学习时间n^o（k）上的对称k-junta
Learning symmetric k-juntas in time n^o(k)
摘要：
本文给出了均匀分布下PAC模型中对称k-juntas（$n$布尔变量的布尔函数，只依赖于这些变量的未知$k$集）的学习算法，该算法在n^{O（k/ \log k）}内运行.我们的界是通过证明以下结果得到的：每个k元对称布尔函数，除了奇偶和常数函数，有一个非零的傅里叶系数的阶至少为1，最多为O（k/ \log k）。这改进了以前最好的已知的（3/31）k的界，并提供了第一个学习对称juntas的n^{o（k）}时间算法。
英文摘要：
We give an algorithm for learning symmetric k-juntas (boolean functions of $n$ boolean variables which depend only on an unknown set of $k$ of these variables) in the PAC model under the uniform distribution, which runs in time n^{O(k/\log k)}. Our bound is obtained by proving the following result: Every symmetric boolean function on k variables, except for the parity and the constant functions, has a non-zero Fourier coefficient of order at least 1 and at most O(k/\log k). This improves the previously best known bound of (3/31)k, and provides the first n^{o(k)} time algorithm for learning symmetric juntas.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
