论文标题
信息理论中的不当措施
Unnormalized Measures in Information Theory
论文作者
论文摘要
信息理论是基于概率度量的，概率度量的总质量为1。使用概率措施来模拟不确定性，并且可能会问总质量是一个。我们声称，标准措施的主要原因是概率度量与Kraft的不平等相关。使用最小描述统计的长度方法，我们将通过未归一化的措施来证明，需要一种新的解释，我们将称为Poisson解释。通过泊松解释，许多问题可以简化。焦点将从概率转变为平均值。我们提供了改进测试程序，改善不平等，简化算法，新投影结果以及对量子系统描述的改进的示例。
Information theory is built on probability measures and by definition a probability measure has total mass 1. Probability measures are used to model uncertainty, and one may ask how important it is that the total mass is one. We claim that the main reason to normalize measures is that probability measures are related to codes via Kraft's inequality. Using a minimum description length approach to statistics we will demonstrate with that measures that are not normalized require a new interpretation that we will call the Poisson interpretation. With the Poisson interpretation many problems can be simplified. The focus will shift from from probabilities to mean values. We give examples of improvements of test procedures, improved inequalities, simplified algorithms, new projection results, and improvements in our description of quantum systems.
