A Lower Bound on the Complexity of Testing Grained Distributions
Electron. Colloquium Comput. Complex.(2023)
摘要
For a natural number m , a distribution is called m -grained, if each element appears with probability that is an integer multiple of 1/m . We prove that, for any constant c<1 , testing whether a distribution over [Θ(m)] is m -grained requires Ω(m^c) samples, where testing a property of distributions means distinguishing between distributions that have the property and distributions that are far (in total variation distance) from any distribution that has the property.
更多查看译文
关键词
Property testing,distributions,68Q25
AI 理解论文
溯源树
样例
生成溯源树,研究论文发展脉络
Chat Paper
正在生成论文摘要