{ "paper_id": "J99-2007", "header": { "generated_with": "S2ORC 1.0.0", "date_generated": "2023-01-19T02:47:12.699984Z" }, "title": "Learning Dependencies between Case Frame Slots", "authors": [ { "first": "Hang", "middle": [], "last": "Li", "suffix": "", "affiliation": { "laboratory": "Real World Computing Partnership Naoki Abe* Real World Computing Partnership", "institution": "", "location": {} }, "email": "" } ], "year": "", "venue": null, "identifiers": {}, "abstract": "A theoretically sound method for learning dependencies between case frame slots is proposed. In particular, the problem is viewed as that of estimating a probability distribution over the case slots represented by a dependency graph (a dependency forest). Experimental results indicate that the proposed method can bring about a small improvement in disambiguation, but the results are largely consistent with the assumption often made in practice that case slots are mutually independent, at least when the data size is at the level that is currently available.", "pdf_parse": { "paper_id": "J99-2007", "_pdf_hash": "", "abstract": [ { "text": "A theoretically sound method for learning dependencies between case frame slots is proposed. In particular, the problem is viewed as that of estimating a probability distribution over the case slots represented by a dependency graph (a dependency forest). Experimental results indicate that the proposed method can bring about a small improvement in disambiguation, but the results are largely consistent with the assumption often made in practice that case slots are mutually independent, at least when the data size is at the level that is currently available.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Abstract", "sec_num": null } ], "body_text": [ { "text": "We address the problem of automatically acquiring case frame patterns (or their near equivalents, selectional patterns and subcategorization patterns) from large corpus data. In our view, the acquisition of case frame patterns involves the following three subtasks: (1) extracting case frame instances from corpus data, i2) generalizing case frame slots within the case frames, and (3) learning dependencies that exist between the (generalized) case frame slots. We consider here the third of these subtasks and propose a method of learning dependencies between case frame slots.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Introduction", "sec_num": "1." }, { "text": "The term \"dependency\" refers to the relationship that may exist between case slots and that indicates strong co-occurrence between the values of those case slots. For example, consider the following sentences:", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Introduction", "sec_num": "1." }, { "text": "(1) She flies jets.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Introduction", "sec_num": "1." }, { "text": "(2) That airline company flies jets.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Introduction", "sec_num": "1." }, { "text": "(3) She flies Japan Airlines.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Introduction", "sec_num": "1." }, { "text": "(4) *That airline company flies Japan Airlines.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Introduction", "sec_num": "1." }, { "text": "We see that airline company can be the value of the argl (subject) slot, when the value of the arg2 (direct object) slot is airplane but not when it is airline company. These sentences indicate that the possible values of case slots depend in general on those of others: dependencies between case slots exist. 1 The knowledge of dependencies between case slots is useful in various tasks in natural language processing, especially in analyzing sentences involving multiple prepositional phrases, such as The girl will fly a jet from Tokyo to Beijing. Note in this example * c/o C&C Media Res. Labs. NEC, 4-1-1 Miyazaki Kawasaki, {lihang, abe}@ccm.d.nec.co.jp 1 One may argue that these examples involve different word senses of fly, and in general, that if word senses were disambiguated there would be no dependency between case slots. But, with that interpretation, word senses would have to be automatically disambiguated given the corpus data, and we would find ourselves left with the same problem. Furthermore, word senses are in general difficult to define precisely, and we feel it is better not to rely on this notion in a natural language application, unless it is necessary.", "cite_spans": [ { "start": 619, "end": 628, "text": "Kawasaki,", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": "Introduction", "sec_num": "1." }, { "text": "Example case frames generated by a class-based model.