Two New Frameworks for Learning

Natarajan, B. K.; Tadepalli, Prasad

doi:10.1016/b978-0-934613-64-4.50046-3

Cited by 18 publications

(20 citation statements)

References 9 publications

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“…Loosely speaking, a meta-algorithm for a family M is an algorithm that takes as input the specification of a problem D in M and attempts to construct an algorithm for D. Given the scope of our definition of a family of problems, it is easy to see that the task of the meta-algorithm will be NP-hard for most non-trivial families. See [4]. This is true, even if we guarantee that every problem in the family has a polynomial-time algorithm -the difficulty lies in finding such an algorithm, given the specification of the problem.…”

Section: Defnmentioning

confidence: 98%

“…By Theorem 1, the output of the meta-algorithm will indeed be a good algorithm for the class of integrals in question. Tadepalli, in [4] implemented this algorithm and verified this to be the case.…”

Section: An Application To Symbolic Integrationmentioning

confidence: 99%

“…Theorem 1 identifies conditions sufficient to guarantee the existence of a meta-algorithm. Necessary conditions appear to be much harder to obtain, perhaps requiring a greater understanding of learning with "advice" as explored in [4]. The statement and proof of Theorem 1 are based on previous results on learning sets with one-sided error (31.…”

Section: Defnmentioning

confidence: 99%

“…instances. Early steps in this direction were taken in [4]. In a sense, this can be viewed as learning to improve computational efficiency as opposed to concept learning in the sense of Valiant.…”

Section: Introductionmentioning

confidence: 99%

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On Learning From Exercises

Natarajan¹

1989

Proceedings of the Second Annual Workshop on Computational Learning Theory

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This paper explores a new direction in the formal theory of learning -learning in the sense of improving computational efficiency as opposed to concept learning in the sense of Valiar'. Specifically, the paper concerns algorithms that learn to solve problems from sample instances ot the problems. We develop a general framework for such learning and study the framework over two distinct random sources of sample instances. The first source provides sample instances together with their solutions, while the second source provides unsolved instances or "exercises". We prove two theorems identifying conditions sufficient for learning over the two sources, our proofs being constructive in that they exhibit learning algorithms. To illustrate the scope of our results, we discuss their application to a program that learns to solve restricted classes of symbolic integrals.

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Section: Defnmentioning

confidence: 98%

Section: An Application To Symbolic Integrationmentioning

confidence: 99%

Section: Defnmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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On Learning From Exercises

Natarajan¹

1989

Proceedings of the Second Annual Workshop on Computational Learning Theory

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“…We stated our definitions of learnability in terms of both the concept class C and the hypothesis class H, but assumed throughout that H D C. Considerations in the more general case have been discussed in [1,3,18]. The use of more powerful oracles (i.e., protocols which allow the learner to get information other than just random samples) have been considered in [1,23] Finally, [19] has considered learnability of continuous valued functions (as opposed to the usual binary valued functions).…”

Section: Discussionmentioning

confidence: 99%

On Metric Entropy, Vapnik-Chervonenkis Dimension, and Learnability for a Class of Distributions

Kulkarni¹

1989

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In [23], Valiant proposed a formal framework for distribution-free concept learning which has generated a great deal of interest. A fundamental result regarding this framework was proved by Blumer et al. [6] characterizing those concept classes which are learnable in terms of their Vapnik-Chervonenkis (VC) dimension. More recently, Benedek and Itai [4] studied learnability with respect to a fixed probability distribution (a variant of the original distribution-free framework) and proved an analogous result characterizing learnability in this case. They also stated a conjecture regarding learnability for a class of distributions.In this report, we first point out that the condition for learnability obtained in [4] is equivalent to the notion of finite metric entropy (which has been studied in other contexts). Some relationships, in addition to those shown in [4], between the VC dimension of a concept class and its metric entropy with respect to various distributions are then discussed. Finally, we prove some partial results regarding learnability for a class of distributions.

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Learning Conformation Rules

et al. 2001

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We define a hypergraph representation of a protein which captures its tertiary structure in a loose way. By using the notions of hypergraphs, we define a conformation rule as-a kind of hypergraph rewriting. With a conformation rule, a procedure of conformation from sequences is described. Then we discuss a method of learning a conformation rule from a collection of hypergraph representations of proteins. A polynomial-time PAClearning algorithm is shown for a class of conformations. This algorithm is now being implemented with Common Lisp for experiments.

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Two New Frameworks for Learning

Cited by 18 publications

References 9 publications

On Learning From Exercises

On Learning From Exercises

On Metric Entropy, Vapnik-Chervonenkis Dimension, and Learnability for a Class of Distributions

Learning Conformation Rules

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