Results 1  10
of
14
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 ..."
Abstract

Cited by 44 (11 self)
 Add to MetaCart
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 ..."
Abstract

Cited by 12 (0 self)
 Add to MetaCart
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 Angluin’s (1980b) Condition 2 (the subset principle for circumventing overgeneralization). 1
Synthesizing noisetolerant language learners
 Theoretical Computer Science A
, 1997
"... 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 ..."
Abstract

Cited by 7 (3 self)
 Add to MetaCart
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. 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. Many positive results, as well as some negative results, are presented regarding the existence of such synthesizers. The proofs of most of the positive results yield, as pleasant corollaries, strict subsetprinciple or telltale style characterizations for the noisetolerant learnability of the corresponding classes or families indexed. 1
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 ..."
Abstract

Cited by 6 (0 self)
 Add to MetaCart
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...
Extensional Set Learning
 Proceedings of The Twelfth Annual Conference on Computational Learning Theory (COLT '99
, 2000
"... We investigate the model recBC of learning of r.e. sets, where changes in hypotheses only count when there is an extensional difference. We study the learnability of collections that are uniformly r.e. We prove that, in contrast with the case of uniformly recursive collections, identifiability d ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
We investigate the model recBC of learning of r.e. sets, where changes in hypotheses only count when there is an extensional difference. We study the learnability of collections that are uniformly r.e. We prove that, in contrast with the case of uniformly recursive collections, identifiability does not imply recursive BCidentifiability. This answers a question of D. de Jongh. In contrast to the model of recursive identifiability, we prove that the BCmodel separates the notions of finite thickness and finite elasticity. 1 Introduction In this paper we consider a model of learning where two hypotheses about the data under consideration are considered equal when they denote the same object, i.e. when they are extensionally the same. This model was first defined for identification of functions in Feldman [6], Barzdin [3]. The first reference for this model in the context of set learning (learning from text) seems to be Osherson and Weinstein [14]. The model, and similar ones, ha...
On the Role of Search for Learning from Examples
 Journal of Experimental and Theoretical Artificial Intelligence
"... Gold [Gol67] discovered a fundamental enumeration technique, the socalled identificationbyenumeration, a simple but powerful class of algorithms for learning from examples (inductive inference). We introduce a variety of more sophisticated (and more powerful) enumeration techniques and charac ..."
Abstract

Cited by 4 (0 self)
 Add to MetaCart
Gold [Gol67] discovered a fundamental enumeration technique, the socalled identificationbyenumeration, a simple but powerful class of algorithms for learning from examples (inductive inference). We introduce a variety of more sophisticated (and more powerful) enumeration techniques and characterize their power. We conclude with the thesis that enumeration techniques are even universal in that each solvable learning problem in inductive inference can be solved by an adequate enumeration technique. This thesis is technically motivated and discussed. Keywords: Learning from examples, learning by search, identification by enumeration, enumeration techniques. Role of Search 1 1 Introduction The role of search, for learning from examples, is examined in a theoretical setting. Gold's seminal paper [Gol67] on inductive inference introduced a simple but powerful learning technique which became known as identificationby enumeration. Identificationbyenumeration begins with an infi...
On the Synthesis of Strategies Identifying Recursive Functions
 Proceedings of the 14th Annual Conference on Computational Learning Theory, Lecture Notes in Artificial Intelligence 2111
, 2001
"... Abstract. A classical learning problem in Inductive Inference consists of identifying each function of a given class of recursive functions from a finite number of its output values. Uniform learning is concerned with the design of single programs solving infinitely many classical learning problems. ..."
Abstract

Cited by 3 (3 self)
 Add to MetaCart
Abstract. A classical learning problem in Inductive Inference consists of identifying each function of a given class of recursive functions from a finite number of its output values. Uniform learning is concerned with the design of single programs solving infinitely many classical learning problems. For that purpose the program reads a description of an identification problem and is supposed to construct a technique for solving the particular problem. As can be proved, uniform solvability of collections of solvable identification problems is rather influenced by the description of the problems than by the particular problems themselves. When prescribing a specific inference criterion (for example learning in the limit), a clever choice of descriptions allows uniform solvability of all solvable problems, whereas even the most simple classes of recursive functions are not uniformly learnable without restricting the set of possible descriptions. Furthermore the influence of the hypothesis spaces on uniform learnability is analysed. 1
Learning by Erasing
 IN "PROC. 7TH INT. WORKSHOP ON ALGORITHMIC LEARNING THEORY," LECTURE NOTES IN ARTIFICIAL INTELLIGENCE
, 1996
"... Learning by erasing means the process of eliminating potential hypotheses from further consideration thereby converging to the least hypothesis never eliminated and this one must be a solution to the actual learning problem. The present paper deals with learnability by erasing of indexed families ..."
Abstract

Cited by 3 (1 self)
 Add to MetaCart
Learning by erasing means the process of eliminating potential hypotheses from further consideration thereby converging to the least hypothesis never eliminated and this one must be a solution to the actual learning problem. The present paper deals with learnability by erasing of indexed families L of languages from both positive data as well as positive and negative data. This refers to the following scenario. A family L of target languages and a hypothesis space for it are specified. The learner is fed eventually all positive examples (all labeled examples) of an unknown target language L chosen from L. The target language L is learned by erasing if the learner erases some set of possible hypotheses and the least hypothesis never erased correctly describes L. The capabilities of learning by erasing are investigated in dependence on the requirement of what sets of hypotheses have to be or may be, erased, and in dependence of the choice of the hypothesis space. Class prese...
The Complexity of Universal TextLearners
 Proceedings of the eleventh International Symposium on the Foundations of Computation Theory (FCT), Springer Lecture Notes in Computer Science
, 1997
"... The present work deals with language learning from text. It considers universal learners for classes of languages in models of additional information and analyzes their complexity in terms of Turingdegrees. The following is shown: If the additional information is given by a set containing at least ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
The present work deals with language learning from text. It considers universal learners for classes of languages in models of additional information and analyzes their complexity in terms of Turingdegrees. The following is shown: If the additional information is given by a set containing at least one index for each language from the class to be learned but no index for any language outside the class then there is a universal learner having the same Turing degree as the inclusion problem for recursively enumerable sets. This result is optimal in the sense that any further learner has the same or higher Turing degree. If the additional information is given by the index set of the class of languages to be learned then there is a computable universal learner. Furthermore, if the additional information is presented as an upper bound on the size of some grammar that generates the language then a high oracle is necessary and sufficient. Finally, it is shown that for the concepts of finite l...