{ "paper_id": "J96-2001", "header": { "generated_with": "S2ORC 1.0.0", "date_generated": "2023-01-19T02:16:42.362375Z" }, "title": "Estimating Lexical Priors for Low-Frequency Morphologically Ambiguous Forms", "authors": [ { "first": "Harald", "middle": [], "last": "Baayen", "suffix": "", "affiliation": {}, "email": "baayen@mpi.nl" }, { "first": "Richard", "middle": [], "last": "Sproat", "suffix": "", "affiliation": {}, "email": "" } ], "year": "", "venue": null, "identifiers": {}, "abstract": "Given a form that is previously unseen in a sufficiently large training corpus, and that is morphologically n-ways ambiguous (serves n different lexical functions) what is the best estimator for the lexical prior probabilities for the various functions of the form? We argue that the best estimator is provided by computing the relative frequencies of the various functions among the hapax legomena-the forms that occur exactly once in a corpus; in particular, a hapax-based estimator is better than one based on the proportion of the various functions among words of all frequency ranges. As we shall argue, this is because when one computes an overall measure, one is including high-frequency words, and high-frequency words tend to have idiosyncratic properties that are not at all representative of the much larger mass of(productively formed) low-frequency words. This result has potential importance for various kinds of applications requiring lexical disambiguation, including, in particular, stochastic taggers. This is especially true when some initial hand-tagging of a corpus is required:for predicting lexical priors for very low-frequer~cy morphologically ambiguous types (most of which would not occur in any given corpus), one should concentrate on tagging a good representative sample of the hapax legomena, rather than extensively tagging words of all frequency ranges.", "pdf_parse": { "paper_id": "J96-2001", "_pdf_hash": "", "abstract": [ { "text": "Given a form that is previously unseen in a sufficiently large training corpus, and that is morphologically n-ways ambiguous (serves n different lexical functions) what is the best estimator for the lexical prior probabilities for the various functions of the form? We argue that the best estimator is provided by computing the relative frequencies of the various functions among the hapax legomena-the forms that occur exactly once in a corpus; in particular, a hapax-based estimator is better than one based on the proportion of the various functions among words of all frequency ranges. As we shall argue, this is because when one computes an overall measure, one is including high-frequency words, and high-frequency words tend to have idiosyncratic properties that are not at all representative of the much larger mass of(productively formed) low-frequency words. This result has potential importance for various kinds of applications requiring lexical disambiguation, including, in particular, stochastic taggers. This is especially true when some initial hand-tagging of a corpus is required:for predicting lexical priors for very low-frequer~cy morphologically ambiguous types (most of which would not occur in any given corpus), one should concentrate on tagging a good representative sample of the hapax legomena, rather than extensively tagging words of all frequency ranges.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Abstract", "sec_num": null } ], "body_text": [ { "text": "As a number of writers on morphology have noted (most recently and notably Beard [1995] ), it is common to find that a particular affix or other morphological marker serves more than one function in a language. For example, in many morphologically complex languages it is often the case that several slots in a paradigm are filled with the same form; put in another way, it is common to find that a particular morphological form is in fact ambiguous between several distinct functions. This phenomenon-which in the domain of inflectional morphology is termed syncretism---can be illustrated by a Dutch example such as lopen 'walk', which can either be the infinitive form ('to walk') or the finite plural (present tense) form ('we, you, or they walk'). In some cases, syncretism is completely systematic: for example the case cited in Dutch, where the -en suffix can always function in the two ways cited; or in Latin, where the plural dative and ablative forms of nouns and adjectives are always identical, no matter what paradigm the noun belongs to. In other cases, a particular instance of syncretism may be displayed only in some paradigms: for example, Russian feminine norms, such as loshad' 'horse' (Cyrillic aoma~b), have the same form for both the genitive singular --loshadi (Cyrillic aoma~i4) --and the nominative plural, whereas masculine nouns typically distinguish these forms. In still other cases, the syncretism may be partial in that two forms may be identical at one level of representation --say, orthography -but not another --say, pronunciation. For example the written form goroda in Russian (Cyrillic ropo~a) may either be the nominative plural or the genitive singular of 'city'. In the genitive singular, the stress is on the first syllable (/g%rodA/), whereas in the nominative plural the stress resides on the final syllable (/gorAd~a/); note that the difference in stress results in