Abstract
This paper studies the robustness of PAC learning algorithms when the instance space is {0,1}n, and the examples are corrupted by purely random noise affecting only the attributes (and not the labels). Foruniform attribute noise, in which each attribute is flipped independently at random with the same probability, we present an algorithm that PAC learns monomials for any (unknown) noise rate less than 12 . Contrasting this positive result, we show thatproduct random attribute noise, where each attributei is flipped randomly and independently with its own probability pi, is nearly as harmful as malicious noise-no algorithm can tolerate more than a very small amount of such noise.
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Communicated by D. T. Lee.
The research of S. A. Goldman was supported in part by a GE Foundation Junior Faculty grant and NSF Grant CCR-9110108. Part of this research was conducted while the author was at the M.I.T. Laboratory for Computer Science and supported by NSF Grant DCR-8607494 and a grant from the Siemens Corporation. The research of R. H. Sloan was supported in part by NSF Grant CCR-9108753. Part of this research was conducted while the author was at Harvard and supported by ARO Grant DAAL 03-86-K-0171.
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Goldman, S.A., Sloan, R.H. Can PAC learning algorithms tolerate random attribute noise?. Algorithmica 14, 70–84 (1995). https://doi.org/10.1007/BF01300374
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DOI: https://doi.org/10.1007/BF01300374