the numbers of appearances of (c1), (c2), (c5), (ART cz VI), (PREP c2 NULL) and (VT es ADV) are collected from the whole corpus. NULL stands for a blank tag representing the beginning or ending mark of a sentence.", |
| "cite_spans": [], |
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| "start": 37, |
| "end": 45, |
| "text": "Figure 1", |
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| "section": "Distributional Analysis", |
| "sec_num": "3.1" |
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| "text": "Utilizing divergence as a similarity measure, there is a serious problem caused by the sparseness of existing data or the characteristic of language itself. In the formula of relative entropy, there is a possibility that P2(e) becomes zero. In this condition, we cannot calculate the divergence of two probability distributions. To cope with this problem, we extend the original probability to one shown in the following formula.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Sparse Data Considerations", |
| "sec_num": null |
| }, |
| { |
| "text": "N(~) s 2", |
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| "section": "P(ac~ b) = A N(ac~b) ~.(l_A)Nt~g", |
| "sec_num": null |
| }, |
| { |
| "text": "where, N(a) is the occurrence frequency of o~, Ntag8 is the number of terminal categories and A is a interpolation coefficient. The first term in the right part of the formula is the original estimated probability. The second term is generally called a uniform distribution, where the probability of an unseen event is estimated to a uniform fixed number. A is applied as a balancing weight between the observed distribution and the uniform distribution. Intuitively, when the size of data is large, the small number should be used as A. In the experimental results in this paper, we assigned A with a value of 0.6.", |
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| "section": "P(ac~ b) = A N(ac~b) ~.(l_A)Nt~g", |
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| "text": "As a probabilistic method, hierarchical Bayesian clustering was proposed by Iwaya~na [Iwa95] to automatically classify given texts. It was applied to improve the efficiency and the effectiveness of text retrieval/categorization. Referring to this method,we try to make use of Baycsiar~ posterior probability as another similarity measure for grouping the similar brackets. In this section, we conclude the concept of this measure as follows.", |
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| "text": "[Iwa95]", |
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| "section": "Hierarchical Bayesian Clustering Method", |
| "sec_num": "3.2" |
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| "text": "Let's denote a posterior probability with P(GIC), where C is a collection of data (i.e., in Figure 2 , C = {c1,e2, ..., CN}) and G is a set of groups(clusters) (i.e., G = {gz,g2, ...}). Each group(cluster) gj is a set of data and the groups are mutually exclusive. In the initial stage, each group is a singleton set; g~ = {~} for all i. The method tries to select and merge the group pair that brings about the maximum value of the posterior probability ~ P(GIC). That is, in each step of merging, this method searches for the most plausible situation that the data in C are partitioned in the certain groups G. For instance, at a merge step h + 1 (0 < b < N -1), a data collection C has been partitioned into a set of groups G~. That is each datum e belongs to a group g E Gk. The posterior probability at the merging step/\u00a2 + 2 can be calculated using the posterior probability at the merging step/\u00a2 + 1 as shown below (for more detail, see [Iwa95] ).", |
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| "text": "Figure 2", |
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| "section": "Hierarchical Bayesian Clustering Method", |
| "sec_num": "3.2" |
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| "text": "Here PC(G~) corresponds to the prior probability that N random data are classified in to a set of groups O~. As for the factor of ~ a well known estimate[Ris89] is applied and it is reduced", |
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| "section": "PC(Gh) SC(g=)SC(g,)", |
