Computer and Information Science and Engineering, University of Florida, Gainesville, FL 32611, USA.
Neural Comput. 2011 Jul;23(7):1862-98. doi: 10.1162/NECO_a_00144. Epub 2011 Apr 14.
For any memoryless communication channel with a binary-valued input and a one-dimensional real-valued output, we introduce a probabilistic lower bound on the mutual information given empirical observations on the channel. The bound is built on the Dvoretzky-Kiefer-Wolfowitz inequality and is distribution free. A quadratic time algorithm is described for computing the bound and its corresponding class-conditional distribution functions. We compare our approach to existing techniques and show the superiority of our bound to a method inspired by Fano's inequality where the continuous random variable is discretized.
对于具有二进制输入和一维实值输出的无记忆通信信道，我们基于 Dvoretzky-Kiefer-Wolfowitz 不等式引入了一个关于信道经验观测的互信息概率下界。该界是无分布的。本文还描述了一种计算界及其相应的类条件分布函数的二次时间算法。我们将我们的方法与现有技术进行了比较，并表明我们的界优于受 Fano 不等式启发的方法，其中连续随机变量被离散化。
