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Learning via Queries in ...
, 1992
"... We prove that the set of all recursive functions cannot be inferred using firstorder queries in the query language containing extra symbols [+; !]. The proof of this theorem involves a new decidability result about Presburger arithmetic which is of independent interest. Using our machinery, we ..."
Abstract

Cited by 41 (12 self)
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We prove that the set of all recursive functions cannot be inferred using firstorder queries in the query language containing extra symbols [+; !]. The proof of this theorem involves a new decidability result about Presburger arithmetic which is of independent interest. Using our machinery, we show that the set of all primitive recursive functions cannot be inferred with a bounded number of mind changes, again using queries in [+; !]. Additionally, we resolve an open question in [7] about passive versus active learning. 1) Introduction This paper presents new results in the area of query inductive inference (introduced in [7]); in addition, there are results of interest in mathematical logic. Inductive inference is the study of inductive machine learning in a theoretical framework. In query inductive inference, we study the ability of a Query Inference Machine 1 Supported, in part, by NSF grants CCR 8803641 and 9020079. 2 Also with IBM Corporation, Application Solutions...
Ignoring Data May be the Only Way to Learn Efficiently
, 1994
"... In designing learning algorithms it seems quite reasonable to construct them in a way such that all data the algorithm already has obtained are correctly and completely reflected in the hypothesis the algorithm outputs on these data. However, this approach may totally fail, i.e., it may lead to t ..."
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Cited by 23 (13 self)
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In designing learning algorithms it seems quite reasonable to construct them in a way such that all data the algorithm already has obtained are correctly and completely reflected in the hypothesis the algorithm outputs on these data. However, this approach may totally fail, i.e., it may lead to the unsolvability of the learning problem, or it may exclude any efficient solution of it. In particular, we present a natural learning problem and prove that it can be solved in polynomial time if and only if the algorithm is allowed to ignore data.
Learning and consistency
 In Algorithmic Learning for KnowledgeBased Systems, GOSLER Final Report
, 1995
"... In designing learning algorithms it seems quite reasonable to construct them in such a way that all data the algorithm already has obtained are correctly and completely reflected in the hypothesis the algorithm outputs on these data. However, this approach may totally fail. It may lead to the unsolv ..."
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Cited by 11 (2 self)
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In designing learning algorithms it seems quite reasonable to construct them in such a way that all data the algorithm already has obtained are correctly and completely reflected in the hypothesis the algorithm outputs on these data. However, this approach may totally fail. It may lead to the unsolvability of the learning problem, or it may exclude any efficient solution of it. Therefore we study several types of consistent learning in recursiontheoretic inductive inference. We show that these types are not of universal power. We give “lower bounds ” on this power. We characterize these types by some versions of decidability of consistency with respect to suitable “nonstandard ” spaces of hypotheses. Then we investigate the problem of learning consistently in polynomial time. In particular, we present a natural learning problem and prove that it can be solved in polynomial time if and only if the algorithm is allowed to work inconsistently. 1.
Learning Algebraic Structures from Text
"... . The present work investigates the learnability of classes of substructures of some algebraic structure: submonoids and subgroups of some given group, ideals of some given commutative ring, subfields of a vector space. The learner sees all positive data but no negative one and converges to a progra ..."
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Cited by 5 (0 self)
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. The present work investigates the learnability of classes of substructures of some algebraic structure: submonoids and subgroups of some given group, ideals of some given commutative ring, subfields of a vector space. The learner sees all positive data but no negative one and converges to a program enumerating or computing the set to be learned. Besides semantical (BC) and syntactical (Ex) convergence also the more restrictive ordinal bounds on the number of mind changes are considered. The following is shown: (a) Learnability depends much on the amount of semantic knowledge given at the synthesis of the learner where this knowledge is represented by programs for the algebraic operations, codes for prominent elements of the algebraic structure (like 0 and 1 in fields) and certain parameters (like the dimension of finite dimensional vector spaces). For several natural examples good knowledge of the semantics may enable to keep ordinal mind change bounds while restricted knowledge may ...
Too Much Information Can be Too Much for Learning Efficiently
, 1992
"... In designing learning algorithms it seems quite reasonable to construct them in a way such that all data the algorithm already has obtained are correctly and completely reflected in the description the algorithm outputs on these data. However, this approach may totally fail, i.e., it may lead to the ..."
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In designing learning algorithms it seems quite reasonable to construct them in a way such that all data the algorithm already has obtained are correctly and completely reflected in the description the algorithm outputs on these data. However, this approach may totally fail, i.e., it may lead to the unsolvability of the learning problem, or it may exclude any efficient solution of it. In particular, we present a natural learning problem and prove that it can be solved in polynomial time if and only if the algorithm is allowed to ignore data.
Identification Criteria in Uniform Inductive Inference
"... Uniform Inductive Inference is concerned with the existence and the learning behaviour of strategies identifying infinitely many classes of recursive functions. The success of such strategies depends on the hypothesis spaces they use, as well as on the chosen identification criteria resulting from a ..."
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Uniform Inductive Inference is concerned with the existence and the learning behaviour of strategies identifying infinitely many classes of recursive functions. The success of such strategies depends on the hypothesis spaces they use, as well as on the chosen identification criteria resulting from additional demands in the basic learning model. These identification criteria correspond to different hierarchies of learning power – depending on the choice of hypothesis spaces. In most cases finite classes of recursive functions are sufficient to expose an increase in the learning power given by the uniform learning models corresponding to a pair of identification
Inconsistency can be . . .
"... In designing learning algorithms it seems quite reasonable to construct them in a way such that all data the algorithm already has obtained are correctly and completely reflected in the hypothesis the algorithm outputs on these data. However, this approach may totally fail, i.e., it may lead to the ..."
Abstract
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In designing learning algorithms it seems quite reasonable to construct them in a way such that all data the algorithm already has obtained are correctly and completely reflected in the hypothesis the algorithm outputs on these data. However, this approach may totally fail, i.e., it may lead to the unsolvability of the learning problem, or it may exclude any efficient solution of it. In particular, we present a natural learning problem and prove that it can be solved in polynomial time if and only if the algorithm is allowed to ignore data.
reports/701 Uniform Inductive Improvement *
, 1989
"... We examine uniform procedures for improving the scientific competence of inductive inference machines. Formally, such procedures are construed as recursive operators. Several senses of improvement are considered, including (a) enlarging the class of functions on which sucess is certain, and (b) tran ..."
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We examine uniform procedures for improving the scientific competence of inductive inference machines. Formally, such procedures are construed as recursive operators. Several senses of improvement are considered, including (a) enlarging the class of functions on which sucess is certain, and (b) transforming probable success into certain success.