very different vowel qualities for the two forms, as indicated in the phonetic transcriptions.", "cite_spans": [ { "start": 75, "end": 87, "text": "Beard [1995]", "ref_id": "BIBREF4" } ], "ref_spans": [], "eq_spans": [], "section": "Introduction", "sec_num": "1." }, { "text": "Syncretism and related morphological ambiguities present a problem for many NL applications where lexical disambiguation is important; cases where the orthographic form is identical but the pronunciations of the various functions differ are particularly important for speech applications, such as text-to-speech, since appropriate word pronunciations must be computed from orthographic forms that underspecify the necessary information. Ideally one would like to build models that use contextual information to perform lexical disambiguation (Yarowsky 1992 (Yarowsky , 1994 , but such models must be trained on specialized tagged corpora (either hand-generated or semi-automatically generated) and such training corpora are often not available, at least in the early phases of constructing a particular application. Lacking good contextual models, one is forced to fall back on estimates of the lexical prior probabilities for the various functions of a form. Following standard terminology, a lexical prior can be defined as follows: Imagine that a given form is n-ways ambiguous; the lexical prior probability of sense i of this form is simply the probability of sense i independent of the context in which the particular instantiation of the form occurs. Assuming one has a tagged corpus, one can usually get reasonable estimates of the lexical priors for the frequent forms (such as Dutch lopen 'walk') by simply counting the number of times the form occurs in each of its various functions and dividing by the total number of instances of the form (in any function). This yields the Maximum Likelihood Estimate (MLE) for the lexical prior probability. But for infrequent or unseen forms, it is less clear how to compute the estimate. Consider another Dutch example like aanlokken 'entice, appeal'. This form occurs only once, as an infinitive, in the Uit den Boogaart (henceforth UdB) corpus (Uit den Boogaart 1975); in other words it is a hapax legomenon (< Greek hapax 'once', legomenon 'said') in this corpus. Obviously the lexical prior probability of this form expressing the finite plural is not zero, the MLE is a poor estimate in such cases. When one considers forms that do not occur in the training corpus (e.g., bedraden 'to wire') the situation is even worse. The problem, then, is to provide a more reasonable estimate of the relative probabilities of the various potential functions of such forms. 1", "cite_spans": [ { "start": 542, "end": 556, "text": "(Yarowsky 1992", "ref_id": "BIBREF11" }, { "start": 557, "end": 573, "text": "(Yarowsky , 1994", "ref_id": "BIBREF12" } ], "ref_spans": [], "eq_spans": [], "section": "Introduction", "sec_num": "1." }, { "text": "For a common form such as lopen 'walk' a reasonable estimate of the lexical prior probabilities is the MLE, computed over all occurrences of this form. So, in the UdB corpus, lopen occurs 92 times as an infinitive and 43 times as a finite plural, so the MLE Relative frequency of Dutch infinitives versus finite plurals in the Uit den Boogaart corpus, as a function of the (natural) log of the frequency of the word forms. The horizontal solid line represents the overall MLE, the relative frequency of the infinitive as computed over all tokens; the horizontal dashed line represents the relative frequency of the infinitive among the hapax legomena. The solid curve represents a locally weighted regression smoothing (Cleveland 1979 ).", "cite_spans": [ { "start": 719, "end": 734, "text": "(Cleveland 1979", "ref_id": "BIBREF6" } ], "ref_spans": [], "eq_spans": [], "section": "Estimating the Lexical Priors for Rare Forms", "sec_num": "2." }, { "text": "estimate of the probability of the infinitive is 0.68. For low-frequency forms such as aanlokken or bedraden, one might consider basing the MLE on the aggregate counts of all ambiguous forms in the corpus. In the UdB corpus, there are 21,703 infinitive tokens, and 9,922 finite plural tokens, so the MLE for aanlokken being an infinitive would be 0.69. Note, however, that the application of this overall MLE presupposes that the relative frequencies of the various functions of a particular form are independent of the frequency of the form itself. For the Dutch example at hand, this presupposition predicts that if we were to classify -en forms according to their frequency, and then for each frequency class thus defined, plot the relative frequency of infinitives and finite plurals, the regression line should have a slope of approximately zero. Figure 1 shows that this prediction is not borne out. This scatterplot shows the relative frequency of the infinitive versus the finite plural, as a function of the log-frequency of the -en form. At the left-hand edge of the graph, the relative frequency of the infinitives for the hapax legomena is shown. This proportion is also highlighted by the dashed horizontal line. As we proceed to the right, we observe that there is a general downward curvature representing a lowering of the proportion of infinitives for the higher-frequency words. This trend is captured by the solid nonparametric regression