Lange, S., & Wiehagen, R. (1991). Polynomial-time inference of arbitrary pattern languages. New Generation Computing, 8, 361-370.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... patterns) but it is open if there are polynomialtime algorithms computing descriptive k variable patterns for any fixed k 1 (cf. 9, 12] On the other hand, k variable patterns are PAC learnable with respect to unions of k variable patterns as hypothesis space (cf. 11] Lange and Wiehagen [13] provided a learner LWA for all pattern languages that may output inconsistent guesses. The LWA achieves polynomial update time. It is set driven (cf. 21] and even iterative, thus beating Angluin s [1] algorithm with respect to its space complexity. For the LWA, the expected total learning ....

....provided range(H) PAT (cf. 3] This result may be easily extended to PAT 1 . However, positive results are also known. First, PAT is exactly learnable using polynomially many disjointness queries with respect to the hypothesis space PAT [FIN , where FIN is the set of all finite languages (cf. [13]) The proof technique easily extends to PAT 1 , too. Second, Angluin [3] established an algorithm exactly learning PAT with respect to PAT by asking O(jj jjjAj) many superset queries. However, it requires choosing general patterns for asking the queries, and does definitely not work if the ....

S. Lange and R. Wiehagen. Polynomial-time inference of arbitrary pattern languages. New Generation Computing, 8:361--370, 1991.

....and monotonicity constraints can be transformed to trivial learning functions that have polynomial update time (see Subsection 1.2) It is an open question whether there exist intelligent inconsistent learning functions that have polynomial update time for the classes under discussion. In [LW91] an example of such a function can be found that learns the class of all pattern languages ( Ang79] and is computationally well behaved given certain assumption about the distribution of the input. ....

Steen Lange and Rolf Wiehagen. Polynomial time inference of arbitrary pattern languages. New Generation Computing, 8:361-370, 1991.

....constraints (see e.g. ZL95] can be transformed to trivial learning functions that have polynomial update time (see Subsection 1.2) It is an open question whether there exist intelligent inconsistent learning functions that have polynomial update time for the classes under discussion. In [LW91] an example of such a function can be found that learns PAT ( Ang79] Note that PAT is also an indexed family. This result was conjectured to remain valid for learning from strings. XIV A final remark, note that the proof of Theorem 13 relies on a subclass of languages that can all be ....

Ste#en Lange and Rolf Wiehagen. Polynomial time inference of arbitrary pattern languages. New Generation Computing, 8:361--370, 1991. XV

....some sort of uniform distributions might make the analysis easier, but such results may not have any implications for typical distributions that occur in practice. Analyzing the expected total learning time of limit learners has been initiated by Zeugmann [Ze95] who studied Lange and Wiehagen s [LW91] pattern language learning algorithm. Their algorithm has an expected total learning time that is exponential in the number k of different variables occurring in the target pattern (cf. Zeugmann [Ze95] Moreover, the point of convergence definitely depends on the appearance of sufficiently many ....

S. Lange and R. Wiehagen. Polynomial-time inference of arbitrary pattern languages, New Generation Computing 8:361--370, 1991.

....known results. Finally, we show how the improved analysis can be used to arrive at a new learning model. In this model, learning in the limit is transformed into finite learning with high confidence. 1. Introduction The present paper deals with the average case analysis of the Lange Wiehagen [10] algorithm (LWA for short) that learns the class of all pattern languages in the limit from positive data. That means the learner is fed successively example strings and its previously made hypothesis, and it computes from these input data a new pattern as its hypothesis. The sequence of all ....

S. Lange and R. Wiehagen. Polynomial-time inference of arbitrary pattern languages. New Generation Computing, 8:361--370, 1991.

....and constant symbols. Each variable in the pattern can be substituted with a non empty string of constant symbols to produce instances that match that pattern (Angluin, 1980) It has been shown that string patterns can be learned with a polynomial number of disjointness queries in polynomial time (Lange Wiehagen, 1991). The disjointness query asks if A T T = fg where T is the target and gives a counterexample if the answer is no . Disjointness queries appear very powerful since the set A need not be in the hypothesis space. Unfortunately, the membership problem for string patterns with repeated variables is ....

Lange, S., & Wiehagen, R. (1991). Polynomial-time inference of arbitrary pattern languages. New Generation Computing, 8, 361--370.

