By Michael J. Kearns
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Additional resources for The Computational Complexity of Machine Learning
Thus far we have made the idealized assumption that the oracles POS and NEG always faithfully return untainted examples of the target representation drawn according to the target distributions. In many environments, however, there is always some chance that an erroneous example is given to the learning algorithm. In a training session for an expert system, this might be due to an occasionally faulty teacher; in settings where the examples are being transmitted electronically, it might be due to unreliable communication equipment.
There are some technical issues involved in properly de ning the problem of learning nite automata in the distribution-free model; see Pitt and Warmuth 79 for details. Gold's results were improved by Li and Vazirani 69 , who show that nding an automaton 9=8 larger than the smallest consistent automaton is still NP -complete. As we have already discussed, Pitt and Valiant 78 prove that for k 2, learning k-term-DNF by k-term-DNF is NP -hard by giving a randomized reduction from a generalization of the graph coloring problem.
Recently generalizations of Occam's Razor to models more complicated than concept learning have been given by Kearns and Schapire 63 . 1 is that the hypothesis output by the learning algorithm must have a polynomial-size representation as a string of bits for the result to apply. Thus, it is most appropriate for discrete domains, where instances are speci ed as nite strings of bits, and does not apply well to representation classes over real-valued domains, where the speci cation of a single instance may not have any nite representation as a bit string.
The Computational Complexity of Machine Learning by Michael J. Kearns