Kearns, M., & Pitt, L. (1989). A polynomial-time algorithm for learning k{variable pattern languages from examples. In R. Rivest, D. Haussler & M.K. Warmuth (Eds.), Proceedings of the Second Annual ACM Workshop on Computational Learning Theory (pp. 57-71). San Mateo, CA: Morgan Kaufmann.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... in a pattern (k variable 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 ....

M. Kearns and L. Pitt. A polynomial-time algorithm for learning k--variable pattern languages from examples. In Proc. 2nd Ann. ACM Workshop on Computational Learning Theory, pp. 57--71, Morgan Kaufmann Publ., San Mateo, 1989.

....a random access machine that performs a reasonable menu of operations each in unit time on registers of length O(log n) bits, where n is the input length. The inputs are read via a serial input device, and reading a string of length n is assumed to require n steps. In contrast to previous work [An80, KP89, Sch90, WZ94], we like to measure the efficiency of a learning algorithm by estimating the overall time taken by the learner until convergence. This time is referred to as the total learning time. We aim to determine the total learning time in dependence on the parameter n introduced above, i.e. with respect ....

M. Kearns and L. Pitt. A polynomial-time algorithm for learning k -variable pattern languages from examples, Proc. of the 2nd Ann. Workshop on Computational Learning Theory, COLT'89 (Santa Cruz, CA), pages 57--71, San Mateo, CA, 1989. Morgan Kaufmann.

....for short) are a prominent and important concept class that can be learned from positive data (cf. e.g. Salomaa [14, 15] and Shinohara and Arikawa [17] for an overview) Nevertheless, despite its importance there is still a bottleneck concerning efficient learning algorithms. Kearns and Pitt [8], Ko, Marron and Tzeng [9] and Schapire S90 intensively studied the learnability of pattern languages in the PAC learning model. In particular, Schapire [16] proved that the class PAT is not PAC learnable regardless of the representation used by the learning algorithm, provided only that the ....

....hypothesis that can be evaluated in polynomial time, unless P =poly = NP =poly . However, the class Pat of all patterns is not a polynomial time representation for PAT, since the membership problem for PAT with respect to Pat is NP complete (cf. 1] On the other hand, Kearns and Pitt [8] designed a polynomial time PAC learner for the set of all k variable pattern languages ( k arbitrarily fixed) under the assumption the only product distributions are allowed. Unfortunately, the constant in the running time achieved depends doubly exponential on k , and thus, their algorithm ....

[Article contains additional citation context not shown here]

M. Kearns and L. Pitt. A polynomial-time algorithm for learning k --variable pattern languages from examples. In R. Rivest, D. Haussler and M.K. Warmuth, editors, Proc. 2nd Annual ACM Workshop on Computational Learning Theory pp. 57--71, 1991, Morgan Kaufmann Publishers Inc., San Mateo.

....the hypothesis ml99rzfin.tex; 15 03 2001; 3:57; p. 3 4 Peter Rossmanith and Thomas Zeugmann space consisting of all canonical patterns (Pat for short) Since the membership problem for this hypothesis space is NP complete, it is not polynomially evaluable (cf. 1] In contrast, Kearns and Pitt [12] have established a PAC learning algorithm for the class of all k variable pattern languages. Positive examples are generated with respect to arbitrary product distributions while negative examples are allowed to be generated with respect to any distribution. Additionally, the length of ....

....over the alphabet of constants have a known lower bound on their probability. In general, its running time is exponential in the length of the target pattern. However, if we assume the additional prior knowledge that all target patterns have at most k distinct variables as done by Kearns and Pitt [12] then the total learning time is linearly bounded in the expected length of sample strings fed to the learner. Now, the constant depends only exponentially on the number k of different variables occurring in the target pattern (cf. Corollary 3) 1 More precisely, the number of allowed unions is ....

[Article contains additional citation context not shown here]

Kearns, M., & Pitt, L. (1989). A polynomial-time algorithm for learning k--variable pattern languages from examples. In R. Rivest, D. Haussler & M.K. Warmuth (Eds.), Proceedings of the Second Annual ACM Workshop on Computational Learning Theory (pp. 57--71). San Mateo, CA: Morgan Kaufmann.

....power as the class being learned is considered. However, she gave an algorithm for exactly learning the class with a polynomial number of superset queries. many membership queries, but where the initial sample consists of only a single positive example. In the PAC setting, Kearns and Pitt [11] showed that k variable pattern languages can be PAC learned under product distributions 3 from polynomially many strings. At first blush, their result appears to contradict our claim that k variable patterns have an unbounded VC dimension. A closer look at their result reveals that they assume ....