....and constant symbols. Each variable in the pattern can be substituted with a non empty string of constant symbols to produce instances that match that pattern (Angluin, 1980) It has been shown that string patterns can be learned with a polynomial number of disjointness queries in polynomial time (Lange and Wiehagen, 1991). The disjointness query asks if A T T = fg (where T is the target) and gives a counterexample if the answer is no . Disjointness queries appear very powerful since the set A need not be in the hypothesis space. However, string pattern languages are too hard to learn in the ....

Lange, S. and R. Wiehagen: 1991, `Polynomial-time Inference of arbitrary Pattern Languages'. New Generation Computing 8, 361--370.

....some sort of uniform distributions might make the analysis easier, but such results may not have any implications for typical distributions that occur in practice. Analyzing the expected total learning time of limit learners has been initialized by Zeugmann [Ze95] who studied Lange and Wiehagen s [LW91] pattern language Learning One Variable Pattern Languages in Linear Average Time 5 learning algorithm. Their algorithm has an expected total learning time that is exponential in the number k of different variables occurring in the target pattern (cf. Zeugmann [Ze95] Moreover, the point of ....

S. Lange and R. Wiehagen. Polynomial-time inference of arbitrary pattern languages, New Generation Computing 8:361--370, 1991. 24 R udiger Reischuk and Thomas Zeugmann

....(PAC) learning. 1 Now, we might be satisfied and just exploit and scaleup the results of a mature field. However, if we compare the stimulating origin of language learning with the theoretically well based approaches to learning pattern languages (e.g. Angluin 1980; Angluin Smith 1983) (Lange Wiehagen 1991)) or context free grammars (e.g. Berwick Pilato 1987) we might feel disappointed. First, the approaches cannot be fed back to insights or observations of linguistics as could well be the approaches towards concept learning to cognitive science (e.g. Mechelen et al. 1993) Muhlenbrock ....

Lange, S., and Wiehagen, R. 1991. Polynomial-time inference of arbitrary pattern languages. New Generation Computing 8:361--370.

....that any concept that is consistent with this test set is close to the target in a probabilistic sense. There has been some work on teaching in the inductive inference community. Though neither presents a complete model of teaching, both Freivalds, Kinber and Wiehagen [9] and Lange and Wiehagen [20] have examined inference from good 6 H. D. MATHIAS examples chosen by a helpful teacher. By presenting the learner with a superset of the teaching set prepared by the teacher, encoding is prevented in both of these models. Lange and Wiehagen [20] examine learning pattern languages and show that ....

....Kinber and Wiehagen [9] and Lange and Wiehagen [20] have examined inference from good 6 H. D. MATHIAS examples chosen by a helpful teacher. By presenting the learner with a superset of the teaching set prepared by the teacher, encoding is prevented in both of these models. Lange and Wiehagen [20] examine learning pattern languages and show that this can be achieved with good examples. 3. Preliminaries The teaching model that we present in this paper is based on the model of learning with queries developed by Angluin [1] In this model the learner s goal is to infer an unknown target ....

Stefan Lange and Rolf Wiehagen. Polynomial-time inference of arbitrary pattern languages. New Generation Computing, 8:361--370, 1991.

....2 = 11; x 3 = 001. Pattern languages were rst introduced by Angluin [4, 5] Since then, they have been extensively investigated in the identi cation in the limit framework [44, 41, 40, 21, 31, 45, 20, 1, 16, 38, 46] They have also been studied in the PAC learning [33, 24, 39] and exact learning [11, 19, 27, 32, 33] frameworks. They are applicable to text processing [36] automated data entry systems [41] case based reasoning [22] and genome informatics [7 9, 13, 35, 42, 43] Supported in part by NSF Grant CCR 9734940. Learning general pattern languages is a very dicult problem. In fact, even if the ....

S. Lange and R. Wiehagen. Polynomial time inference of arbitrary pattern languages. New Generation Computing, 8:361-370, 1991.

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S. Lange and R. Wiehagen, Polynomial-time inference of arbitrary pattern languages, New Generation Computing 8 (1991), 361 -- 370.

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S. Lange and R. Wiehagen, Polynomial-time inference of arbitrary pattern languages, New Generation Computing 8 (1991) 361--370.