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Table 1", "sec_num": null }, { "text": "(fly (argl (person))(arg2 (airplane))) 3 (fly (argl (company))(arg2 (airplane))) 2 (fly (argl (person))(arg2 (company))) 1 (fly (argl (person))(to (place/)) 1 (fly (argl (person) )(from (place/)(to (place))) 1 (fly (argl (company))(from (place))(to (place))) 1", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Case Frame Frequency", "sec_num": null }, { "text": "that the slot of from and that of to should be considered dependent and the attachment site of one of the prepositional phrases (case slots) can be determined by that of the other with high accuracy and confidence. There has not been a general method proposed to date, however, that learns dependencies between case slots. Methods of resolving ambiguities have been based, for example, on the assumption that case slots are mutually independent (Hindle and Rooth 1991) , or at most two case slots are dependent (Collins and Brooks 1995) . In this article, we propose an efficient and general method of learning dependencies between case frame slots.", "cite_spans": [ { "start": 445, "end": 468, "text": "(Hindle and Rooth 1991)", "ref_id": "BIBREF1" }, { "start": 511, "end": 536, "text": "(Collins and Brooks 1995)", "ref_id": "BIBREF0" } ], "ref_spans": [], "eq_spans": [], "section": "Case Frame Frequency", "sec_num": null }, { "text": "Suppose that we have frequency data of the type shown in Table 1 automatically extracted from a corpus, in which words in the slots are replaced by the classes they belong to. We assume that case frame instances with a given verb are generated by a discrete joint probability distribution of the form", "cite_spans": [], "ref_spans": [ { "start": 57, "end": 64, "text": "Table 1", "ref_id": null } ], "eq_spans": [], "section": "Learning Method", "sec_num": "2." }, { "text": "Py(Xl, x2 ..... xn),", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Learning Method", "sec_num": "2." }, { "text": "where Py stands for the verb, and each of the random variables Xi, i = 1, 2 .... , n, represents a case slot. We then formulate the dependencies between case slots as the probabilistic dependencies between these random variables. Such a joint distribution can be represented by three alternative types of probabilistic models according to the type of values each random variable Xi assumes. When Xi assumes a word or a special symbol \"0\" as its value, we refer to the corresponding model as a word-based model. Here 0 indicates the absence of the case slot in question. When Xi assumes a word-class (such as (person) or (company)) or 0 as its value, the corresponding model is called a class-based model. When Xi takes on 1 or 0 as its value, we call the model a slot-based model. Here the value of 1 indicates the presence of the case slot in question, and 0 the absence thereof.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Learning Method", "sec_num": "2." }, { "text": "The number of parameters in a joint distribution will be exponential, however, if we allow interdependencies among all of the variables (even the slot-based model has 0(2 n) parameters), and thus their accurate and efficient estimation may not be feasible in practice. It is often assumed implicitly in statistical natural language processing that case slots (or the corresponding random variables) are mutually independent. Although assuming that they are mutually independent would drastically reduce the number of parameters (e.g., under the independence assumption, the number of parameters in a slot-based model becomes O(n)), as illustrated above, this assumption is not necessarily valid in practice.