....1 ffl but depends exponentially on the parameters l min and k. An algorithm that learns a k variable pattern still has a run time which grows exponentially in l min . Under an additional assumption on D and on the length of substitution strings, they become efficiently learnable for fixed k [11]. Patterns with k variable occurrences. If we restrict the patterns to have at most k occurrences of any variables, they become even more easily learnable. The number of k occurrence patterns which are consistent with an initial example x is at most as large as the number of k variable patterns ....

M. Kearns and L. Pitt. A polynomial-time algorithm for learning k-variable pattern languages. In R. Rivest, D. Haussler, and M. Warmuth, editors, Proceedings of the Second Annual Workshop on Computational Learning Theory. Morgan Kaufmann, 1989.

....a random access machine that performs a reasonable menu of operations each in unit time on registers of length O(log n) bits, where n is the input length. The inputs are read via a serial input device, and reading a string of length n is assumed to require n steps. In contrast to previous work [An80, KP89, Sch90, WZ94], we like to measure the efficiency of a learning algorithm by estimating the overall time taken by the learner until convergence. This time is referred to as the total learning time. We aim to determine the total learning time in dependence on the parameter n introduced above, i.e. with respect ....

M. Kearns and L. Pitt. A polynomial-time algorithm for learning k -variable pattern languages from examples, Proc. of the 2nd Ann. Workshop on Computational Learning Theory, COLT'89 (Santa Cruz, CA), pages 57--71, San Mateo, CA, 1989. Morgan Kaufmann.

....to the hypothesis ml99rzfin.tex; 3 12 1999; 0:06; p. 3 4 Peter Rossmanith and Thomas Zeugmann space consisting of all canonical patterns (Pat for short) Since the membership problem for this hypothesis space is NP complete, it is not polynomially evaluable (cf. 1] In contrast, Kearns and Pitt [12] have established a PAC learning algorithm for the class of all k variable pattern languages. Positive examples are generated with respect to arbitrary product distributions while negative examples are allowed to be generated with respect to any distribution. Additionally, the length of ....

....over the alphabet of constants have a known lower bound on their probability. In general, its running time is exponential in the length of the target pattern. However, if we assume the additional prior knowledge that all target patterns have at most k distinct variables as done by Kearns and Pitt [12] then the total learning time is linearly bounded in the expected length of sample strings fed to the learner. Now, the constant depends only exponentially on the number k of different variables occurring in the target pattern (cf. Corollary 3) 1 More precisely, the number of allowed unions is ....

[Article contains additional citation context not shown here]

Kearns, M., & Pitt, L. (1989). A polynomial-time algorithm for learning k--variable pattern languages from examples. In R. Rivest, D. Haussler & M.K. Warmuth (Eds.), Proceedings of the Second Annual ACM Workshop on Computational Learning Theory (pp. 57--71). San Mateo, CA: Morgan Kaufmann.

....the substitutions x 1 = 101; x 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 ....

.... to restrict the number of occurrences of each variable symbol in the pattern to one [40] or at most some constant k [33] Another approach is to bound the number of variables by some constant (though there is no restriction on the number of times each variable symbol can be used) Kearns and Pitt [24] gave a polynomial time PAClearning algorithm for learning such k variable patterns under the assumption that examples are drawn from a product distribution. However, for arbitrary distributions, the problem seems to be dicult even if k = 2 [4, 18] We present an ecient algorithm that does not ....

M. Kearns and L. Pitt. A polynomial-time algorithm for learning k-variable pattern languages from examples. In Proc. 2nd Annu. Workshop on Comput. Learning Theory, pages 57-71, San Mateo, CA, 1989. Morgan Kaufmann.

....with nearly all future positive and negative examples from the source. Recently, Mitchell et al. 22] have shown that the class of all one variable pattern languages has infinite VC dimension. Thus, even the one variable pattern languages are not PAC learnable. On the other hand, Kearns and Pitt [17] have shown that under certain assumptions k variable pattern languages can be learned in this model for any fixed k. However, it should be noted that Kearns and Pitt [17] allow only substitutions having an a priori bounded length for the variables in the target pattern. Thus, all the target ....