| "sec_num": null |
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| { |
| "text": "PC(G~) '", |
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| "section": "PC(Gh) SC(g=)SC(g,)", |
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| "text": "to a constant value A -1 regardless of the merged pair. For a certain merging step, P(G~IC ) is identical independently of which groups are merged together. Therefore we can use the following measure to select the best group pair to merge. The similarity between two bracket groups(labels), g= and gv, can be defined by SIM(g=,gv). Here, the larger SIM(g=,g~) is, the more similar two brackets are.", |
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| "section": "PC(Gh) SC(g=)SC(g,)", |
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| "text": "SIM where SC(g) expresses the probability that all the labels in a group g are produced from the group, an elementai probability P(c[g) means the probability that a group g produces its member c and P(elc ) denotes a relative frequency of an environment e of a label e, P(elg ) means a relative frequency of an environment e of a group g and P(e) is a relative frequency of an environment e of the entire label set. In the calculation of SIM(g=,gv), we can ignore the value of P(c) because it occurs Ig= U gvl times in both denominator and numerator. Normally, SIM(g=,gy) is ranged between 0 and 1 due to the fact that P(c[g= U gy) _< P(clg= ) when c E g=.", |
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| "section": "SO(g, U g,)", |
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| "text": "During iteratively merging the most similar labels, all labels will finally be gathered to a single group. Due to this, it is necessary to provide a criterion for determining whether this merging process should be continued or terminated. In this section, we describe a criterion named differential entropy which is a measure of entropy (perplexity) fluctuation before and after merging a pair of labels, Let cl and c2 be the most similar pair of labels based on divergence or Bayesia~u posterior probability. Also let c3 be the result label. P~i (e), Pc= (e) and Pc3(e) are probability distributions over environment e of cl, e2 and c3, respectively. Pc1, Pc= and P~3 are estimated probabilities of cl, c2 and c3, respectively. The differentiaJ entropy (Z~E) is defined as follows. where ~, Pc~ (e) log Pc, (e) is the total entropy over various environments of label c~. The larger ~E is, the larger the information fluctuation before aad after merging becomes. Generally, we prefer a small fluctuation to a larger one. When ZXE is large, the current merging process introduces a large amount of information fluctuation and its reliability should be low. From this viewpoint, we apply this measure as a criterion for determining the termination of the merging process which will be given in the next section.", |
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| "section": "Differential Entropy as Termination Condition", |
| "sec_num": "4" |
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| "text": "In this section, we show some results of our preliminary experiments to confirm effectiveness of the proposed techniques. The corpus we used is constructed by EDR and includes nearly 48,000 bracketed, tagged sentences [EDR94] . As mentioned in the previous sections, we focus on only the rules with lexical categories as their right hand side 4. Figure 1 . To evaluate our method, we use the rule tokens which appear more than 500 times in the corpus. Table I gives some characteristics of the corpus. From the 35 initial rules, we calculate the similarity between any two rules (i.e., any rule pair) based on divergence and Bayesian posterior probability (BPP). For the divergence measure, the smaller the vaiue is, the more similar the rule pair is. Inversely, for BPP, the larger the value is, the more similar the pair looks. After calculating all pairs' similarities, we merge the most similar pair (the minimum divergence or the maximum BPP) to a new label and recalculate the similarity of the new label with other remaining labels. The merging process is carried out in an iterative way. Figure 3 shows the minimum divergence (left) and the maximum Bayesian posterior probability (right) of each merge step.", |