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Learning Method", "sec_num": "2." }, { "text": "What seems to be true in practice is that some case slots are in fact dependent on one another, but that the overwhelming majority of them are mutually independent, due partly to the fact that usually only a few case slots are obligatory; the others are optional. (Optional case slots are not necessarily independent, but if two optional case slots are randomly selected, it is very likely that they are independent of one another.) Thus the target joint distribution is likely to be approximatable as the product of lowerorder component distributions, and thus has, in fact, a reasonably small number of parameters.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Learning Method", "sec_num": "2." }, { "text": "In general, any n-dimensional joint distribution can be written as", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Learning Method", "sec_num": "2." }, { "text": "n P(X1, X2,.. .,Xn) = 1-I P(Xm, I Xm, ..... Xrni_l) i----1", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Learning Method", "sec_num": "2." }, { "text": "for some permutation (ml, m2 ..... m,) of (1, 2 ..... n), letting P(Xml I Xmo) denote P(Xml).", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Learning Method", "sec_num": "2." }, { "text": "A plausible assumption regarding the dependencies between these random variables is that each variable directly depends on at most one other variable. This is one of the simplest assumptions that can be made to relax the independence assumption. For example, if the joint distribution P(X1, X2, X3) over 3 random variables X1, X2, X3 can be written (approximated) as P(X1).P(X2 I X1).P(X3 I X2), it (approximately) satisfies such an assumption. We call such a distribution a dependency forest model. A dependency forest model can be represented by a dependency forest (i.e., a set of dependency trees), whose nodes represent random variables (each labeled with a number of parameters), and whose directed links represent the dependencies that exist between these random variables. A dependency forest model is thus a restricted form of the Bayesian network (note that it is also an extension of the first-order Markov chain model). Now we turn to the problem of how to select the best dependency forest model from among all possible ones to approximate a target joint distribution based on input data. This problem has already been investigated in the area of machine learning and related fields. In particular, Suzuki (1993) has devised an algorithm, based on the Minimum Description Length (MDL) principle (Rissanen 1989) , which estimates the target joint distribution as a dependency forest model (see Li [1998] for a derivation of this algorithm from MDL). Figure 1 shows this algorithm, for which k i and kj denote, Algorithm: Output T as the set of edges of the dependency forest.", "cite_spans": [ { "start": 1212, "end": 1225, "text": "Suzuki (1993)", "ref_id": "BIBREF5" }, { "start": 1308, "end": 1323, "text": "(Rissanen 1989)", "ref_id": "BIBREF4" }, { "start": 1406, "end": 1415, "text": "Li [1998]", "ref_id": "BIBREF2" } ], "ref_spans": [ { "start": 1462, "end": 1470, "text": "Figure 1", "ref_id": null } ], "eq_spans": [], "section": "Learning Method", "sec_num": "2." }, { "text": "Let T := 0, V = {{Xi},i = 1,2,..-,n}; Calculate the value O(Xi, Xj) for all node pairs (Xi, Xj); O(Xi, Xj) = I(Xi, Xj) -(ki -1). (kj -1). ~ where mutual information 2.N ' / \\ I ( Xi, X i) = 7~:,c x,,", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Learning Method", "sec_num": "2." }, { "text": "The learning algorithm. A dependency forest as case frame patterns.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Figure 1", "sec_num": null }, { "text": "respectively, the number of possible values assumed by random variables Xi and Xj, and N the input data size. We employ Suzuki's algorithm to learn case frame patterns as a dependency forest model. Let us now consider an example to see how the algorithm works. Suppose that the input data is as given in Table 1 and there are four nodes (random variables) Xargl,Xarg2,Xfrom , and Xto. The table in Figure 2 shows the 0 values for all node pairs. Our program actually induces the set of possible values of a random variable from those in the input data and thus here kargl = 2. Probabilities are calculated based on maximum-likelihood estimation. Also, the base of logarithm is 2, and 0 \u2022 log 0 = 0 is assumed. The dependency forest