| { |
| "paper_id": "W94-0107", |
| "header": { |
| "generated_with": "S2ORC 1.0.0", |
| "date_generated": "2023-01-19T04:46:53.170587Z" |
| }, |
| "title": "Complexity of Description of Primitives: Relevance to Local Statistical Computations", |
| "authors": [ |
| { |
| "first": "Aravind", |
| "middle": [ |
| "K" |
| ], |
| "last": "Joshi", |
| "suffix": "", |
| "affiliation": { |
| "laboratory": "", |
| "institution": "University of Pennsylvania Philadelphia", |
| "location": { |
| "postCode": "19104", |
| "region": "PA", |
| "country": "USA" |
| } |
| }, |
| "email": "joshi@linc.cis.upenn.edu" |
| }, |
| { |
| "first": "B", |
| "middle": [], |
| "last": "Srinivas", |
| "suffix": "", |
| "affiliation": { |
| "laboratory": "", |
| "institution": "University of Pennsylvania Philadelphia", |
| "location": { |
| "postCode": "19104", |
| "region": "PA", |
| "country": "USA" |
| } |
| }, |
| "email": "" |
| } |
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| "year": "", |
| "venue": null, |
| "identifiers": {}, |
| "abstract": "", |
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| "paper_id": "W94-0107", |
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| "abstract": [], |
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| "text": "In this paper we pursue the idea that by making the descriptions of primitive items (lexical items in the linguistic context) more complex, we can make the computation of linguistic structure more local 1. The idea is that by making the descriptions of primitives more complex, we can not only make more complex constraints operate more locally but also verify these constraints more locally. Statistical techniques work better when such localities are taken into account 2 Of course, there is a price for making the descriptions of primitives more complex. The number of different descriptions for each primitive item is now much larger than when the descriptions are less complex. For example, in a lexicalized tree-adjoining grammar (LTAG), the number of trees associated with each lexical item is much larger than the number of standard parts-of-speech (POS) associated with that item. Even when the POS ambiguity is removed the number of LTAG trees associated with each item can be large, on the order of 10 trees in the current English grammar in the XTAG system s. This is because in LTAG, roughly speaking, each lexical item 1 Let ~ be the alphabet consisting of the names of elmentary trees in an LTAG. Then ~* is the set of all strings over this alphabet including the null string. The tree 71 and 7~ in a string of tree names axe said to be ~*-local if they are separated by any string in ~*. For brevity, we will continue to use the term local instead of the term ~*-local.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Introduction", |
| "sec_num": null |
| }, |
| { |
| "text": "2The work described here is completely different from the work reported in (Resnik, 1992) and (Schabes, 1992) concerning stochastic TAGs.", |
| "cite_spans": [ |
| { |
| "start": 75, |
| "end": 89, |
| "text": "(Resnik, 1992)", |
| "ref_id": "BIBREF1" |
| }, |
| { |
| "start": 94, |
| "end": 109, |
| "text": "(Schabes, 1992)", |
| "ref_id": "BIBREF4" |
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| ], |
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| "section": "Introduction", |
| "sec_num": null |
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| { |
| "text": "3See Section on Data Collection is associated with as many trees as the numb~,r of different syntactic contexts in which the iexical item can appear. This, of course, increases the local ambiguil.y for the parser. The parser has to decide which complex description (LTAG tree) out of the set of descriptions associated with each lexical item is to be used for a given reading of a sentence, even before combining the descriptions together. The obvious solution is to put the burden of this job entirely on the parser. The parser will eventually disambiguate all the descriptions and pick one per object, for a given reading of the sentence. This is what the parser is expected to do for disambiguating the standard POS, unless a separate POS disambiguation module is used (Church, 1988) . Many parsers, including XTAG, use such a module ('alh'd a POS tagger.", |
| "cite_spans": [ |
| { |
| "start": 772, |
| "end": 786, |
| "text": "(Church, 1988)", |
| "ref_id": "BIBREF0" |
| } |
| ], |
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| "eq_spans": [], |
| "section": "Introduction", |
| "sec_num": null |
| }, |
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| "text": "LTAGs present a novel opportunity to reduce the amount of disambiguation done by the parser. We can treat the LTAG trees associated with each lexic'al item as more complex parts-of-speech which we call supertags. In this paper, we report on some experiments on direct supertag disambiguation, without parsing in the strict sense, using lexical preference and local lexical dependencies (acquired from a corpus parsed by the XTAG system). The information extracted from the XTAG-parsed corpus contains, for each item and its supertag, a probability distribution of the distances of other items and their supertags that are expectcd by it.. We have devised a method somewhat akin to tile stare dard POS tagger that disambiguates supertags without doing any parsing.", |
