Results 1  10
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22
Biometric identification
 Communications of the ACM
, 2000
"... Identification of grammars (r. e. indices) for recursively enumerable languages from positive data by algorithmic devices is a well studied problem in learning theory. The present paper considers identification of r. e. languages by machines that have access to membership oracles for noncomputable s ..."
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Cited by 60 (4 self)
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Identification of grammars (r. e. indices) for recursively enumerable languages from positive data by algorithmic devices is a well studied problem in learning theory. The present paper considers identification of r. e. languages by machines that have access to membership oracles for noncomputable sets. It is shown that for any set A there exists another set B such that the collections of r. e. languages that can be identified by machines with access to a membership oracle for B is strictly larger than the collections of r. e. languages that can be identified by machines with access to a membership oracle for A. In other words, there is no maximal inference degree for language identification.
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...
Computational Limits on Team Identification of Languages
, 1993
"... A team of learning machines is essentially a multiset of learning machines. ..."
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Cited by 17 (7 self)
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A team of learning machines is essentially a multiset of learning machines.
The intrinsic complexity of language identification
 Journal of Computer and System Sciences
, 1996
"... A new investigation of the complexity of language identification is undertaken using the notion of reduction from recursion theory and complexity theory. The approach, referred to as the intrinsic complexity of language identification, employs notions of ‘weak ’ and ‘strong ’ reduction between learn ..."
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Cited by 17 (7 self)
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A new investigation of the complexity of language identification is undertaken using the notion of reduction from recursion theory and complexity theory. The approach, referred to as the intrinsic complexity of language identification, employs notions of ‘weak ’ and ‘strong ’ reduction between learnable classes of languages. The intrinsic complexity of several classes is considered and the results agree with the intuitive difficulty of learning these classes. Several complete classes are shown for both the reductions and it is also established that the weak and strong reductions are distinct. An interesting result is that the self referential class of Wiehagen in which the minimal element of every language is a grammar for the language and the class of pattern languages introduced by Angluin are equivalent in the strong sense. This study has been influenced by a similar treatment of function identification by Freivalds, Kinber, and Smith. 1
Synthesizing Enumeration Techniques For Language Learning
 In Proceedings of the Ninth Annual Conference on Computational Learning Theory
, 1996
"... this paper we assume, without loss of generality, that for all oe ` ø , [M(oe) 6=?] ) [M(ø) 6=?]. ..."
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Cited by 16 (7 self)
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this paper we assume, without loss of generality, that for all oe ` ø , [M(oe) 6=?] ) [M(ø) 6=?].
Complexity issues for vacillatory function identification
 Information and Computation
, 1995
"... It was previously shown by Barzdin and Podnieks that one does not increase the power of learning programs for functions by allowing learning algorithms to converge to a finite set of correct programs instead of requiring them to converge to a single correct program. In this paper we define some new, ..."
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Cited by 12 (9 self)
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It was previously shown by Barzdin and Podnieks that one does not increase the power of learning programs for functions by allowing learning algorithms to converge to a finite set of correct programs instead of requiring them to converge to a single correct program. In this paper we define some new, subtle, but natural concepts of mind change complexity for function learning and show that, if one bounds this complexity for learning algorithms, then, by contrast with Barzdin and Podnieks result, there are interesting and sometimes complicated tradeoffs between these complexity bounds, bounds on the number of final correct programs, and learning power. CR Classification Number: I.2.6 (Learning – Induction). 1
Learning in the presence of inaccurate information
 in "Proceedings of the 2nd Annual ACM Conference on Computational Learning Theory
, 1989
"... The present paper considers the effects of introducing inaccuracies in a learner’s environment in Gold’s learning model of identification in the limit. Three kinds of inaccuracies are considered: presence of spurious data is modeled as learning from a noisy environment, missing data is modeled as ..."
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Cited by 9 (3 self)
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The present paper considers the effects of introducing inaccuracies in a learner’s environment in Gold’s learning model of identification in the limit. Three kinds of inaccuracies are considered: presence of spurious data is modeled as learning from a noisy environment, missing data is modeled as learning from incomplete environment, and the presence of a mixture of both spurious and missing data is modeled as learning from imperfect environment. Two learning domains are considered, namely, identification of programs from graphs of computable functions and identification of grammars from positive data about recursively enumerable languages. Many hierarchies and tradeoffs resulting from the interplay between the number of errors allowed in the final hypotheses, the number of inaccuracies in the data, the types of inaccuracies, and the type of success criteria are derived. An interesting result is that in the context of function learning, incomplete data is strictly worse for learning than noisy data. 1
On Aggregating Teams of Learning Machines
 Theoretical Computer Science A
, 1994
"... The present paper studies the problem of when a team of learning machines can be aggregated into a single learning machine without any loss in learning power. The main results concern aggregation ratios for vacillatory identification of languages from texts. For a positiveinteger n,amachine is said ..."