in Figure 2 is then constructed. The dependency forest indicates that there is dependency between the to slot and the arg2 slot, and between the to slot and the from slot, but the argl slot is independent from all others. Note that this algorithm in fact outputs a forest consisting of labeled free trees. A labeled free tree is a tree in which each node is uniquely associated with a label and the root node is left unspecified. After applying the algorithm, any node can be designated as the root of that tree, since the dependency models based on the same labeled free tree are all equivalent (cf. Li 1998).", "cite_spans": [], "ref_spans": [ { "start": 304, "end": 311, "text": "Table 1", "ref_id": null }, { "start": 398, "end": 406, "text": "Figure 2", "ref_id": null }, { "start": 735, "end": 743, "text": "Figure 2", "ref_id": null } ], "eq_spans": [], "section": "Figure 1", "sec_num": null }, { "text": "In the first experiment, we used the proposed method to learn slot-based dependencies. As training data, we used the entire bracketed data of the Wall Street Journal corpus (Penn Treebank). We extracted case frame data from the corpus using some heuristic rules. There were 3,678 verbs for which case frame instances were extracted. We considered only the 354 verbs for which more than 50 case frame instances were extracted, since dependencies are not likely to be found with smaller data sizes (see Section 3.4.) Also, we only considered the 12 most frequently occurring case slots (argl, arg2, on, in, for, at, by, from, to, as, with, against) and ignored the others.", "cite_spans": [ { "start": 584, "end": 646, "text": "(argl, arg2, on, in, for, at, by, from, to, as, with, against)", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": "Experiment 1: Slot-based Model", "sec_num": "3.1" }, { "text": "Example Case Frame Patterns. We acquired slot-based case frame patterns for the 354 verbs using our method. There were on the average 484/354 = 1.4 dependency links acquired for each of the 354 verbs. We found that there were some verbs whose arg2 slot is dependent on a preposition (referred to as p) slot. Table 2 shows some of the verbs with large P(Xarg2 = 1, Xp = 1) values. We also found that there were some verbs having preposition slots that depend on each other (referred to as pl and p2). Table 2 also shows some of the verbs with large P(Xpl = 1, Xp2 = 1) values. The dependencies found by our method seem to agree with human intuition. gain 10 to 100 compare profit with estimate invest share in fund convert share to cash add 1 to 3 withdraw application from office prepare case for trial file suit against company sell facility to firm lose million to 10% range from 100 to 200 climb from million to million rise from billion to billion shift from stock to bond soar from 10% to 20% fall from million to million increase from million to million climb from million in period apply to commission for permission boost from 1% to 2%", "cite_spans": [], "ref_spans": [ { "start": 308, "end": 315, "text": "Table 2", "ref_id": "TABREF2" }, { "start": 500, "end": 507, "text": "Table 2", "ref_id": "TABREF2" } ], "eq_spans": [], "section": "Experiment 1: Slot-based Model", "sec_num": "3.1" }, { "text": "Perplexity Reduction. We evaluated the acquired case frame patterns (using the slotbased models) for all of the 354 verbs in terms of reduction in test data perplexity. 2 We conducted the evaluation through a 10-fold cross validation. That is, to acquire case frame patterns for a given verb, we used nine-tenths of the case frames for that verb as training data, saving what remained for use as test data, and then calculated the test data perplexity. We repeated this process 10 times and calculated the average perplexity. We then compared this with the average perplexity for independent models, which were acquired based on the assumption that each case slot is independent. The experimental results indicate that for some verbs the use of dependency forest models results in a reduction of perplexity as compared to that of independent models. For 30 of the 354 verbs (8%), perplexity reduction exceeded 10%, while the average perplexity reduction overall was only 1%. Nonetheless, it seems safe to say that, with the currently available amount of data, the dependency forest model is more suitable as a representation for the true model of case frames than the independent model, at least for 8% of the 354 verbs.