错误、总变差、α熵与猜测之间的相互作用：法诺不等式和平斯克不等式的正反向不等式

LTCI, Télécom Paris, Institut Polytechnique de Paris, 91120 Palaiseau, France.

Entropy (Basel). 2023 Jun 25;25(7):978. doi: 10.3390/e25070978.

Using majorization theory via "Robin Hood" elementary operations, optimal lower and upper bounds are derived on Rényi and guessing entropies with respect to either error probability (yielding reverse-Fano and Fano inequalities) or total variation distance to the uniform (yielding reverse-Pinsker and Pinsker inequalities). This gives a general picture of how the notion of randomness can be measured in many areas of computer science.

通过“罗宾汉”基本运算运用优化理论，针对错误概率（产生反向法诺不等式和法诺不等式）或与均匀分布的总变差距离（产生反向平斯克不等式和平斯克不等式），得出了关于雷尼熵和猜测熵的最优上下界。这给出了一幅关于在计算机科学许多领域中如何度量随机性概念的总体图景。