....infinite VC dimension. Thus, even the one variable pattern languages are not PAC learnable. On the other hand, Kearns and Pitt [17] have shown that under certain assumptions k variable pattern languages can be learned in this model for any fixed k. However, it should be noted that Kearns and Pitt [17] allow only substitutions having an a priori bounded length for the variables in the target pattern. Thus, all the target languages are in fact finite. The paper is structured as follows. Subsection 1.1 formally defines the pattern languages and some additional preliminaries. The different ....

M. Kearns and L. Pitt, A polynomial-time algorithm for learning k- variable pattern languages from examples, in: Proc. 2nd Ann. Workshop on Computational Learning Theory (Morgan Kaufmann, San Mateo, CA, 1989) 57--71.

....again considering learning in the limit. 3 This work has been supported by the Grant in Aid for Scientific Research (C) from the Japanese Ministry of Education, Science, Sports, and Culture under grant no. 07680403. T. Zeugmann Average Case Analysis of Pattern Learning 2 Kearns and Pitt [9], Ko, Marron and Tzeng [11] and Schapire [22] intensively studied the learnability of pattern languages in the PAC learning model. In particular, Schapire [22] proved that the class PAT is not PAC learnable regardless of the representation used by the learning algorithm, provided only that the ....

M. Kearns and L. Pitt (1989), A polynomial-time algorithm for learning k--variable pattern languages from examples, in: Proc. 2nd Annual ACM Workshop on Computational Learning Theory, eds. R. Rivest, D. Haussler and M.K. Warmuth (Morgan Kaufmann Publishers Inc., San Mateo, 1989) pp. 57 -- 71.

....of pattern languages. Nix (1983) outlined interesting applications of pattern inference algorithms. Recently, Jantke (1991) and Lange and Zeugmann (1993) as well as Zeugmann, Lange and Kapur (1995) dealt with the learnability of pattern languages under monotonicity constraints. Moreover, Kearns and Pitt (1989), Ko, Marron and Tzeng (1990) and Schapire (1990) intensively studied the learnability of pattern languages in the PAC learning model; thus, Schapire (1990) proved that the class PAT of all pattern languages is not PAC learnable unless P =poly = NP =poly . So let us define pattern languages. Let ....

Kearns, M., and Pitt, L. (1989), A polynomial-time algorithm for learning k-- variable pattern languages from examples, in "Proceedings 1st Annual Workshop on Computational Learning Theory," (D. Haussler and L. Pitt, Eds.), pp. 196 --205, Morgan Kaufmann Publishers Inc., San Mateo.

....= f L(p) j p 2 P g. This quite simple concept reflects very well the intuitive notion of text patterns as explained in the introduction. During the last decade, learnability of pattern languages has been intensively investigated within different learning models (cf. Ang80] Shi82] Mar88] KP89] LW91] and others) Pattern languages also form the basis of a couple of applications in different fields, e.g. in the intelligent text processing system EBE (cf. Nix83] and in a classification system for transmembrane proteins (cf. AKM 92] 2.3 Inductive Pattern Inference Inductive ....

Michael Kearns and Leonard Pitt. A polynomial-time algorithm for learning kvariable pattern languages from examples. In Proc. of the 2nd ACM Workshop on Computational Learning Theory, COLT'89, July 31 - August 2, 1989, Santa Cruz, CA, USA, pages 57--71, 1989.

....a random access machine that performs a reasonable menu of operations each in unit time on registers of length O(log n) bits, where n is the input length. The inputs are read via a serial input device, and reading a string of length n is assumed to require n steps. In contrast to previous work [1, 6, 14, 16], we measure the efficiency of a learning algorithm by estimating the overall time taken by the learner until convergence. This time is referred to as the total learning time. We aim to determine the total learning time in dependence on the length of the target pattern. Of course, if examples are ....

M. Kearns and L. Pitt. A polynomial-time algorithm for learning k -variable pattern languages from examples, in R. Rivest, D. Haussler and M. K. Warmuth (Eds.), Proc. 2nd Annual ACM Workshop on Computational Learning Theory, 1989, 57--71, Morgan Kaufmann.

....be learned from positive data (cf. 1, 10, 12] There are also numerous interesting applications for pattern language learners (cf. e.g. 12] and the references therein) Nevertheless, despite its importance there is still a bottleneck concerning efficient learning algorithms. Kearns and Pitt [5], Ko, Marron and Tzeng [6] and Schapire [11] intensively studied the learnability of pattern languages in the PAC learning model. In particular, Schapire [11] proved that the class PAT is not PAC learnable regardless of the representation used by the learning algorithm, provided only that the ....

