On the Intrinsic Complexity of Learning

Freivalds, Rūsiņš; Kinber, Efim; Smith, Carl H.

doi:10.1006/inco.1995.1158

Cited by 47 publications

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“…This approach can be traced to the work of Freivalds [Fre91] and was proposed for identification in the limit of functions by Freivalds, Kinber, and Smith [FKS95] and for identification in the limit of languages by Jain and Sharma [JS94,JS96].…”

Section: Introductionmentioning

confidence: 99%

The structure of intrinsic complexity of learning

Jain¹,

Sharma²

1997

J. symb. log.

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Limiting identification of r.e. indexes for r.e. languages (from a presentation of elements of the language) and limiting identification of programs for computable functions (from a graph of the function) have served as models for investigating the boundaries of learnability. Recently, a new approach to the study of "intrinsic" complexity of identification in the limit has been proposed. This approach, instead of dealing with the resource requirements of the learning algorithm, uses the notion of reducibility from recursion theory to compare and to capture the intuitive difficulty of learning various classes of concepts. Freivalds, Kinber, and Smith have studied this approach for function identification and Jain and Sharma have studied it for language identification.The present paper explores the structure of these reducibilities in the context of language identification. It is shown that there is an infinite hierarchy of language classes that represent learning problems of increasing difficulty. It is also shown that the language classes in this hierarchy are incomparable, under the reductions introduced, to the collection of pattern languages.Richness of the structure of intrinsic complexity is demonstrated by proving that any finite, acyclic, directed graph can be embedded in the reducibility structure. However, it is also established that this structure is not dense. The question of embedding any infinite, acyclic, directed graph is open.

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Section: Introductionmentioning

confidence: 99%

The structure of intrinsic complexity of learning

Jain¹,

Sharma²

1997

J. symb. log.

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“…Still, the characterization of completeness here reveals a weakness of the general idea of intrinsic complexity, namely -as in the non-uniform case -complete classes have a low algorithmic complexity (see Theorem 7). All in all, this shows that intrinsic complexity, as in [4], is on the one hand a useful approach, because it can be adapted to match the intuitively desired results in uniform learning. On the other hand, the doubts in [8] are corroborated.…”

Section: Introductionmentioning

confidence: 94%

“…A reduction-based approach for comparing the learning complexity is proposed in [4], using the notion of recursive operators.…”

Section: Learning In the Limit And Intrinsic Complexitymentioning

confidence: 99%

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Intrinsic Complexity of Uniform Learning

Zilles

2003

Lecture Notes in Computer Science

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Abstract. Inductive inference is concerned with algorithmic learning of recursive functions. In the model of learning in the limit a learner successful for a class of recursive functions must eventually find a program for any function in the class from a gradually growing sequence of its values. This approach is generalized in uniform learning, where the problem of synthesizing a successful learner for a class of functions from a description of this class is considered. A common reduction-based approach for comparing the complexity of learning problems in inductive inference is intrinsic complexity. In this context, reducibility between two classes is expressed via recursive operators transforming target functions in one direction and sequences of corresponding hypotheses in the other direction. The present paper is the first one concerned with intrinsic complexity of uniform learning. The relevant notions are adapted and illustrated by several examples. Characterizations of complete classes finally allow for various insightful conclusions. The connection to intrinsic complexity of non-uniform learning is revealed within several analogies concerning firstly the role and structure of complete classes and secondly the general interpretation of the notion of intrinsic complexity.

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“…The intrinsic complexity compares the difficulty of learning by using some reducibility notion, see [12]. With every reducibility notion comes a notion of completeness.…”

Section: Intrinsic Complexitymentioning

confidence: 99%

Learning Recursive Functions Refutably

Jain

Kinber²,

Wiehagen

et al. 2001

Lecture Notes in Computer Science

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Abstract. Learning of recursive functions refutably means that for every recursive function, the learning machine has either to learn this function or to refute it, i.e., to signal that it is not able to learn it. Three modi of making precise the notion of refuting are considered. We show that the corresponding types of learning refutably are of strictly increasing power, where already the most stringent of them turns out to be of remarkable topological and algorithmical richness. All these types are closed under union, though in different strengths. Also, these types are shown to be different with respect to their intrinsic complexity; two of them do not contain function classes that are "most difficult" to learn, while the third one does. Moreover, we present characterizations for these types of learning refutably. Some of these characterizations make clear where the refuting ability of the corresponding learning machines comes from and how it can be realized, in general. For learning with anomalies refutably, we show that several results from standard learning without refutation stand refutably. Then we derive hierarchies for refutable learning. Finally, we show that stricter refutability constraints cannot be traded for more liberal learning criteria.

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On the Intrinsic Complexity of Learning

Cited by 47 publications

References 0 publications

The structure of intrinsic complexity of learning

The structure of intrinsic complexity of learning

Intrinsic Complexity of Uniform Learning

Learning Recursive Functions Refutably

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