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Improved learning of k-parities
Theoretical Computer Science ( IF 0.747 ) Pub Date : 2020-08-27 , DOI: 10.1016/j.tcs.2020.08.025
Arnab Bhattacharyya; Ameet Gadekar; Ninad Rajgopal

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 η(0,12). 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.

更新日期:2020-09-15

 

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