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Experiment 1: Slot-based Model", "sec_num": "3.1" }, { "text": "In order to quantitatively evaluate the acquired knowledge of case slot dependencies, we conducted a PP-attachment disambiguation experiment, in which we make a decision of the following type: Whether from Tokyo should be attached to fly or jet in the sentence he will fly a jet from Tokyo.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Experiment 2: Slot-based Disambiguation", "sec_num": "3.2" }, { "text": "A simple way to disambiguate is to compare the following likelihood values, based on acquired slot-based models, Pfly(Xarg2 = 1, Xfrom = 1)\" Pjet(Xfrom = 0), and", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Experiment 2: Slot-based Disambiguation", "sec_num": "3.2" }, { "text": "Pfly(Xarg2 = 1, Xfrorn = 0)-Pjet(Xfrom = 1)", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Experiment 2: Slot-based Disambiguation", "sec_num": "3.2" }, { "text": "assuming that there are only two case slots arg2 and from for the verb fly, and there is only one case slot from for the noun jet. This means that we need to compare", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Experiment 2: Slot-based Disambiguation", "sec_num": "3.2" }, { "text": "Pfly (Xfrom = l [ Xarg2 = l) (1-Pfly(Xfrom ~-1 I Xarg2 = 1))\" Pjet(Xfrom = 1) = Pjet(Xfrom = 1) -Pfly(Xfrom = 1 [ Xarg2 -~ 1))\" Pjet(Xfrom = 1).", "cite_spans": [ { "start": 5, "end": 28, "text": "(Xfrom = l [ Xarg2 = l)", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": "Experiment 2: Slot-based Disambiguation", "sec_num": "3.2" }, { "text": "Since the second term is common to both expressions, we actually only need to compare Pfly(Xfrom = 1 [Xarg 2 = 1) and Pjet(Xfrom = 1).", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Experiment 2: Slot-based Disambiguation", "sec_num": "3.2" }, { "text": "Obviously, if we assume that case slots are independent, then we only need to compare Pfly(Xfrom = 1) and Piet(Xfrom = 1). This is nearly equivalent to the disambiguafion method proposed by Hindle and Rooth (1991) . Their method, referred to here as the Lexical Association (LA) method, actually compares the two probabilities by means of hypothesis testing. Specifically, it calculates the so-called t-score, which is a statistic about the difference between the two probabilities.", "cite_spans": [ { "start": 190, "end": 213, "text": "Hindle and Rooth (1991)", "ref_id": "BIBREF1" } ], "ref_spans": [], "eq_spans": [], "section": "Experiment 2: Slot-based Disambiguation", "sec_num": "3.2" }, { "text": "Here, we first employ the proposed dependency learning method to judge if slots Xarg2 and Xfrom with respect to verb fly are mutually dependent. Then, if they are dependent, we make the disambiguation decision based on the t-score between Pfly(Xfrom = 1 [ Xfrom = 1) and Pjet(Xfrom = 1). Otherwise, we consider the two slots independent and make a decision based on the t-score between Pfly(Xfrom = 1) and Pjet(Xfrom = 1). We call this disambiguation method DepenLA, since it is a natural extension of LA. First, we randomly selected the files under one directory of the Wall Street Journal corpus, containing roughly 1/26 of the entire bracketed corpus data, and extracted (v, nl, p, n2) quadruples (e.g., (fly, jet, from, Tokyo)) as test data. We then extracted case frames from the remaining bracketed corpus data as we did in Experiment I and used them as training data. We repeated this process 10 times and obtained 10 data sets consisting of different training data and test data. In each training data set, there were roughly 128, 000 case frames on the average for verbs and roughly 59, 000 case frames for nouns. On the average, there were 820 quadruples in each test data set.", "cite_spans": [ { "start": 674, "end": 688, "text": "(v, nl, p, n2)", "ref_id": null } ], "ref_spans": [], "eq_spans": [], "section": "Experiment 2: Slot-based Disambiguation", "sec_num": "3.2" }, { "text": "We used these 10 data sets to conduct cross-validation on the disambiguation accuracy. We used the training data to acquire dependency forest models, which we then used