Renyi entropy, guesswork moments, and large deviations
Renyi entropy, guesswork moments, and large deviations
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DOI：
10.1109/tit.2004.836665
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发表时间：
2004-11-01
影响因子：
2.5
通讯作者：
Sullivan, WG
中科院分区：
文献类型：
--
作者：
Pfister, CE;Sullivan, WG
对于A（N）上的一大类平稳概率测度，其中A是一个有限字母表，我们计算了α阶的特定Renyi熵和β>-1阶的特定猜测矩.我们证明了β阶的特定猜测矩等于α阶的特定Renyi熵= 1/（1 + β）乘以β。该方法基于统计物理学提出的能量熵估计。该技术还产生了一个简单的证明大偏差原则的经验措施的空间上的一个不可约sofic移位与参考概率措施nu，这是固定的，并满足率条件的概率允许的话。
For a large class of stationary probability measures on A(N), where A is a finite alphabet, we compute the specific Renyi entropy of order alpha and the specific guesswork moments of order beta > -1. We show that the specific guesswork moment of order beta equals the specific Renyi entropy of order alpha = 1/(1 + beta) multiplied by beta. The method is based on energy-entropy estimates suggested by statistical physics. The technique also yields a simple proof of the large deviation principle for the empirical measure on the space of an irreducible sofic shift with reference probability measure nu, which is stationary and satisfies a rate condition on the probability of allowed words.