line; an explanation for this trend will be forthcoming in Section 3. (It will be noted that in Figure 1 the variance is fairly small for the lower-frequency ranges, higher for the middle ranges, and then small again for the high-frequency ranges; anticipating somewhat, we note the same trends in Figures 2 and 3 . This variance pattern follows from the high variability in the absolute numbers of types realized, especially in the middle log-frequency classes, in combination with the assumption that for any log-frequency class, the proportion for that class is itself a random variable.) The solid horizontal line represents the proportion of infinitives calculated over all frequency classes, and the dashed horizontal line represents the proportion of infinitives calculated over just the hapax legomena. The two horizontal lines can be interpreted as MLEs for the probability of an -en form being an infinitive: the solid line or overall MLE clearly provides an estimate based on the whole population, whereas the dashed line or hapax-based MLE provides an estimate for the hapaxes. The overall MLE computes a lower relative frequency for the infinitives, compared to the hapax-based MLE. The question, then, is: Which of these MLEs provides a better estimate for low-frequency types? In particular, for types that have not been seen in the training corpus, and for which we therefore have no direct estimate of the word-specific prior probabilities, we would like to know whether the hapax-based or overall MLE provides a better estimate.", "cite_spans": [], "ref_spans": [ { "start": 852, "end": 860, "text": "Figure 1", "ref_id": null }, { "start": 1554, "end": 1562, "text": "Figure 1", "ref_id": null }, { "start": 1756, "end": 1771, "text": "Figures 2 and 3", "ref_id": "FIGREF2" } ], "eq_spans": [], "section": "Estimating the Lexical Priors for Rare Forms", "sec_num": "2." }, { "text": "To answer this question we compared the accuracy of the overall and hapax-based MLEs using tenfold cross-validation. We first randomized the list of -en tokens from the UdB corpus, then divided the randomized list into ten equal-sized parts. Each of the ten parts was held out as the test set, and the remaining nine-tenths was used as the training set over which the two MLE estimates were computed. The results are shown in Table 1 . In this table, No(inf) and No(pl) represent the observed number of tokens of infinitives and plurals in the held-out portion of the data, representing types that had not been seen in the training data. The final four rows compare the estimates for these numbers of tokens given the overall MLE (EoINo (infl] and Eo[No(pl) ]), versus the hapax-based MLE (Eh[No(inf)] and Eh[No(pl)] ). For all ten runs, the hapax-based MLE is clearly a far better predictor than the overall MLE. 2", "cite_spans": [ { "start": 451, "end": 458, "text": "No(inf)", "ref_id": null }, { "start": 737, "end": 743, "text": "(infl]", "ref_id": null }, { "start": 748, "end": 757, "text": "Eo[No(pl)", "ref_id": null }, { "start": 789, "end": 801, "text": "(Eh[No(inf)]", "ref_id": null }, { "start": 806, "end": 816, "text": "Eh[No(pl)]", "ref_id": null } ], "ref_spans": [ { "start": 426, "end": 433, "text": "Table 1", "ref_id": null } ], "eq_spans": [], "section": "Dutch Verb Forms in -en", "sec_num": "2.1" }, { "text": "The pattern that we have observed for the Dutch infinitive-plural ambiguity can be replicated for other cases of morphological ambiguity. Consider the case of English verbs ending in -ed, which are systematically ambiguous between being simple past tenses and past participles. The upper panel of Figure 2 shows the distribution of the relative frequencies of the two functions, plotted against the natural log of the frequency for the Brown corpus (Francis and Kucera 1982) . (All lines, including the nonparametric regression line are interpretable as in Figure 1 .) Results of a tenfold cross-validation are shown in Table 2 . Clearly, in this case the magnitude of the difference between the overall MLE and the hapax-based MLE is smaller than in the previous example: indeed in cross validations 6, 8, and 9, the overall MLE is superior. Nonetheless, the hapax-based MLE remains a significantly better predictor overall. 3 Table 1 Results of tenfold cross-validation for Dutch -en verb forms from the Uit den Boogaart corpus. Columns represent different cross-validation runs. N(inf) and N(pl) are the number of tokens of the infinitives and finite plurals, respectively, in the training set. N1 (in J9 and N1 (pl) are the number of tokens of the infinitives and finite plurals, respectively, among the hapaxes in the training set. OMLE and HMLE are, respectively, the overall and hapax-based MLEs. No (inf) and No(pl) denote the number of tokens in the held-out portion that have not been observed in the training set. The expected numbers of tokens of infinitives and plurals for types unseen in the training set, using the overall MLE are denoted as Eo[No(inf) ", "cite_spans": [ { "start": 449, "end": 474, "text": "(Francis and Kucera 1982)", "ref_id": "BIBREF7" }, { "start": 1082, "end": 1088, "text": "N(inf)", "ref_id": null }, { "start": 1407, "end": 1412, "text": "(inf)", "ref_id": null }, { "start": 1658, "end": 1668, "text": "Eo[No(inf)", "ref_id": null } ], "ref_spans": [ { "start": 297, "end": 305, "text": "Figure 