to perform disambiguation on the test data based on DepenLA. We also tested the performance of LA for comparison. We set the threshold for the t-score to 1.28 for both methods. In both cases, some quadruples remained whose attachment .4 + 0.5 97.5 :t: 0.5 sites could not be determined. In such cases, we made a default decision--namely, we forcibly attached (p, n2) to v. This is because we found empirically for our data set that for what remains after applying LA or DepenLA, it is most likely that (p, n2) goes with v. Table 3 summarizes the results, which are evaluated in terms of disambiguation accuracy, averaged over the ten trials. Table 3 also gives the standard deviation (+) of each accuracy value, calculated based on the assumption that the 10 cross-validation trials are statistically independent. We found that as a whole it is still difficult to judge if DepenLA significantly improves upon LA, indicating that it is almost justifiable to rely on the independence assumption in practice, at least when the data size is at the level that is currently available. For about 11% of the verbs, however, for which the dependencies are detected and are strong enough (i.e., P(Xp = 1 I Xarg2 = 1) > 0.2 or P(Xp = 1 [ Xarg 2 = 1) < 0.002),", "cite_spans": [], "ref_spans": [ { "start": 692, "end": 699, "text": "Table 3", "ref_id": "TABREF3" }, { "start": 811, "end": 818, "text": "Table 3", "ref_id": "TABREF3" } ], "eq_spans": [], "section": "Experiment 2: Slot-based Disambiguation", "sec_num": "3.2" }, { "text": "DepenLA significantly improves upon LA. (The cutoff points were set heuristically by observing the obtained dependencies, but not after the accuracy was calculated.) It is interesting to note that on the subset of data for which DepenLA is found to significantly improve upon LA, LA is already doing quite well: 93.8% as compared to 78.1%. We found that in cases in which dependencies are detected (i.e., P(Xp = 1 I Xarg2 = 1~ >> P(Xp = 1) or the converse), the probability value P(Xp = 1) is already highly discriminative, that is, either very large or very small. This is probably due to the fact that the verbs for which dependencies are detected are those for which the amount of training data is sufficient (relative to the inherent difficulty of disambiguation for that verb), and hence that are easy to disambiguate.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Experiment 2: Slot-based Disambiguation", "sec_num": "3.2" }, { "text": "We also used the proposed method to acquire case frame patterns as class-based dependency forest models, using the 354 verbs in Experiment 1. As before, we considered only the 12 most frequent slots. We generalized the values of the case slots within these case frames using the method proposed in Li and Abe (1998) to obtain class-based case frame data. We then used these data as input to the learning algorithm. The results were rather discouraging: very few case slots were determined to be dependent in the case frame patterns. To be more precise, there were on the average only 64/354 -0.2 dependency links found for each verb. This is because the number of parameters in a class-based model was large as compared to the size of the data we had available.", "cite_spans": [ { "start": 298, "end": 315, "text": "Li and Abe (1998)", "ref_id": "BIBREF3" } ], "ref_spans": [], "eq_spans": [], "section": "Experiment 3: Class-based Model", "sec_num": "3.3" }, { "text": "These experimental results seem to justify the commonly made assumption that class-based case slots, and hence word-based case slots, are mutually independent, when the data size available is at the level of what is currently provided by the Penn Treebank.