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The Power of Vacillation in Language Learning
, 1992
"... Some extensions are considered of Gold's influential model of language learning by machine from positive data. Studied are criteria of successful learning featuring convergence in the limit to vacillation between several alternative correct grammars. The main theorem of this paper is that there are ..."
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Cited by 44 (11 self)
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Some extensions are considered of Gold's influential model of language learning by machine from positive data. Studied are criteria of successful learning featuring convergence in the limit to vacillation between several alternative correct grammars. The main theorem of this paper is that there are classes of languages that can be learned if convergence in the limit to up to (n+1) exactly correct grammars is allowed but which cannot be learned if convergence in the limit is to no more than n grammars, where the no more than n grammars can each make finitely many mistakes. This contrasts sharply with results of Barzdin and Podnieks and, later, Case and Smith, for learnability from both positive and negative data. A subset principle from a 1980 paper of Angluin is extended to the vacillatory and other criteria of this paper. This principle, provides a necessary condition for circumventing overgeneralization in learning from positive data. It is applied to prove another theorem to the eff...
The synthesis of language learners
 Information and Computation
, 1999
"... An index for an r.e. class of languages (by definition) is a procedure which generates a sequence of grammars defining the class. An index for an indexed family of languages (by definition) is a procedure which generates a sequence of decision procedures defining the family. Studied is the metaprobl ..."
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Cited by 12 (0 self)
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An index for an r.e. class of languages (by definition) is a procedure which generates a sequence of grammars defining the class. An index for an indexed family of languages (by definition) is a procedure which generates a sequence of decision procedures defining the family. Studied is the metaproblem of synthesizing from indices for r.e. classes and for indexed families of languages various kinds of languagelearners for the corresponding classes or families indexed. Many positive results, as well as some negative results, are presented regarding the existence of such synthesizers. The negative results essentially provide lower bounds for the positive results. The proofs of some of the positive results yield, as pleasant corollaries, subsetprinciple or telltale style characterizations for the learnability of the corresponding classes or families indexed. For example, the indexed families of recursive languages that can be behaviorally correctly identified from positive data are surprisingly characterized by Angluinâ€™s (1980b) Condition 2 (the subset principle for circumventing overgeneralization). 1
On the Strength of Incremental Learning
, 1999
"... . This paper provides a systematic study of incremental learning from noisefree and from noisy data, thereby distinguishing between learning from only positive data and from both positive and negative data. Our study relies on the notion of noisy data introduced in [22]. The basic scenario, nam ..."
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Cited by 7 (4 self)
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. This paper provides a systematic study of incremental learning from noisefree and from noisy data, thereby distinguishing between learning from only positive data and from both positive and negative data. Our study relies on the notion of noisy data introduced in [22]. The basic scenario, named iterative learning, is as follows. In every learning stage, an algorithmic learner takes as input one element of an information sequence for a target concept and its previously made hypothesis and outputs a new hypothesis. The sequence of hypotheses has to converge to a hypothesis describing the target concept correctly. We study the following refinements of this scenario. Bounded examplememory inference generalizes iterative inference by allowing an iterative learner to additionally store an a priori bounded number of carefully chosen data elements, while feedback learning generalizes it by allowing the iterative learner to additionally ask whether or not a particular data ele...
Synthesizing Learners Tolerating Computable Noisy Data
 In Proc. 9th International Workshop on Algorithmic Learning Theory, Lecture
, 1998
"... An index for an r.e. class of languages (by definition) generates a sequence of grammars defining the class. An index for an indexed family of languages (by definition) generates a sequence of decision procedures defining the family. F. Stephan's model of noisy data is employed, in which, roughly, c ..."
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Cited by 6 (0 self)
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An index for an r.e. class of languages (by definition) generates a sequence of grammars defining the class. An index for an indexed family of languages (by definition) generates a sequence of decision procedures defining the family. F. Stephan's model of noisy data is employed, in which, roughly, correct data crops up infinitely often, and incorrect data only finitely often. In a completely computable universe, all data sequences, even noisy ones, are computable. New to the present paper is the restriction that noisy data sequences be, nonetheless, computable! Studied, then, is the synthesis from indices for r.e. classes and for indexed families of languages of various kinds of noisetolerant languagelearners for the corresponding classes or families indexed, where the noisy input data sequences are restricted to being computable. Many positive results, as well as some negative results, are presented regarding the existence of such synthesizers. The main positive result is surpris...