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| "section": "Introduction", |
| "sec_num": null |
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| "text": "'File idea of using complex descriptions for primitives to capture constraints locally has some precursors in AI. For example, the Waltz algorithm (Waltz, 1975) for la-I)eling vertices of polygonal solid objects can be thought of in these terms, although it is not usually described in this way. There is no statistical computations in the Waltz algorithm, however. The supertag disambiguation experiments, as far as we know, are the first to use these ideas in the linguistic context. Of course, we :ds(~ show how the supertag disambiguation naturally lends itself to the application of statistical techniques. I1, tl,, lbllowing sections we will briefly describe our approach and some preliminary results of supertag disambiguation as an illustration of our main theme: the relationship of the complexity of descriptions of primitives to local statistical computations. A more complete analysis of this technique and experimental results will eventually be reported elsewhere.", |
| "cite_spans": [ |
| { |
| "start": 147, |
| "end": 160, |
| "text": "(Waltz, 1975)", |
| "ref_id": "BIBREF5" |
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| "section": "Introduction", |
| "sec_num": null |
| }, |
| { |
| "text": "l,exicalized Tree Adjoining Grammar (LTAG) is a lexicalized tree rewriting grammar formalism (Schabes, 1990) . The primary structures of LTAG are called EL-EMEN'FARY TREES. Each elementary tree has a lexical item (anchor) on its frontier and serves as a com-plt~x description of the anchor. An elementary tree provides a domain of locality larger than that provided by CFG rules over which syntactic and semantic (predicate-argument) constraints can be specified. Elementary trees are of two kinds: INITIAL TREES and AUXI,,IARY TREES. Examples of initial trees (as) and ~u]xi[iary trees (,Ss) are shown in Figure 1 . Nodes on th(. frontier of initial trees are marked as substitution sites by a '~', while exactly one node on the frontier ~)[\" an auxiliary tree, whose label matches the label of the root of the tree, is marked as a foot node by a '.'. 'l'hv other nodes on the frontier of an auxiliary tree are marked as substitution sites. LTAG factors out recursi()n f,-om the statement of the syntactic dependencies. Eh,n,,,,,tary tr~,es (initial and auxiliary) are the domain I;,r sp,,cifying dependencies. Recursion is specified via i,h~\" auxiliary trees. ", |
| "cite_spans": [ |
| { |
| "start": 93, |
| "end": 108, |
| "text": "(Schabes, 1990)", |
| "ref_id": "BIBREF3" |
| } |
| ], |
| "ref_spans": [ |
| { |
| "start": 606, |
| "end": 614, |
| "text": "Figure 1", |
| "ref_id": null |
| } |
| ], |
| "eq_spans": [], |
| "section": "Lexicalized Tree Adjoining Grammars", |
| "sec_num": null |
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| "text": "As a result of localization in LTAG, a lexical item may be associated with more than one supertag. The example in Figure 3 illustrates the initial set of supertags a.,~sigm~d to each word of the sentence John saw a man with the telescope. The order of the supertags for each h'xi~'al item in tile example is completely irrelevant.", |
| "cite_spans": [], |
| "ref_spans": [ |
| { |
| "start": 114, |
| "end": 122, |
| "text": "Figure 3", |
| "ref_id": "FIGREF1" |
| } |
| ], |
| "eq_spans": [], |
| "section": "Example of Supertagging", |
| "sec_num": null |
| }, |
| { |
| "text": "I\"iglire 3 also shows the final supertag sequence assigned I,y the s.pertagger, which picks the best supertag seq.,,mlce .sing statistical information (described in the v.,,x! s,,cl.i(m) ahout individual supertags and their dep,'mh'm:i~s on other supertags. The chosen supertags axe combined to derive a parse, as explained in the previous section. The parser without the supertagger would have to process combinations of the entire set of 28 trees; the parser with it need only process combinations of 7 trees.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Example of Supertagging", |
| "sec_num": null |
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| "text": "One might think that a n-gram model of standard POS tagging would be applicable to supertagging as well. However, in the n-gram model for standard POS tagging, dependencies between parts-of-speech of words that appear beyond the n-word window cannot be incorporated into the model. This limitation does not have ", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Dependency model of Supertagging", |
| "sec_num": null |
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| "text": "(1) shows the data required for the dependency model of supertag disambiguation. Ideally each entry would be indexed by a (word, supertag) pair but, due to sparseness of data, we have backed-off to a (POS, supertag) pair. Each entry contains the following information.", |