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Experiment 3: Class-based Model", "sec_num": "3.3" }, { "text": "In order to test how large a data size is required to estimate a dependency forest model, we conducted the following experiment. We defined an artificial model in the form of a dependency forest model and generated data according to its distribution. We then used the data obtained to estimate a model, and evaluated the estimated model by measuring the KL divergence between the estimated model and the true model. We also checked the number of dependency links in the obtained model. We repeatedly generated data and observed the learning curve, namely the relationship between the data size and the KL divergence between the estimated and true models, and the relationship between the data size and the number of dependencies in the estimated model. We repeated this experiment on three artificial models. Figure 3 shows the results of these experiments averaged over 10 trials. The number of parameters in Model 1, Model 2, and Model 3 are 18, 30, and 44 respectivel~ and the number of links in them 1, 3, and 5. Note that the KL divergence between the estimated model and the true model converges to 0, as expected. Also note that the number of links in the estimated model converges to the correct value (1, 3, and 5) in each of the three examples.", "cite_spans": [], "ref_spans": [ { "start": 809, "end": 817, "text": "Figure 3", "ref_id": null } ], "eq_spans": [], "section": "Experiment 4: Simulation", "sec_num": "3.4" }, { "text": "These simulation results verify that the dependencies between case slots can be accurately learned when there is enough data, given that the true model is representable as a dependency forest model. We also see that to estimate a model reasonably accurately, the data size required is as large as 5 to 10 times the number of parameters. For example, for the KL divergence to go below 0.1, we need more than 200 examples, which is roughly 5 to 10 times the number of parameters. (Recall that there were only 354 verbs, having frequencies greater than 50 in our experiments, see Subsection 3.1.)", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Experiment 4: Simulation", "sec_num": "3.4" }, { "text": "In Experiment 2, there were 12 binary-valued random variables associated with each verb, and hence its distribution is thought to be approximatable by a model with a comparable number of parameters. So having 50 to 100 examples for each of these verbs approaches the minimum data size required for reasonable estimation of their dependencies. In Experiment 3 there were also 12 slots, but each slot could take on roughly 10 classes as its values and thus a class-based model tended to have about 120 parameters. The corpus data available to us was in no way sufficient for this case.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Experiment 4: Simulation", "sec_num": "3.4" }, { "text": "We have proposed a method of learning dependencies between case slots, based on an estimation method for dependency forest models. When using slot-based models, it was found empirically that some case slots are dependent, and when such dependencies are detected, using that knowledge of dependencies can significantly improve PP-attachment disambiguation accuracy. For class-based models, however, most case slots were judged independent. These empirical findings indicate that the assumption often made in practice that case slots in a class-based model are mutually independent is indeed justified, at least with the data size currently available in the Penn Treebank.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Summary", "sec_num": "4." }, { "text": "Test data perplexity is a measure of how well an estimated probability model predicts future data, and is defined as 2 H(PT'PM), H(PT, PM) = --~-~x PT(X) \u2022 logPM(x), where PM(X) denotes the estimated model, PT(X) the empirical distribution of the test data. It is in general the case that the smaller perplexity a model has, the closer to the true model it is.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "", "sec_num": null } ], "back_matter": [ { "text": "We are grateful to Mr. K. Nakamura, Mr. T. Fujita, and Dr. S. Doi of NEC and Ms. Y. Yamaguchi of NIS for their encouragement and collaboration. We thank the anonymous CL reviewers for their valuable comments and criticisms.", "cite_spans": [], "ref_spans": [], "eq_spans": [], "section": "Acknowledgments", "sec_num": null } ], "bib_entries": { "BIBREF0": { "ref_id": "b0", "title": "Prepositional phrase attachment through a backed-off model", "authors": [ { "first": "Michael", "middle": [], "last": "Collins", "suffix": "" }, { "first": "James", "middle": [], "last": "Brooks", "suffix": "" } ], "year": 1995, "venue": "Proceedings of the 3rd Workshop on Very Large Corpora", "volume": "", "issue": "", "pages": "", "other_ids": {}, "num": null, "urls": [], "raw_text": "Collins, Michael and James Brooks. 