### BibTeX

@MISC{05learningjuntas,

author = {},

title = {Learning Juntas in the Presence of Noise},

year = {2005}

}

### OpenURL

### Abstract

The combination of two major challenges in machine learning is investi-gated: dealing with large amounts of irrelevant information and learning from noisy data. It is shown that large classes of Boolean concepts that depend on a small number of variables|so-called juntas|can be learned eciently from random examples corrupted by random attribute and classication noise. To accomplish this goal, a two-phase algorithm is presented that copes with several problems arising from the presence of noise: rstly, a suitable method for approximating Fourier coecients in the presence of noise is applied to infer the relevant variables. Secondly, as one cannot simply read o a truth table from the examples as in the noise-free case, an alternative method to build a hypothesis is established and applied to the examples restricted to the relevant variables. In particular, for the class of monotone juntas depending on d out of n variables, the sample complexity is polynomial in log(n=), 2d, da, and 1 b, where is the condence parameter and a; b> 0 are noise parameters bounding the noise rates away from 1=2. The running time is bounded by the sample complexity times a polynomial in n. So far, all results hold for the case of uniformly distributed examples|the only case that (apart from side notes) has been studied in the literature yet. We show how to extend our methods to non-uniformly distributed examples and derive new results for monotone juntas. For the attribute noise, we have to assume that it is generated by a product distribution since otherwise fault-tolerant learning is in general impossible: we construct a noise distribution P and a concept class C such that it is impossible to learn C under P-noise.

### Keyphrases

sample complexity relevant variable monotone junta noise-free case noise parameter large class alternative method fourier coecients classication noise two-phase algorithm random attribute noise rate variable so-called junta distributed example several problem fault-tolerant learning noisy data boolean concept running time side note noise distribution derive new result suitable method product distribution concept class small number irrelevant information major challenge truth table attribute noise condence parameter machine learning large amount random example