Machine learning of higher-order programs

Baliga, Ganesh; Case, John; Jain, Sanjay; Suraj, M. G.

doi:10.2307/2275402

Cited by 11 publications

(6 citation statements)

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“…2000). The J48 decision tree inducer, based on the C4.5 algorithm, was implemented with the parameter ‘MinNumObj’ set at a value of 11 to limit the complexity of theories and minimize the risk of over-fitting (Baliga et al 1992). Classifiers were evaluated using 100 iterations of stratified 10-fold cross-validations, a procedure designed to conservatively reflect the performance of classification models on novel data sets (Witten and Frank.…”

Section: Methodsmentioning

confidence: 99%

Genetic features of cerebrospinal fluid-derived subtype B HIV-1 tat

et al. 2012

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Section: Methodsmentioning

confidence: 99%

Genetic features of cerebrospinal fluid-derived subtype B HIV-1 tat

et al. 2012

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“…This is interesting since, for example, if the universe is completely algorithmic, then all real language texts generated by parents for their children are recursive! 7 Definition 2. -identification are required to be "nearly" minimal size and, hence, even more likely to fit in one's head.…”

Section: Preliminariesmentioning

confidence: 99%

“…In this way results about learning programs for functions can be interpreted as results about finding predictive explanations for phenomena-as results about scientific induction. For more on this see [3,31,22,7,21,56]. Regarding the names of the learning criteria studied in the present paper, originally [31] "Ex" stood for "explanatory," "Fex" stood for "finitely explanatory," and Bc for "behaviorally correct."…”

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confidence: 98%

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The Power of Vacillation in Language Learning

Case¹

1999

SIAM J. Comput.

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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 avoiding overgeneralization in learning from positive data. It is applied to prove another theorem to the effect that one can optimally eliminate half of the mistakes from final programs for vacillatory criteria if one is willing to converge in the limit to infinitely many different programs instead. Child language learning may be sensitive to the order or timing of data presentation. It is shown, though, that for the vacillatory success criteria of this paper, there is no loss of learning power for machines which are insensitive to order in several ways simultaneously. For example, partly set-driven machines attend only to the set and length of sequence of positive data, not the actual sequence itself. A machine M is weakly n-ary order independent def ⇔ for each language L on which, for some ordering of the positive data about L, M converges in the limit to a finite set of grammars, there is a finite set of grammars D (of cardinality ≤ n) such that M converges to a subset of this same D for each ordering of the positive data for L. The theorem most difficult to prove in the paper implies that machines which are simultaneously partly set-driven and weakly n-ary order independent do not lose learning power for converging in the limit to up to n grammars. Several variants of this theorem are obtained by modifying its proof, and some of these variants have application in this and other papers. Along the way it is also shown, for the vacillatory criteria, that learning power is not increased if one restricts the sequence of positive data presentation to be computable. Some of these results are nontrivial lifts of prior work for the n = 1 case done by the Blums; Wiehagen; Osherson, Stob, and Weinstein; Schäfer; and Fulk.

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“…26 Fulk [Ful85] argues that the set of distinguishable experiments one can actually do and record on a phenomenon is countable: lab manuals can and do contain only finite notations from a finite alphabet and/or bounded-size, finite-precision images. 27 The difference is somewhat analogous to the difference between predicting the location of planet at any time and predicting the shape of the planet's orbit [CJS92,BCJS94]. 28 The trick is to express the limiting computable partial functions as the uniform limit of a single, suitable computable function [RC94,CS06].…”

Section: Theorem 2 (Bārzdiņš [B74] Blum and Blum [Bb75])mentioning

confidence: 99%

Directions for Computability Theory Beyond Pure Mathematical

Case

International Mathematical Series

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This paper begins by briefly indicating the principal, non-standard motivations of the author for his decades of work in Computability Theory (CT), a.k.a. Recursive Function Theory.Then it discusses its proposed, general directions beyond those from pure mathematics for CT. These directions are as follows.1. Apply CT to basic sciences, for example, biology, psychology, physics, chemistry, and economics.2. Apply the resultant insights from 1 to philosophy and, more generally, apply CT to areas of philosophy in addition to the philosophy and foundations of mathematics.3. Apply CT for insights into engineering and other professional fields.Lastly, this paper provides a progress report on the above non-pure mathematical directions for CT, including examples for biology, cognitive science and learning theory, philosophy of science, physics, applied machine learning, and computational complexity. Interweaved with the report are occasional remarks about the future.

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Machine learning of higher-order programs

Cited by 11 publications

References 21 publications

Genetic features of cerebrospinal fluid-derived subtype B HIV-1 tat

Genetic features of cerebrospinal fluid-derived subtype B HIV-1 tat

The Power of Vacillation in Language Learning

Directions for Computability Theory Beyond Pure Mathematical

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