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| "text": "Figure 3", |
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| "section": "Preliminary Experimental Results", |
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| "text": "In each iterative step of the merging process, we calculate differential entropy for both cases. The differential entropy of each step equals to the entropy difference between the entropy of two rules before merging and the entropy of a new rule after merging as described in the previous section.", |
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| "section": "For instance, cx --~ (ADJ)(NOUN), e2 --* (ART)(NOUN) and cs --* (PRON)(NOUN) in", |
| "sec_num": null |
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| "text": "4Other types of rules can be acquired in almost the same way and are left now as our further work. Figure 4 indicate the results of differential entropy (LXE calculated by the formula in section 4) when the merging process advanced with divergence and BPP as its similarity measures. There are some sharp peaks indicating the rapid fluctuation of entropy in the graphs. In this work, we use these peaks as a clue to find the timing we should to terminate the merging process. As the result, we halt up the process at the 22nd step and the 27th step for the cases of divergence and BPP, respectively. Table 2 shows the obtained grouping results. In these tables, there axe 13 groups for divergence and 8 groups for Bayesian posterior probability. To clarify the result in the tables, Some sample words of each label axe given in the appendix. Figure 4 : Differential entropy during the merging processes using divergence (left) and BPP (right)", |
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| "section": "For instance, cx --~ (ADJ)(NOUN), e2 --* (ART)(NOUN) and cs --* (PRON)(NOUN) in", |
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| "text": "We also made an experiment to evaluate these results with the solution given by three human evaluators (later called A, B and C) who axe non-natlve but high-educated with more than 20 years of English education. The evaluators were told to construct 7-15 groups from the 35 initial rules, based on the grammatical similarity as they thought. As the result, the evaluators A, B and C classified the rules into 14, 13 and 14 groups, respectively. (NOUN)(NUM), (ADV)(BE), (PRON)(VT) Table 3 . This table model was introduced in [Swe69] and widely used in Information Retrieval and Psychology. In the table, a is the number of the label pairs which an evaiuator assigned in the same group and so did the system, b is the number of the pairs which an evaluator did not assign in the same group but the system did, e is the number of the pairs which an evaluator assigned but the system did not, and d is the number of the pairs which both an evaluator and the system did not assign in the same group. From this table, we define seven measures, as shown below, for evaluating performance of the proposed methods. This evaluation technique was also applied partly for computing \"closeness\" between a system's answer and an evaluator's answer in The F-measure is used as a combined measure of recall and precision, where fl is the weight of recall relative to precision. Here, we use fl = 1.0, which corresponds to equal weighting of the two measures. The results compared with three human evaluators are shown in From these results, we observe some features as follows. The divergence gives a better solution than Bayesian posterior probability does. Normally, the positive measures (PR and PP) have smaller values than the negative ones (NR and NP) do. This means that it is difficult to judge two labels to be in a same group rather than to judge them to be in a separate group. Using divergence as a similarity measure, we get, on average, 84 % positive recall and 67 ~ positive precision and up to 90 ~ and 82 % when considering both positive and negative measures. Even for the worst result(Evaluator B), we can get up to 84 % and 81% for averaged recall and precision. In order to confirm the performance