Bhattacharyya, A and Gadekar, A and Rajgopal, N (2020) Improved learning of k-parities. In: Theoretical Computer Science, 840 . pp. 249-256.
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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.
| Item Type: | Journal Article |
|---|---|
| Publication: | Theoretical Computer Science |
| Publisher: | Elsevier B.V. |
| Additional Information: | The copyright of this article belongs to the Author. |
| Keywords: | Economic and social effects; Learning systems, Hamming weights; Hidden vectors; Mistake bound models; Noise rate; Non-trivial; Time complexity; Trade off, Learning algorithms |
| Department/Centre: | Division of Electrical Sciences > Computer Science & Automation |
| Date Deposited: | 13 Sep 2022 10:11 |
| Last Modified: | 13 Sep 2022 10:16 |
| URI: | https://eprints.iisc.ac.in/id/eprint/76902 |
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