Complexity Issues for Vacillatory Function Identification
John Case,Sanjay Jain,Arun Sharma +2 more
- 17 Dec 1991
- pp 121-140
TL;DR: This paper defines some new, subtle, but natural concepts of mind change complexity for function learning and shows that, if one bounds this complexity for learning algorithms, then there are interesting and sometimes complicated tradeoffs between these complexity bounds, bounds on the number of final correct programs, and learning power.
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Abstract: It was previously shown by Barzdin and Podnieks that one does not increase the power of learning programs for functions by allowing learning algorithms to converge to a finite set of correct programs instead of requiring them to converge to a single correct program. In this paper we define some new, subtle, but natural concepts of mind change complexity for function learning and show that, if one bounds this complexity for learning algorithms, then, by contrast with Barzdin and Podnieks result, there are interesting and sometimes complicated tradeoffs between these complexity bounds, bounds on the number of final correct programs, and learning power.
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Citations
Strong separation of learning classes
TL;DR: It is shown that for many separated learning classes from the literature a much stronger separation holds, and a philosophical heuristic toward the design of artificially intelligent learning programs is presented with each strong separation result.
Vacillatory learning of nearly minimal size grammars
TL;DR: The power of the size-restricted criteria is characterized and it is used to prove that some classes of languages, which can be learned by converging in the limit to up to n + 1 nearly minimal size correct grammars, cannot be learned using this criterion even if these lattergrammars are allowed to have a finite number of anomalies per grammar.
8
Counting extensional differences in BC-learning
TL;DR: It is proved that there is a trade-off between the number of semantic mind changes and the numberOf anomalies in the hypotheses of a learner, and the family of classes that are confidently BC-learnable from text is not closed under finite unions.
2
Anomalous learning helps succinctness
TL;DR: It is shown that allowing a bounded number of anomalies (mistakes) in the final programs learned by an algorithmic procedure can considerably “succinctify” those final programs.
2
Strong Separation of Learning Classes
John Case,Keh-Jiann Chen,Sanjay Jain +2 more
- 05 Oct 1992
TL;DR: It is shown that for many separated learning classes from the literature a much stronger separation holds, and a philosophical heuristic toward the design of artificially intelligent learning programs is presented with each strong separation result.
References
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