2", "ref_id": "FIGREF2" }, { "start": 557, "end": 565, "text": "Figure 1", "ref_id": null }, { "start": 620, "end": 627, "text": "Table 2", "ref_id": "TABREF1" }, { "start": 928, "end": 935, "text": "Table 1", "ref_id": null } ], "eq_spans": [], "section": "English Verb Forms in -ed", "sec_num": "2.2" }, { "text": "In the two examples we have just considered, the hapax-based MLE, while being a better predictor of the a priori lexical probability for unseen cases than the overall MLE, does not actually yield a different prediction as to which function of a form is more likely. This does not hold generally, however, and the bottom panel of Figure 2 presents a case where the hapax-based MLE does yield a different prediction as to which function is more likely. In this plot we consider Dutch word forms from the UdB corpus ending in -en. As we have seen, Dutch -en is used as a verb marker: it marks the infinitive, present plural, and for strong verbs, also the past plural; it is also used as a marker of noun plurals. The case of noun plurals is somewhat different from the preceding two cases since it is not, strictly speaking, a case of morphological syncretism. However, it is a potential source of ambiguity in text analysis, since a low frequency form in -en, where one may not have seen the stem of the word, could potentially be either a noun or a verb. Also, systematic ambiguity exists among cases of noun-verb conversion: for examplefluiten is either a noun meaning 'flutes' or a verb meaning 'to play the flute'; spelden means either 'pins' or 'to pin'; and ploegen means either 'ploughs' or 'to plough'. Results for a tenfold cross-validation for these data are shown in Table 3 . 4 Lrl this case, the overall MLE would lead one to predict that for an unseen form in -en, the verbal function would be more likely. Contrariwise, the hapax-based MLE predicts that the nominal function would be more likely. Again, it is the hapax-based MLE that proves to be superior. Table 3 Cross-validation statistics for Dutch verbs in -en versus plural nouns in -en. ", "cite_spans": [], "ref_spans": [ { "start": 329, "end": 337, "text": "Figure 2", "ref_id": "FIGREF2" }, { "start": 1377, "end": 1384, "text": "Table 3", "ref_id": null }, { "start": 1672, "end": 1679, "text": "Table 3", "ref_id": null } ], "eq_spans": [], "section": "Dutch Words in -en: A More General Problem", "sec_num": "2.3" }, { "text": "One final example--also not a case of syncretism--concerns the ambiguity of the sequence -er in Dutch, which occurs word-finally in monomorphemic nouns (moeder, 'mother'), adjectives (donker, 'dark'), and proper names (Pieter, 'Peter'), but which is also used as a suffix to form comparatives (sneller, 'faster') and \"agentive\" nouns (schrijver, 'writer'). Since monomorphemic nouns and adjectives in this class are mostly disyllabic, we will restrict our attention to the disyllabic instances of words ending in -er. Again we find that the hapax-based MLE is superior to the overall MLE for predicting to which of these five categories an unseen disyllabic word belongs. Table 4 lists the overall MLE, the hapax-based MLE and the statistics on which these estimates are based; Figure 3 plots the corresponding proportions as a function of log-frequency. Table 4 also lists the results of tenfold cross-validation by specifying, for each category, its contribution to the X2-statistic summing Over the ten cross-validation runs. (A more condensed format was chosen for this table than for the previous tables, since here we are dealing with a fivefold ambiguity; the previous format would have resulted in a rather large table in the present case.) Clearly, predictions based on the Table 4 Results of tenfold cross-validation for Dutch disyllabic -er words. N and N1 are the number of tokens and number of hapax legomena in the Uit den Boogaart corpus for simplex and complex adjectives and nouns, and proper names. OMLE and HMLE are, respectively, the overall and hapax-based MLEs based on N and N1. For each category, the columns headed by X2(OMLE) and X2(HMLE) list the summed contribution to the X2-measures over ten cross-validation runs for the overall and hapax-based estimates. hapax-based MLE are superior to those based on the overall MLE (X~36) = 462.97, p < .001 for the overall MLE, X 2 = 33.50, p > .5 for the hapax-based MLE). In particular,", "cite_spans": [], "ref_spans": [ { "start": 672, "end": 679, "text": "Table 4", "ref_id": null }, { "start": 778, "end": 786, "text": "Figure 3", "ref_id": null }, { "start": 1283, "end": 1290, "text": "Table 4", "ref_id": null } ], "eq_spans": [], "section": "Disyllabic Dutch Words Ending in -er", "sec_num": "2.4" }, { "text": "proper names in -er have a much higher probability of occurrence than the overall MLE would suggest. Of course, in orthography-based applications, one can rely to some extent on capitalization to indicate proper names, so one might want to eliminate those from consideration here on this basis. Removing the category of proper names from the analysis, a cross-validation test again reveals significantly better predictions for the hapax-based MLE (X~27) = 43.61, p = .023) than for the overall MLE (X~27) = 120.03,p < .001).", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Disyllabic Dutch Words Ending in -er", "sec_num": "2.4" }, { "text": "We have