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| "eq_spans": [], |
| "section": "Table", |
| "sec_num": null |
| }, |
| { |
| "text": "\u2022 POS and Supertag pair.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Table", |
| "sec_num": null |
| }, |
| { |
| "text": "\u2022 List of + and -, representing the direction of the dependent supertags with respect to the indexed supertag. (Size of this list indicates the total number of dependent supertags required.)", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Table", |
| "sec_num": null |
| }, |
| { |
| "text": "\u2022 Dependent supertag.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Table", |
| "sec_num": null |
| }, |
| { |
| "text": "\u2022 Signed number representing the direction and the ordinal position of the particular dependent supertag mentioned in the entry from the position of the indexed supertag.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Table", |
| "sec_num": null |
| }, |
| { |
| "text": "\u2022 A probability of occurrence of such a dependency. The sum probability over all the dependent supcrt:ags at all ordinal positions in the same direction is one.", |
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| "eq_spans": [], |
| "section": "Table", |
| "sec_num": null |
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| { |
| "text": "For example, the fourth entry in the Table 1 reads that the tree a2, anchored by a verb (V), has a left, and a right dependent (-, +) and the first word to the left (-1) with the tree as serves as a dependent of the current word. The strength of this association is represented by the probabilit3/0.300.", |
| "cite_spans": [], |
| "ref_spans": [ |
| { |
| "start": 37, |
| "end": 44, |
| "text": "Table 1", |
| "ref_id": "TABREF1" |
| } |
| ], |
| "eq_spans": [], |
| "section": "Table", |
| "sec_num": null |
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| "text": "The dependency model of disambiguation works as follows. Suppose a2 is a member of the set of supertags associated with a word at position n in the sentence. The algorithm proceeds to satis|~ the dependency requirement of a2 by picking up the dependency entries for each of the directions. It picks a dependency data entry (fourth entry, say) from the database that is indexed by a2 and proceeds to sct up a path with the first word to the left that has the dependent supertag (as) as a member of its set of supertags. If the first. word that has as as a member of its set of supertags is at position m, then an arc is set up between c~ and as.. Also, the arc is verified so that it does not kitestring-tangle s with any other arcs in the path up to a2. The path probability up to a2 is incremcntcd by log0.300 to reflect the success of the match. The path probability up to as incorporates the unigram probability of as. On the other hand, if no word is found that has as as a member of its set of supertags then the entry is ignored. A successflH supertag sequence is one which assigns a supertag to each position such that STwo arcs (a,c) and (b,d) ,'m'h supertag has all of its dependents and maximizes the accumulated path probability. The direction of the dcp~mdcmt supertag and the probability information are us\u00a2.,d t.o prune the search. A more detailed and formal description of this algorithm will appear elsewhere. \"l'l/t. implementation and testing of this model of su-I,,'rl.ag disanlbiguation is underway. Preliminary experilm,ld.s oil short fragments show a success rate of 88% i.e.a, sequence of correct supertags is assigned.", |
| "cite_spans": [ |
| { |
| "start": 1146, |
| "end": 1151, |
| "text": "(b,d)", |
| "ref_id": null |
| } |
| ], |
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| "eq_spans": [], |
| "section": "Table", |
| "sec_num": null |
| }, |
| { |
| "text": "The data needed for disambiguating supertags (Sect.ion ) have been collected by parsing the Wall Street Journal s. IBM-manual and ATIS corpora using the wide-cow:rag c English grammar being developed as part of the XTAG system (XTAG Tech. Report, 1994) . The parses generated for these sentences are not sub-.iectcd to any kind of filtering or selection. All the derivation structures are used in the collection of the sta.l.istics.", |
| "cite_spans": [ |
| { |
| "start": 227, |
| "end": 252, |
| "text": "(XTAG Tech. Report, 1994)", |
| "ref_id": null |
| } |
| ], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Data Collection", |
| "sec_num": null |
| }, |
| { |
| "text": "XTAG is a large ongoing project to develop a widecov,.rage grammar for English, based on the LTAG forrealism. It also serves as an LTAG grammar develolnuent system and includes a predictive left-to-right parser, a morphological analyzer and a POS tagger. The wide-coverage English grammar of the XTAG syst,.m contains 317,000 inflected items in the morphology (21;L000 h~r nouns amt 46,500 for verbs among others) and 37,00(I eul.ries in the syntactic lexicon. The syntactic h,xicon associates words with the trees that they an-,'l,,r. There arc 385 l.rt'cs in all, in the grammar which is ,',,,Ul,.scd of 411 dilG'rcut sul~catcgorization frames.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Data Collection", |