of the system, the evaluators' results axe compared with each other. This comparison is useful for investigating the difficulty of the grouping problem. The comparison result is shown in Table 5 . At this point, we can observe that the label grouping process is a hard problem that may make an evaluator's solution inconsistent with the others' solutions. However, our proposed method seem to give a reconciliation solution between those solutions. Especially, the method which applies divergence as the similarity measure, has a good performance in grouping brackets in the bracketed corpus. We also make an experiment to evaluate whether divergence is a better measure than BPP, and whether the application of differential entropy to cut off the merging process is appropriate. This examination can be held by plotting values of recall, precision and F-measure during each step of merging process. Figure 5 shows the fluctuation of positive recall(PR), positive preclsion(AP), averaged recall(AR), averaged precision and F-measure (FM).", |
| "cite_spans": [], |
| "ref_spans": [ |
| { |
| "start": 480, |
| "end": 487, |
| "text": "Table 3", |
| "ref_id": "TABREF5" |
| }, |
| { |
| "start": 2391, |
| "end": 2398, |
| "text": "Table 5", |
| "ref_id": "TABREF7" |
| }, |
| { |
| "start": 3104, |
| "end": 3112, |
| "text": "Figure 5", |
| "ref_id": "FIGREF7" |
| } |
| ], |
| "eq_spans": [], |
| "section": "For instance, cx --~ (ADJ)(NOUN), e2 --* (ART)(NOUN) and cs --* (PRON)(NOUN) in", |
| "sec_num": null |
| }, |
| { |
| "text": "From the graphs, we found out that the maximum value of F-measure is 0.75 in the case of divergence while it is only 0.65 in the case of BPP. That is, divergence provides a better solution than BPP. Moreover, the 22nd an 25th merge steps were the most suitable points to terminate the merging process for divergence and BPP, respectively. This result is consistent with the grouping result of our system (13 groups) in the case of divergence. Although differential entropy leads us to terminate the merging process at the 27th merge step in the case of BPP, we observe that there is just a little difference between the F-measure value of the 25th merge step and that of the 27th merge step. From this result, we conclude that differential entropy can be used a good measure to predict the cut-off timing of the merging process. ", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "For instance, cx --~ (ADJ)(NOUN), e2 --* (ART)(NOUN) and cs --* (PRON)(NOUN) in", |
| "sec_num": null |
| }, |
| { |
| "text": "There has been an increase of the construction of many types of corpora, including bracketed corpora. In this work, we attempt to use a bracketed (tagged) corpus for grammar inference. Towards the automatic acquisition of a context-free grammar, we proposed some statistical techniques to group brackets in a bracketed corpus (with lexical tags), according to their local contextual information. Two measures, divergence and Bayesian posterior probability, were introduced to express the similarity between two brackets. Merging the most similar bracket pair iteratively, a set of label groups was constructed. To terminate a merging process at appropriate timing, we proposed differential entropy as a measure to represent the entropy difference before and after merging two brackets and stopl~ed the merging process at a large fluctuation. From the experimental results compared with the model solutions given by three human evaluators, we observed that divergence gave a better solution than Bayesian posterior probability. For divergence, we obtained 84 % recall and 67 % precision, and up to 90 ~ and 82 % when considering both positive and negative measures. We also investigated the fitness of using differential entropy for terminating the merging process by way of experiment and confirmed it. In this paper, we focus on only rules with lexical categories as their right hand side. As a further work, we are on the way to introduce the techniques introduced here to acquire the other rules(rules with nonterminal categories as their right hand side). At that time, it is also necessary for us to develop some suitable evaluation techniques for assessing the obtained grammar.", |