demonstrated with four separate examples that the hapax-based MLE is superior to the overall MLE in predicting the proportions, among unseen forms, of the various functions of morphologically ambiguous categories. Could an even better estimator be obtained by taking not only the proportion for the hapax legomena into account but also the proportions for other low-log-frequency classes? To answer this question, note that the scatterplot in the bottom panel of Figure 2 reveals a downward curvature at the very left-hand side: even for the lowest-log-frequency classes, the likelihood of a word being a verb decreases with decreasing log-frequency. This suggests that for this particular example the hapax legomena alone should be used to estimate the probability that an unseen word is a noun or verb, rather than the hapax legomena in combination with other low-frequency classes (the words occurring twice, three times, etc.). Interestingly, the top panel of Figure 2 does not reveal even a hint of a trend among the lowest-log-frequency classes, and in Figure 1 the observed proportions for log-frequency less than 2 also do not reveal a clear pattern. For Figure 3 , clear trends for the lower-log-frequency classes seem to obtain in all cases except the plot showing the proportion of simplex adjectives. Taken jointly, these observations suggest informally that an MLE based on the hapax legomena will never be inferior to MLEs that take additional log-frequency classes at the lower end of the log-frequency range into account. At the same time, the example of Dutch verb and noun forms in -en suggests that the hapax-based MLE can be superior to such MLEs--in this particular case, inclusion of these lower-frequency classes would bring the adjusted MLE more in line with the overall MLE, resulting in a loss of accuracy. These considerations lead us to conclude that the hapax-based MLE is to be preferred to an adjusted MLE that includes other low-log-frequency classes. ", "cite_spans": [], "ref_spans": [ { "start": 471, "end": 479, "text": "Figure 2", "ref_id": "FIGREF2" }, { "start": 972, "end": 980, "text": "Figure 2", "ref_id": "FIGREF2" }, { "start": 1067, "end": 1075, "text": "Figure 1", "ref_id": null }, { "start": 1171, "end": 1179, "text": "Figure 3", "ref_id": null } ], "eq_spans": [], "section": "Summary", "sec_num": "2.5" }, { "text": "The distribution in the Uit den Boogaart corpus of the relative frequencies of disyllabic words in -er, plotted against log-frequency. Five types of words are distinguished: monomorphemic words in -er (moeder, 'mother'); bimorphemic nouns in -er (schrijver, 'writer'); monomorphemic adjectives in -er (donker, 'dark'); bimorphemic adjectives in -er (groter, 'greater'); and proper names in -er (Pieter, 'Peter'). Lines are interpreted as in Figure 1 .", "cite_spans": [], "ref_spans": [ { "start": 441, "end": 449, "text": "Figure 1", "ref_id": null } ], "eq_spans": [], "section": "Figure 3", "sec_num": null }, { "text": "As we have seen in the four examples discussed above, the MLE computed over hapax legomena yields a better prediction of lexical prior probabilities for unseen cases than does an MLE computed over the entire training corpus. We now have to consider why this result holds. As we shall see, the reasons are different from case to case, but nonetheless share a commonality: in all four cases, idiosyncratic lexical properties of high-frequency words dominate the statistical properties of the high-frequency ranges, thus making the overall MLE a less reliable predictor of the properties of the lowfrequency and unseen cases. First let us discuss the final case, that of -er ambiguity in Dutch, beginning with the derived and underived nouns. The hapax-based MLE estimate for derived nouns in -er is somewhat higher than the overall MLE; for underived nouns, the hapax-based MLE is significantly lower --half --of the overall MLE. This can be explained by the observation that a good many of the underived nouns in -er are high-frequency words such as moeder 'mother' and vader 'father'. Such words contribute to the overall proportional mass of the underived nouns, thus boosting the estimate of the overall MLE for this class. A similar argument holds for the derived and underived adjectives. Turning to proper names, we see that the hapax-based MLE is much larger than the overall MLE. Proper names differ from ordinary words in that there are relatively few proper names that are highly frequent, in comparison with words in general, but there are large numbers of types of names that occur rarely. Thus, we expect an imbalance of the kind we observe.