1995. Prepositional phrase attachment through a backed-off model. Proceedings of the 3rd Workshop on Very Large Corpora.", "links": null }, "BIBREF1": { "ref_id": "b1", "title": "Structural ambiguity and lexical relations", "authors": [ { "first": "Donald", "middle": [], "last": "Hindle", "suffix": "" }, { "first": "Mats", "middle": [], "last": "Rooth", "suffix": "" } ], "year": 1991, "venue": "Proceedings of the 29th Annual Meeting", "volume": "", "issue": "", "pages": "229--236", "other_ids": {}, "num": null, "urls": [], "raw_text": "Hindle, Donald and Mats Rooth. 1991. Structural ambiguity and lexical relations. Proceedings of the 29th Annual Meeting, pages 229-236. Association for Computational Linguistics.", "links": null }, "BIBREF2": { "ref_id": "b2", "title": "A Probabilistic Approach to Lexical Semantic Knowledge Acquisition and Structural Disambiguation", "authors": [ { "first": "Hang", "middle": [], "last": "Li", "suffix": "" } ], "year": 1998, "venue": "", "volume": "", "issue": "", "pages": "", "other_ids": {}, "num": null, "urls": [], "raw_text": "Li, Hang. 1998. A Probabilistic Approach to Lexical Semantic Knowledge Acquisition and Structural Disambiguation. Ph.D. Thesis, University of Tokyo.", "links": null }, "BIBREF3": { "ref_id": "b3", "title": "Generalizing case frames using a thesaurus and the MDL principle", "authors": [ { "first": "Hang", "middle": [], "last": "Li", "suffix": "" }, { "first": "Naoki", "middle": [], "last": "Abe", "suffix": "" } ], "year": 1998, "venue": "Computational Linguistics", "volume": "24", "issue": "2", "pages": "217--244", "other_ids": {}, "num": null, "urls": [], "raw_text": "Li, Hang and Naoki Abe. 1998. Generalizing case frames using a thesaurus and the MDL principle. Computational Linguistics, 24(2):217-244.", "links": null }, "BIBREF4": { "ref_id": "b4", "title": "Stochastic Complexity in Statistical Inquiry", "authors": [ { "first": "Jorma", "middle": [], "last": "Rissanen", "suffix": "" } ], "year": 1989, "venue": "", "volume": "", "issue": "", "pages": "", "other_ids": {}, "num": null, "urls": [], "raw_text": "Rissanen, Jorma. 1989. Stochastic Complexity in Statistical Inquiry. World Scientific Publishing Co., Singapore.", "links": null }, "BIBREF5": { "ref_id": "b5", "title": "A construction of Bayesian networks from databases based on an MDL principle", "authors": [ { "first": "Joe", "middle": [], "last": "Suzuki", "suffix": "" } ], "year": 1993, "venue": "Proceedings of the 9th Conference on Uncertainty in Artificial Intelligence", "volume": "", "issue": "", "pages": "266--273", "other_ids": {}, "num": null, "urls": [], "raw_text": "Suzuki, Joe. 1993. A construction of Bayesian networks from databases based on an MDL principle. Proceedings of the 9th Conference on Uncertainty in Artificial Intelligence, pages 266-273.", "links": null } }, "ref_entries": { "FIGREF0": { "text": "\" (1-Pjet(Xfrom = l) I = Pfly(Xfmm = 1 [ Xarg 2 = 1) --Pfly(Xfrom = 1 [ Xarg2 = 1)-Pjet(Xfrom = 1) and", "num": null, "type_str": "figure", "uris": null }, "FIGREF1": { "text": "Figure 3 Simulation results.", "num": null, "type_str": "figure", "uris": null }, "TABREF0": { "text": "Xj belong to different sets W1,W2 in V then Replace W1 and W2 in V with W1 U W2, and add edge (Xi,Xj) to T;", "num": null, "type_str": "table", "content": "
xj~ x j I P( xi, xj ) log P(xi, xj ) -P( xl, xj ) log( P(xi) . P( xj ) ) )
Sort the node pairs in descending order of 0, and store them into queue Q;
while (max(x,,)G)eQ O(Xi, Xj) > 0) do
Remove arg max(x,,xj)eQ O(Xi, Xj) from Q;
ifXi and
", "html": null }, "TABREF2": { "text": "Verbs and their dependent case slots.", "num": null, "type_str": "table", "content": "
VerbDependent SlotsExample
gainarg2 to
comparearg2 with
investarg2 in
convertarg2 to
addarg2 to
withdrawarg2 from
preparearg2 for
filearg2 against
sellarg2 to
losearg2 to
rangefrom to
climbfrom to
risefrom to
shiftfrom to
soarfrom to
fallfrom to
increasefrom to
climbfrom in
applyto for
boostfrom to
", "html": null }, "TABREF3": { "text": "PP-attachrnent disambiguation results.", "num": null, "type_str": "table", "content": "
MethodAccuracy(%) Accuracy for 11% of Data (%)
Default56.255.3
LA78.1 + 0.593.8 -4-0.8
DepenLA78
", "html": null } } } }