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| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Conclusion", |
| "sec_num": "6" |
| }, |
| { |
| "text": "'centimeter' 'percent' '%' 'mm' 'dollar' 'grow' 'delay' 'feed' 'go' 'went' 'gone' ,give' 'gave' 'given'", |
| "cite_spans": [], |
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| "eq_spans": [], |
| "section": "", |
| "sec_num": null |
| } |
| ], |
| "back_matter": [ |
| { |
| "text": "some instances 'specific' 'commercial' 'adequate' 'structural' 'old' 'explicitly' 'enormously' 'quite' 'not' 'the' 'a' 'an' 'may' 'should' 'did' 'could' 'will' 'have' 'be' 'is' 'are' 'and' 'when' 'or' 'this' 'that' 'these' 'such' 'few' 'one' 'any' 'some' 'member' 'Japan' 'merchant' 'tour' 'area' '2' '0.5' '60 billion' 'with' 'in' 'to' 'of' 'I' 'my' 'me' 'your' 'us' 'up' 'to (to V)' 'down' 'out'", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "annex", |
| "sec_num": null |
| } |
| ], |
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| "FIGREF0": { |
| "uris": null, |
| "num": null, |
| "type_str": "figure", |
| "text": "Figure 1. ~In Figure 1, there are three unique labels derived: el---~(ADJ)(NOUN), cc2-*(ART)(NOUN) and cs ~ (PRON)(NOUJV)." |
| }, |
| "FIGREF1": { |
| "uris": null, |
| "num": null, |
| "type_str": "figure", |
| "text": "Figure 2 depicts an example of the grouping process. both, some, any .... } ART ={a, the .... } PRON = { my, his, her, their .... } NOUN = {trip, newspaper .... } ADJ = {high, available .... } Figure 2: A part of the bracket grouping process" |
| }, |
| "FIGREF2": { |
| "uris": null, |
| "num": null, |
| "type_str": "figure", |
| "text": "(g=,g,) = SC(g= )SC(g, ) SC(g) = I~ P(elg) cEg SMaximizing P(GIC ) is a generalization of Mac/mUSh L//cel/hood estimation." |
| }, |
| "FIGREF4": { |
| "uris": null, |
| "num": null, |
| "type_str": "figure", |
| "text": "The minimum divergence (left) and the maximum Bayesian posterior probability (right) of each merge step Two graphs in" |
| }, |
| "FIGREF5": { |
| "uris": null, |
| "num": null, |
| "type_str": "figure", |
| "text": "Averaged Precision (AP) : 2 (fl3-1-1)\u00d7PPxPR \u2022 F-measure (FM) : fla\u00d7PP+PR" |
| }, |
| "FIGREF6": { |
| "uris": null, |
| "num": null, |
| "type_str": "figure", |
| "text": "0,55 0.95 0.96 0.76 0.76 0.56 I, Averaged10\"6110\"61[ 0\"96 [ 0\"96 [ 0\"78 0\"78[0\"61l" |
| }, |
| "FIGREF7": { |
| "uris": null, |
| "num": null, |
| "type_str": "figure", |
| "text": "v'-\"i ............. ! ........................... ! .............. ~ .............. 7 ....... ~-...,...~........\\ ~... ~ ~/ ! ............ ~....,~ ................... ~.....p ......:.,,...w.....~ ............ ~.~ .......... :..,.~.. ............ ~/i'~ ............. P'~: ....... ~i \u0129 { . .............. ~ .............. !--..v---.~.-\u00f7 ........ ~---............. ? ............ I .............. I .............. ! ............. t ...... ........ [ .......... );!~ ........ J ...... i ............ ~:,,::: .......... ~. ............. $.,~,*,::t..~ .............. ~~::~..~[ii:~.,~..~'.~-.~_,.: ..t~.,,.~...~....:~., .......... ~ ............. ~-.......... ~.~::::--/-.~-.------i-.-.-----.:~.-\\-. ~ .,. ~.,,J Recalli i\\\\ i ~.--~\" jPI, Pr~ision~ .... i\\ ......... 7 \" . : : ............. The transition of PR, PP, AR, AP, FM during the merging process using divergence(left) and BPP(right) as the similarity measures" |
| }, |
| "TABREF0": { |
| "content": "<table><tr><td>For example, if (ART)(NOUN)</td></tr><tr><td>and (PRON)(NOUN) are in the same label group, we replace them with a new label (such as</td></tr><tr><td>NP) in the whole corpus.</td></tr><tr><td>6. Repeat (1)-(5) until all brackets(nodes) in the corpus are assigned labels.</td></tr></table>", |
| "text": "2. Calculate the similarity of every pair of the derived labels.3. Merge the most similar pair to a single new label(i.e., a label group) and recalculate the similarity of this new label with other labels.4. Repeat (3) until a termination condition is detected. As the result of this step, a certain set of label groups is derived.5. Replace labels in each label group with a new label in the corpus.", |