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Discussion", "sec_num": "3." }, { "text": "Consider next the ambiguity in Dutch between -en verb forms and -en plural nouns. Ceteris paribus, plural nouns are less frequent than singular nouns; on the other hand, -en for verbs serves both the function of marking plurality and of marking the infinitive. High-frequency verbs include some very common word forms, such as the auxiliaries hebben 'have', zullen 'will', kunnen 'can', and moeten 'must'. Thus, for the high-frequency ranges, the data is weighted heavily towards verbs. On the other hand, while both nouns and verbs are open classes, nouns are far more productive as a class than are verbs (Baayen and Lieber 1991) , and this pattern becomes predominant in the low-frequency ranges: among low-frequency types, most tokens are nouns. Hence, for the low-frequency ranges, the data is weighted towards nouns. These two opposing forces conspire to yield a downward trend in the percentage of verbs as we proceed from the high-to the low-frequency ranges.", "cite_spans": [ { "start": 607, "end": 631, "text": "(Baayen and Lieber 1991)", "ref_id": "BIBREF2" } ], "ref_spans": [], "eq_spans": [], "section": "Discussion", "sec_num": "3." }, { "text": "Next, consider the English past tense versus past participle ambiguity. One of the important functions of the past participle form is as an adjectival modifier or predicate; for example, the parked car. In this function the past participle has a passive meaning with transitive verbs, and a perfective meaning with unaccusative intransitive verbs; see Levin (1993, 86-88) for details. For reasons that are not clear to us, a predominant number of the high-frequency verbs cannot felicitously be used as prenominal adjectives. These verbs include unergative intransitives like walk, for which one would not expect to find the adjectival usage, given the above characterization; but they also include clear transitives like move, try, and ask, and unaccusative intransitives like appear, which are not generally felicitous in this usage. Consider: ?a moved car, ?a tried approach, ?an asked question, ?an appeared ad; but contrast: an oft-tried approach, a frequently asked question, a recently appeared ad, where an adverbial modifier renders the examples felicitous. 5 Among the low-frequency verbs, including accentuate, bottle and incense, the predominate types are those in which the past participle usage is preferred. What is clear from the plot in the top panel of Figure 2 is that the downward trend in the regression curve to the right of the plot is due to the lexical properties of a relatively small number of high-frequency verbs. For the greater part of the frequency range, there is a relatively stable proportion of participles to finite past forms. Thus, the hapax-based MLE yields an estimate that is uncontaminated by the lexical properties of individual high-frequency forms.", "cite_spans": [ { "start": 352, "end": 371, "text": "Levin (1993, 86-88)", "ref_id": null } ], "ref_spans": [ { "start": 1271, "end": 1279, "text": "Figure 2", "ref_id": "FIGREF2" } ], "eq_spans": [], "section": "Discussion", "sec_num": "3." }, { "text": "Finally, consider the Dutch verb forms -en that we started with. In Figure 1 the strong downward trend in the regression curve at the right of the figure is due in large measure to the inclusion of high-frequency auxiliary verbs, examples of which have already been given. These verbs, while possible in the infinitival form, occur predominantly in the finite form. Hence, a form such as hebben 'have' is much more likely to be a plural finite form than it is to be an infinitive. At the low end of the frequency spectrum, we find a great many verbs derived with separable particles, such as afzeggen 'cancel'; note that separable prefixation is the most productive verbforming process in Dutch. In the infinitival form, the particle is always attached to 5 One reviewer has suggested that the infelicity of many adjectival passives relates to the fact that the action denoted by the base verb is not regarded as producing an enduring result that affects the object denoted by the (deep) internal argument: contrast a broken vase, where the vase is enduringly affected by the breaking, with ?a seen movie, where the movie is not affected. However, this cannot be the whole story since the object denoted by the internal argument of kill is presumably enduringly affected by the killing, yet ?a killed man seems about as odd as ?a seen movie.", "cite_spans": [], "ref_spans": [ { "start": 68, "end": 76, "text": "Figure 1", "ref_id": null } ], "eq_spans": [], "section": "Discussion", "sec_num": "3." }, { "text": "the verb. However, in the finite forms in main clauses, the particle must be separated: for example, wij zeggen onze afspraak af 'we are cancelling our appointment'. These properties of Dutch separable verbs boost the likelihood of infinitival forms for the low-frequency ranges, but they also boost the likelihood of (higher-frequency) finite plural forms such as zeggen: since the separated finite plural form zeggen is identical to the finite plural of the underived verb zeggen 'say', any separated finite forms will accrue to the frequency of the generally much more common derivational base. What all of these cases share is that the statistical properties of the high-frequency ranges are dominated by lexical properties of particular sets of high-frequency words. This in turn biases the overall MLE and makes it a poor predictor of novel cases. For example, auxiliaries such as hebben 'have' are among the most common verbs in Dutch, but they have rather different syntactic, and hence morphological, properties from other verbs; these properties in turn contaminate the high-frequency ranges and thus the overall MLE. In contrast, words in the low-frequency ranges, and particularly hapaxes, are heavily populated with (necessarily non-idiosyncratic) neologisms derived via productive morphological processes (Baayen 1989; Baayen and Renouf 1996) . Any lexical biases that are inherent