Improved learning of k-parities

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A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä

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en

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8

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Theoretical Computer Science, Volume 840, pp. 249-256

Abstract

We consider the problem of learning k-parities in the online mistake-bound model: given a hidden vector x∈{0,1}n where the hamming weight of x is k and a sequence of “questions” a1,a2,…∈{0,1}n, where the algorithm must reply to each question with 〈ai,x〉(mod2), what is the best trade-off between the number of mistakes made by the algorithm and its time complexity? We improve the previous best result of Buhrman et al. [3] by an exp⁡(k) factor in the time complexity. Next, we consider the problem of learning k-parities in the PAC model in the presence of random classification noise of rate [Formula Presented]. Here, we observe that even in the presence of classification noise of non-trivial rate, it is possible to learn k-parities in time better than (nk/2), whereas the current best algorithm for learning noisy k-parities, due to Grigorescu et al. [9], inherently requires time (nk/2) even when the noise rate is polynomially small.

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Bhattacharyya, A, Gadekar, A & Rajgopal, N 2020, 'Improved learning of k-parities', Theoretical Computer Science, vol. 840, pp. 249-256. https://doi.org/10.1016/j.tcs.2020.08.025