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| "content": "<table><tr><td>2.5</td><td/><td/><td/><td/><td/><td/><td/><td/><td/><td/><td/><td/><td/><td/></tr><tr><td/><td/><td>i</td><td/><td/><td/><td>[]</td><td/><td>%</td><td/><td/><td/><td/><td/><td/></tr><tr><td/><td/><td/><td/><td/><td/><td/><td>0.75</td><td/><td/><td/><td/><td/><td/><td/></tr><tr><td>8 ==</td><td/><td/><td/><td/><td/><td/><td>0.5</td><td/><td/><td colspan=\"2\">i ~aGa \"</td><td/><td/><td/></tr><tr><td/><td/><td/><td/><td/><td/><td/><td>I</td><td/><td/><td/><td/><td/><td/><td/></tr><tr><td>0.5</td><td>,</td><td>~</td><td>-\"</td><td>~BE]~</td><td/><td/><td>0.25</td><td/><td/><td/><td/><td/><td/><td/></tr><tr><td>0</td><td>5</td><td>10</td><td/><td>i 20</td><td>25</td><td>30</td><td>| 35</td><td>0</td><td>5</td><td>10</td><td>15</td><td>20</td><td>25</td><td>30</td><td>35</td></tr><tr><td/><td/><td/><td colspan=\"2\">Merge Step</td><td/><td/><td/><td/><td/><td/><td colspan=\"2\">\" Merge Step</td><td/><td/></tr></table>", |
| "text": "Some features of the corpus ............. ' ............. 4 .............. ~ .............. , .............. , .............. ,......: ..... 15 ............................................................ . . . . . . . . . . . ......... . . . . .... 1 ................................................................ ............", |
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| }, |
| "TABREF3": { |
| "content": "<table><tr><td>0.5</td><td/><td>I</td><td/><td/><td/><td/><td/><td>0.2</td><td/><td>i</td><td/><td/><td/><td/><td/><td/></tr><tr><td>0.4 O.3 o.e</td><td/><td/><td/><td/><td/><td/><td/><td colspan=\"2\">0.15 /</td><td>i</td><td/><td/><td/><td>/</td><td/><td/></tr><tr><td>0.1</td><td/><td/><td/><td/><td/><td/><td/><td/><td/><td/><td/><td/><td/><td/><td/><td/></tr><tr><td>0</td><td>0</td><td>5</td><td>10</td><td>15</td><td>20</td><td>25</td><td>30</td><td>35</td><td>0</td><td>5</td><td>10</td><td>15</td><td>20</td><td>25</td><td>30</td><td>35</td></tr><tr><td/><td/><td/><td/><td colspan=\"2\">Merge Step</td><td/><td/><td/><td/><td/><td/><td colspan=\"2\">Merge Step</td><td/><td/><td/></tr></table>", |
| "text": "............. \"; .................................................................... ~'\"'\"J .....", |
| "type_str": "table", |
| "html": null, |
| "num": null |
| }, |
| "TABREF4": { |
| "content": "<table><tr><td/><td colspan=\"2\">The Evaluator's Answer</td></tr><tr><td/><td>Yes '</td><td>No</td></tr><tr><td>The system says Yes</td><td>a</td><td>b</td></tr><tr><td>The system says No</td><td>e</td><td>d</td></tr></table>", |
| "text": "The grouping result using divergence (left) and BPP (fight)", |
| "type_str": "table", |
| "html": null, |
| "num": null |
| }, |
| "TABREF5": { |
| "content": "<table/>", |
| "text": "The number of entry pairs for evaluating accuracy To evaluate the system with the model solutions, we applied a contingency table model as one shown in", |
| "type_str": "table", |
| "html": null, |
| "num": null |
| }, |
| "TABREF6": { |
| "content": "<table><tr><td/><td>Similaxity</td><td/><td/><td>Measures</td><td/></tr><tr><td/><td/><td>PR I PP</td><td>NR</td><td>NP</td><td>AR</td><td>AP</td><td>FM</td></tr><tr><td>Evaluator A</td><td colspan=\"6\">Divergence 0.91 i 0.70 0.96 0.99 0.93 0.84 0.79</td></tr><tr><td/><td>BPP</td><td colspan=\"5\">0.63 i 0.46 0.92 0.96 0.77 0.71 0.53</td></tr><tr><td>Evaluator B</td><td colspan=\"6\">Divergence 0.73 i 0.66 0.95 0.97 0.84 0.81 0.69</td></tr><tr><td/><td>BPP</td><td colspan=\"5\">0.68 i 0.59 0.94 0.96 0.81 0.78 0.63</td></tr><tr><td>Evaluator C</td><td colspan=\"6\">Divergence 0.89 i 0.66 0.95 0.99 0.92 0.82 0.76</td></tr><tr><td/><td>BPP</td><td colspan=\"5\">0.80 0.57 0.94 0.98 0.87 0.77 0.66</td></tr><tr><td>Averaged</td><td colspan=\"6\">Divergence 0.84 0.67 0.95 0.98 0.90 0.82 0.75</td></tr><tr><td/><td>BPP</td><td colspan=\"2\">0.70 0.54 0.93</td><td colspan=\"3\">0.971 0.82 0.75 0.61</td></tr><tr><td colspan=\"7\">Table 4: Eva~luation results using three human eva~uators' solutions</td></tr></table>", |
| "text": "", |
| "type_str": "table", |
| "html": null, |
| "num": null |
| }, |
| "TABREF7": { |
| "content": "<table/>", |
| "text": "Comparing the grouping results obtained by the evaluators(A,B,C)", |
| "type_str": "table", |
| "html": null, |
| "num": null |
| } |
| } |
| } |
| } |