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Cited by 7 (4 self)
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The present paper studies the problem of when a team of learning machines can be aggregated into a single learning machine without any loss in learning power. The main results concern aggregation ratios for vacillatory identification of languages from texts. For a positiveinteger n,amachine is said to TxtFex n identify a language L just in case the machine converges to up to n grammars for L on any text for L.For such identification criteria, the aggregation ratio is derived for the n = 2 case. It is shown that the collection of languages that can be TxtFex 2 identified by teams with success ratio greater than 5=6 are the same as those collections of languages that can be TxtFex 2  identified by a single machine. It is also established that 5=6 is indeed the cutoff point by showing that there are collections of languages that can be TxtFex 2 identified bya team employing 6 machines, at least 5 of which are required to be successful, but cannot be TxtFex 2 identified byany single machine. Additionally, aggregation ratios are also derived for finite identification of languages from positive data and for numerous criteria involving language learning from both positive and negative data.
Hard Words
"... How do children acquire the meaning of words? And why are words like know harder for learners to acquire than words like dog or jump? We suggest that a considerable part of the difficulty of acquiring the vocabulary of natural languages consists not in overcoming conceptual difficulties with abstrac ..."
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Cited by 6 (0 self)
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How do children acquire the meaning of words? And why are words like know harder for learners to acquire than words like dog or jump? We suggest that a considerable part of the difficulty of acquiring the vocabulary of natural languages consists not in overcoming conceptual difficulties with abstract word meanings but rather in mapping these meanings onto their corresponding lexical forms. We sketch a theory of word learning that considers acquisition of the lexicon and of the clauselevel syntax to be interlocked throughout their course, rather than distinct and separable parts of language learning. The machinery is set in motion by wordtoworld pairing, a procedure that efficiently solves the mapping problem for a stock of concrete lexical items (mostly nouns), but only these. Armed with this basic stock of items, the learner accomplishes further lexical knowledge by an armoverarm process in which successively more sophisticated representations of linguistic structure are built. Lexical learning thereby can proceed by adding structuretoworld mapping to the earlieravailable machinery. These further linguistic developments enable efficient solution of the mapping problem for the more abstract component of the lexical stock.. The outcome of this procedure is a highly lexicalized grammar whose usefulness does not end with successful learning. Rather, these detailed and highly structured lexical representations serve the purposes of the incremental multiplecue processing machinery by which people produce speech and parse the speech that they hear.
Non UShaped Vacillatory and Team Learning
, 2008
"... Ushaped learning behaviour in cognitive development involves learning, unlearning and relearning. It occurs, for example, in learning irregular verbs. The prior cognitive science literature is occupied with how humans do it, for example, general rules versus tables of exceptions. This paper is most ..."
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Cited by 6 (2 self)
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Ushaped learning behaviour in cognitive development involves learning, unlearning and relearning. It occurs, for example, in learning irregular verbs. The prior cognitive science literature is occupied with how humans do it, for example, general rules versus tables of exceptions. This paper is mostly concerned with whether Ushaped learning behaviour may be necessary in the abstract mathematical setting of inductive inference, that is, in the computational learning theory following the framework of Gold. All notions considered are learning from text, that is, from positive data. Previous work showed that Ushaped learning behaviour is necessary for behaviourally correct learning but not for syntactically convergent, learning in the limit ( = explanatory learning). The present paper establishes the necessity for the hierarchy of classes of vacillatory learning where a behaviourally correct learner has to satisfy the additional constraint that it vacillates in the limit between at most b grammars, where b ∈ {2, 3,...,∗}. Non Ushaped vacillatory learning is shown to be restrictive: every non Ushaped vacillatorily learnable class is already learnable in the limit. Furthermore, if vacillatory learning with the parameter b = 2 is possible then non Ushaped behaviourally correct learning is also possible. But for b = 3, surprisingly, there is a class witnessing that this implication fails.