in these morphological processes --for example, the fact that a low frequency Dutch word ending in -en is more likely to be a noun than a verb --are well-estimated by the hapaxes. Now, for a sufficiently large training corpus, we can be very confident that an unseen complex word is nonidiosyncratic and formed via a productive morphological process, and this confidence increases as the corpus size increases (Baayen and Renouf 1996) . Since the hapaxes of a particular morphological process mostly consist of non-idiosyncratic formations from that process, it makes sense that the distribution of a property among the hapaxes is the least contaminated estimate available for the distribution of that property among the unseen cases.", "cite_spans": [ { "start": 1319, "end": 1332, "text": "(Baayen 1989;", "ref_id": "BIBREF0" }, { "start": 1333, "end": 1356, "text": "Baayen and Renouf 1996)", "ref_id": "BIBREF3" }, { "start": 1806, "end": 1830, "text": "(Baayen and Renouf 1996)", "ref_id": "BIBREF3" } ], "ref_spans": [], "eq_spans": [], "section": "Discussion", "sec_num": "3." }, { "text": "The hapax-based MLE that we have proposed is not only observationally preferable to the overall MLE, it is also firmly grounded in probability theory. The probability of encountering an unseen word given that this word is a word in -en is estimated by:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Discussion", "sec_num": "3." }, { "text": "EQUATION", "cite_spans": [], "ref_spans": [], "eq_spans": [ { "start": 0, "end": 8, "text": "EQUATION", "ref_id": "EQREF", "raw_str": "N1,N(-en) Pr(unseen[-en) ~ N(_en) ,", "eq_num": "(1)" } ], "section": "Discussion", "sec_num": "3." }, { "text": "where N1,N(-en) denotes the number of hapax legomena in -en among the N(-en) tokens in -en in the training sample; see Baayen (1989) , Baayen and Lieber (1991) , Good (1953) , and Church and Gale (1991) . Of course, this estimate is heavily influenced by the highest-frequency words in -en, as these words contribute many tokens to N(-en). In our example, high-frequency auxiliaries such as hebben cause the probability of sampling unseen types in -en to be low --newly sampled tokens have a high probability of being an auxiliary rather than some previously unseen word. Interestingly, (1) can be used to derive an expression for the conditional probability that a word is, say, a noun, given that it is an unseen type in -en (Baayen 1993) :", "cite_spans": [ { "start": 119, "end": 132, "text": "Baayen (1989)", "ref_id": "BIBREF0" }, { "start": 135, "end": 159, "text": "Baayen and Lieber (1991)", "ref_id": "BIBREF2" }, { "start": 162, "end": 173, "text": "Good (1953)", "ref_id": "BIBREF8" }, { "start": 180, "end": 202, "text": "Church and Gale (1991)", "ref_id": "BIBREF5" }, { "start": 727, "end": 740, "text": "(Baayen 1993)", "ref_id": "BIBREF1" } ], "ref_spans": [], "eq_spans": [], "section": "Discussion", "sec_num": "3." }, { "text": "Pr(noun A unseen -en type) (2) Pr(noun [ unseen -en type) = Pr(unseen-en type)", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Discussion", "sec_num": "3." }, { "text": "NLN (-en , noun) N (-en) Nl,t~ (-en ) N (-en) N1,N(-en, noun) N1,N (-en) Note that the estimator exemplified in (1) has been applied twice: once (in the de-nominator) to the distribution of all -en words; and once (in the numerator) to the distribution of the -en nouns --after reclassifying all verbal tokens in -en as representing one (very high-frequency) noun type in the frequency distribution. Similarly, the probability that an unseen word in -en is a verb is given by N1,N(-en, verb) Pr(verb I unseen -en type) ~ N1,N(-en)", "cite_spans": [ { "start": 4, "end": 16, "text": "(-en , noun)", "ref_id": null }, { "start": 19, "end": 24, "text": "(-en)", "ref_id": null }, { "start": 31, "end": 37, "text": "(-en )", "ref_id": null }, { "start": 40, "end": 61, "text": "(-en) N1,N(-en, noun)", "ref_id": null }, { "start": 67, "end": 72, "text": "(-en)", "ref_id": null }, { "start": 476, "end": 491, "text": "N1,N(-en, verb)", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": "Discussion", "sec_num": "3." }, { "text": "Thus the proportion of verbal hapaxes in -en that we have suggested as an adjusted MLE estimator on the basis of the curve shown in Figure 2 is in fact an estimate of the conditional probability that a word is a verb, given that it is an unseen type in -en.", "cite_spans": [], "ref_spans": [ { "start": 132, "end": 140, "text": "Figure 2", "ref_id": "FIGREF2" } ], "eq_spans": [], "section": "Discussion", "sec_num": "3." }, { "text": "The results of the analyses presented in this paper are of potential importance in various applications that require lexical disambiguation and where an estimate of lexical priors is required. For high-frequency words, one can obtain fairly reliable estimates of the lexical priors by tagging a corpus that gives a good coverage to words of various ranges. For predicting the lexical priors for the much larger mass of very low-frequency types, most of which would not occur in any such corpus, the results we have presented suggest that one should concentrate on tagging a good representative sample of the hapaxes, rather than extensively tagging words of all frequency ranges.