.... all patterns is not a polynomial time representation for PAT, since the membership problem for PAT with respect to Pat is NP complete [1] In contrast, we show Pat to be stochastically finite learnable with high confidence with respect to Pat (cf. Theorem 9) On the other hand, Kearns and Pitt [5] designed a polynomial time PAC learner for the set of all k variable pattern languages (k arbitrarily fixed) if only product distributions are allowed. But the constant in the running time achieved depends doubly exponentially on k, and thus, their algorithm becomes rapidly impractical when k ....

[Article contains additional citation context not shown here]

M. Kearns and L. Pitt. A polynomial-time algorithm for learning k--variable pattern languages from examples. In R. Rivest, D. Haussler and M.K. Warmuth, editors, Proc. 2nd Annual ACM Workshop on Computational Learning Theory pp. 57--71, 1991, Morgan Kaufmann Publishers Inc., San Mateo.

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M. Kearns, L. Pitt. A polynomial-time algorithm for learning k-variable pattern languages from examples.

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Michael Kearns and Leonard Pitt. A polynomial-time algorithm for learning k- variable pattern languages from examples. In Proceedings of the Second Annual Workshop on Computational Learning Theory, pages 57--71, July 1989.

.... this approach is: Rivest s algorithm for learning decision lists [19] Haussler s algorithm for learning boolean conjunctions with few relevant variables [8] the algorithm of Blumer et al. for learning a union of axis aligned rectangles in the Euclidean plane; and the algorithm of Kearns and Pitt [13] for learning pattern languages with respect to product distributions. In its original form, the covering method is not noisetolerant, and indeed with the exception of decision lists [14, 20] until now there have been no known efficient noisetolerant algorithms for the above classes. In the full ....

Michael Kearns and Leonard Pitt. A polynomial-time algorithm for learning k-variable pattern languages from examples. In Proceedings of the Second Annual Workshop on Computational Learning Theory, pages 57--71, July 1989.

No context found.

Kearns, M., & Pitt, L. (1989). A polynomial-time algorithm for learning k{variable pattern languages from examples. In R. Rivest, D. Haussler & M.K. Warmuth (Eds.), Proceedings of the Second Annual ACM Workshop on Computational Learning Theory (pp. 57-71). San Mateo, CA: Morgan Kaufmann.

No context found.

M. Kearns and L. Pitt. A polynomial-time algorithm for learning k-variable pattern languages. In R. Rivest, D. Haussler, and M. Warmuth, editors, Proceedings of the Second Annual Workshop on Computational Learning Theory. Morgan Kaufmann, 1989.

No context found.

M. Kearns and L. Pitt, A Polynomial-Time ALgorithm for Learning k -Variable Pattern Languages from Examples, in "Proc. 2nd Annual ACM Workshop on Computational Learning Theory" (R. Rivest, D. Haussler and M. K. Warmuth, Eds.), pp. 57--71, Morgan Kaufmann, San Mateo, CA, 1989.

No context found.

M. Kearns and L. Pitt, A polynomial-time algorithm for learning k--variable pattern languages from examples, in: Proc. of the 2nd Annual Workshop on Computational Learning Theory (Morgan Kaufmann Publishers Inc., San Mateo, 1989) 57 --71.

No context found.

M. Kearns and L. Pitt, A Polynomial-time Algorithm for Learning k-variable Pattern Languages from Examples, Proc. 2nd Workshop on Computational Learning Theory, R . Rivest, D. Haussler and M.K. Warmuth, eds.,(Morgan Kaufmann Publishers Inc., 1989) 57 - 70.

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Kearns, M. and Pitt, L. (1989), A polynomial--time algorithm for learning k--variable pattern languages from examples, In D. Haussler and L. Pitt (eds.) Proc. 1st Workshop on Computational Learning Theory (Los Alto, CA: Morgan Kaufmann Publishers Inc.), 196-205.

No context found.

Kearns, M. and L. Pitt, (1989), A Polynomial--time Algorithm for Learning k-- variable Pattern Languages From Examples. In Proc. 2nd Annual Workshop on Computational Learning Theory, R. Rivest, D. Haussler, and M.K. Warmuth (Eds.), pp. 57 - 70, Morgan Kaufmann Publishers Inc.

No context found.

Kearns, M. and L. Pitt, (1989), A Polynomial-time Algorithm for Learning kvariable Pattern Languages from Examples, In Proc. 2nd Workshop on Computational Learning Theory, R. Rivest, D. Haussler, and M.K. Warmuth (Eds.), pp. 57 - 70, Morgan Kaufmann Publishers Inc.

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