| "sec_num": null |
| }, |
| { |
| "text": "'~S~.ntuuces of length <_ 15 words.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Data Collection", |
| "sec_num": null |
| }, |
| { |
| "text": "Each word in the syntactic lexicon, on the average, depending on the standard POS of the word, is an anchor for about 8 to 40 elementary trees.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Data Collection", |
| "sec_num": null |
| }, |
| { |
| "text": "In this paper we have shown that increasing the complexity of descriptions of primitive objects, lexical items in the linguistic context, enables more complex constraints to be applied locally. However, increasing the complexity of descriptions greatly increases the number of such descriptions for the primitive object. In a lexicalized grammar such as LTAG each lexical item is associated with complex descriptions (supertags) on the average of 10 descriptions. A parser for LTAG, given a sentence, disambiguates a large set of supertags to select one supertag for each lexical item before combining them to derive a parse of the sentence. We have presented a new technique that performs the disambiguation of supertags using local information such as lexical preference and local lexical dependencies as an illustration of our main theme of the relationship of complexity of descriptions of primitives to local statistical computations. This technique, like POS disambiguation, reduces the disambiguation task that needs to be done by the parser. After the disambiguation, we have effectively completed the parse of the sentence and the parser needs 'only' to complete the adjunctions and substitutions.", |
| "cite_spans": [], |
| "ref_spans": [], |
| "eq_spans": [], |
| "section": "Conclusion", |
| "sec_num": null |
| } |
| ], |
| "back_matter": [], |
| "bib_entries": { |
| "BIBREF0": { |
| "ref_id": "b0", |
| "title": "A Stochastic Parts Program and Nouu Phrase Parser lbr Unrestricted Text", |
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| "last": "Church", |
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| "venue": "gnd Applied Natural Language Processing Conference", |
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| "title": "Mathematical and Computational Aspects of Lexicalized Grammars", |
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| "ref_entries": { |
| "FIGREF0": { |
| "type_str": "figure", |
| "text": "Hcm('nt.ary trees are combined by Substitution and Adjuncti,)n operations. Substitution inserts elemenl;iry I.i',.,~s at the substitution nodes of other elementary trees. Adjunction inserts auxiliary trees into elementary trees at the node whose label is the same as the root label of the auxiliary tree. As an example, the component trees ( as, c~2, aa, c~4,/38, as, as), shown inFigure 1can be combined to form the parse tree for the sentence John saw a man with the telescope 4 as follows:1. ors substitutes at the NP0 node in a2.2. aa substitutes at the DetP node in c~4, the result ofwhich is substituted at the NP1 node in c~.3. a5 substitutes at the DetP node in as, the result of which is substituted at the NP node in/3s.4.The result of step (3) above adjoins to the VP node of the result of step (2). The resulting parse tree is shown inFigure 2.The process of combining the elementary trees that yield a parse of the sentence is represented by the derivation tree, shown inFigure 2. The nodes of the derivation tree are the tree names that are anchored by the appropriate lexical item. The composition operation is indicated by the nature of the arcs-broken line for substitution and bold line for adjunction-while the address of the operation is indicated as part of the node label. The derivation tree can also be interpreted as a dependency graph with unlabeled arcs between words of the sentence as shown inFigure 2.We will call the elementary trees associated with each lexical item super part-of-speech tags or supertags.4The parse with the PP attached to the NP has not been shown.", |
| "uris": null, |
| "num": null |
| }, |
| "FIGREF1": { |
| "type_str": "figure", |
| "text": "Supertag Assignment for John saw a man with the telescope a significant effect on the performance of a standard trigram POS tagger, since it is rare for dependencies to occur between POS tags beyond a three-word window. However, since dependencies between supertags do not occur in a fixed sized window, the n-gram model is unsuitable for supertagging. This limitation can be overcome if no a priori bound is set on the size of the window, but instead a probability distribution of the distances of the dependent supertags for each supertag is maintained. A supertag is dependent on another supertag if the former substitutes or adjoins into the later.", |
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| "FIGREF2": { |
| "type_str": "figure", |
| "text": "kite-string-tangle if a < b < c<dorb<a<d<c.", |
| "uris": null, |
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| "TABREF1": { |
| "html": null, |
| "text": "Dependency Data", |
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