....to produce its actual guess exclusively from its previous one and the next element in the positive presentation. Iterative learning has been introduced by Wiehagen [26] who studied it in the setting of learning recursive functions. Further results concerning this learning model can be found in [7, 8, 13, 14, 18, 19, 25, 26, 29, 31]. Osherson et al. 18] also considered the variant that the learner has access to the last k elements, where k is a priori fixed. Interestingly enough, the latter approach does not increase the learning power. Alternatively, Fulk et al. 7] considered learners that are allowed to store k carefully ....

....a straightforward application of Valiant s [23] proof technique directly yields iterative learning algorithms for the class of all concepts describable by a k CNF and k DNF, respectively, that are much more efficient. Another example are the pattern languages. In this case, Lange and Wiehagen s [13] iterative learning algorithm is the much better choice (cf. Zeugmann [30] for a detailed analysis) As our next result states, recursive finite thickness is only a sufficient criterion that ensures the learnability by iterative IIMs. Theorem 13. There is an indexable class C 2 IT which does not ....

S. Lange and R. Wiehagen, Polynomial-time inference of arbitrary pattern languages, New Generation Computing 8 (1991), 361 -- 370.

....(cf. e.g. 6, 9, 20, 24] An iterative learner is required to produce its actual guess exclusively from its previous one and the next element in the information sequence presented. Iterative learning has been introduced in [26] and has further been studied by various authors (cf. e.g. [3, 8, 13, 14, 15, 18, 19]) Alternatively, we consider learners that are allowed to store up to k carefully chosen data elements seen so far, where k is a priori fixed (k bounded example memory inference) Bounded example memory learning has its origins in [18] Furthermore, we study feedback identification. The idea of ....

S. Lange and R. Wiehagen. Polynomial-time inference of arbitrary pattern languages. New Generation Computing, 8:361--370, 1991.

....is required to produce its actual guess exclusively from its previous one and the next element in the information sequence presented. Iterative learning has been introduced in Wiehagen [35] and has further been studied by various authors (cf. e.g. Jantke and Beick [18] Lange and Wiehagen [21], Fulk et al. 10] Kinber and Stephan [19] Lange and Zeugmann [25] Case et al. 5] Alternatively, we consider learners that are allowed to store up to k carefully chosen data elements seen so far, where k is a priori fixed (k bounded example memory inference) Bounded example memory learning ....

S. Lange and R. Wiehagen. Polynomial-time inference of arbitrary pattern languages. New Generation Computing, 8:361--370, 1991.

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S. Lange and R. Wiehagen, Polynomial--Time Inference of Arbitrary Pattern Languages, New Generation Computing 8 (1991) 361 - 370.

....[2] The approach in Goldman and Mathias [9] is essentially the same as in [5] 6] and in the present paper. For some formal definition of unfair coding tricks , there called collusion, it is formally proved in [9] that this approach avoids collusion. Finally, note that in Lange and Wiehagen [11] we proved the learnability of a special indexable family, namely the family of all pattern languages, from polynomially many good text examples in polynomial time. A similar result for learning finite automata from good examples is proved in Wiehagen [17] 3. Learning from Good Text Examples ....

S. Lange and R. Wiehagen, Polynomial--time inference of arbitrary pattern languages, New Generation Computing 8 (1991) 361--370.

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Lange, S. and Wiehagen, R. (1991) Polynomial--time inference of arbitrary pattern languages, New Generation Computing, 8:361 - 370.

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Lange, S. and Wiehagen, R. (1991), Polynomial--time inference of arbitrary pattern languages, New Generation Computing, 8:361 - 370.

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Lange, S., & Wiehagen, R. (1991). Polynomial-time inference of arbitrary pattern languages. New Generation Computing, 8, 361-370.

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S. Lange and R. Wiehagen, Polynomial time inference of arbitrary pattern languages. New Generation Computing 8 (1991) 361--370.

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S. Lange and R. Wiehagen, Polynomial-Time Inference of Arbitrary Pattern Languages, New Generation Computing 8 (1991), 361--370.

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Lange, S., & Wiehagen, R. (1991). Polynomial-time inference of arbitrary pattern languages. New Generation Computing, 8, 361--370.

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Lange, S., & Wiehagen, R. (1991). Polynomial-time inference of arbitrary pattern languages. New Generation Computing, 8, 361--370.

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