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Discussion", "sec_num": "3." }, { "text": "Even models of disambiguation that make use of context, such as statistical n-gram taggers, often presume some estimate of lexical priors, in addition to requiring estimates of the transition probabilities of sequences of lexical tags(Church 1988;DeRose 1988;Kupiec 1992), and this again brings up the question of what to do about unseen or low-frequency forms. In working taggers, a common approach is simply to apply a uniform small probability to the various senses of unseen or low-frequency forms: this was done in the tagger discussed inChurch (1988), for example.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "", "sec_num": null }, { "text": "A paired t-test on the ratios No(inf)/No(pl) versus Eo[No(inf)]/Eo[No(pl)] reveals a highly significant difference (t9 = 13.4, p < 0.001 ); conversely a comparison of No (inf)/No (pl) and E h [No (inf)]/Eh [No (pl)] reveals no difference (t9 = 0.96,p > 0.10). 3 A paired t-test on the ratios No(vbn)/No(vbd) versus Eo[No(vbn)]/Eo[No(vbd)] reveals a significant difference (t9 -~ 2.47,p < 0.05); conversely a comparison ofNo(vbn)/No(vbd ) andEh[No(vbn)]/E h[No (vbd)] reveals no difference (t 9 = 0.48, p > 0.10).", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "", "sec_num": null }, { "text": "A paired t-test on the ratios No(v)/No(n) versus Eo[No(v)]/Eo[No(n)] reveals a highly significant difference (t9 = 95.95,p <~ 0.001); conversely a comparison ofNo(v)/No(n) andEh[No(v)]/Eh[No(n)] reveals no difference (t 9 = 0.12,p > 0.10).", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "", "sec_num": null } ], "back_matter": [ { "text": "The authors wish to thank four anonymous reviewers for Computational Linguistics for useful comments on this paper.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Acknowledgments", "sec_num": null } ], "bib_entries": { "BIBREF0": { "ref_id": "b0", "title": "A Corpus-Based Approach to Morphological Productivity: Statistical Analysis and Psycholinguistic Interpretation", "authors": [ { "first": "Harald", "middle": [], "last": "Baayen", "suffix": "" } ], "year": 1989, "venue": "", "volume": "", "issue": "", "pages": "", "other_ids": {}, "num": null, "urls": [], "raw_text": "Baayen, Harald. 1989. 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COLING.", "links": null }, "BIBREF12": { "ref_id": "b12", "title": "Decision lists for lexical ambiguity resolution", "authors": [ { "first": "David", "middle": [], "last": "Yarowsky", "suffix": "" } ], "year": 1994, "venue": "Proceedings of the 32nd Annual Meeting", "volume": "", "issue": "", "pages": "", "other_ids": {}, "num": null, "urls": [], "raw_text": "Yarowsky, David. 1994. Decision lists for lexical ambiguity resolution. In Proceedings of the 32nd Annual Meeting. Association for Computational Linguistics.", "links": null } }, "ref_entries": { "FIGREF0": { "uris": null, "type_str": "figure", "num": null, "text": "Figure 1" }, "FIGREF1": { "uris": null, "type_str": "figure", "num": null, "text": "......... --..... ,;.-.--;---=~-z,-~---.-............ ......................................................." }, "FIGREF2": { "uris": null, "type_str": "figure", "num": null, "text": "The top panel displays the distribution in the Brown corpus of the relative frequencies of English simple past tense verbs in -ed (Brown corpus tag VBD) versus past participles in -ed (VBN), plotted against log-frequency. The bottom panel displays the relative frequency as a function of log-frequency of Dutch verbs in -en (infinitives, present plurals, and strong past tense plurals), versus plural nouns in -en, computed over the Uit den Boogaart corpus. Lines are interpreted as inFigure 1." }, "FIGREF3": { "uris": null, "type_str": "figure", "num": null, "text": "............. ;'g ................................................................................................." }, "TABREF0": { "content": "
Run12345678910
N(inf)19,509 19,527 19,536 19,526 19,507 19,511 19,533 19,524 19,569 19,585
N(pl)8,953 8,935 8,926 8,936 8,955 8,952 8,930 8,939 8,894 8,878
OMLE0.685 0.686 0.686 0.686 0.685 0.685 0.686 0.686 0.688 0.688
Nl(inf)1,075 1,086 1,066 1,068 1,092 1,091 1,098 1,066 1,094 1,079
Nl(pl)185184180182179185184178179180
HMLE0.853 0.855 0.856 0.854 0.859 0.855 0.856 0.857 0.859 0.857
No(inf)120114133125133123102118121127
No(pl)24192018181615232321
Eo[No(inf)]99911059810395809799102
Eo[No(pl)]45424845484437444546
Eh [No (inf)]123114131122130119100121124127
Eh[No(pl)]21192221212017202021
", "type_str": "table", "text": "] and Eo[No(pl)]; the corresponding estimates using the hapax-based MLE are denoted as Eh[No(irlf)] andEh [No(pl)].", "num": null, "html": null }, "TABREF1": { "content": "
Run12345678910
N(vbn)20,386 20,360 20,376 20,372 20,388 20,451 20,431 20,431 20,426 20,400
N(vbd)13,845 13,871 13,855 13,859 13,843 13,781 13,801 13,801 13,806 13,832
OMLE0.596 0.595 0.595 0.595 0.596 0.597 0.597 0.597 0.597 0.596
Nl(vbn)701695678700693705690692710711
N1 (vbd)395401405406406403404405393403
HMLE0.640 0.634 0.626 0.633 0.631 0.636 0.631 0.631 0.644 0.638
N0(vbn)808610183716185757277
N0(vbd)49523741434541504842
Eo[N0(vbn)]77828274686375757271
Eo[N0(vbd)]52565650464351504848
Eh [N0(vbn)]83888678726779797776
Eh[N0(vbd)]46505246423947464343
", "type_str": "table", "text": "Cross-validation statistics for English past participles versus simple past tense verbs.", "num": null, "html": null } } } }