论文标题
基于PPM和其他通用代码的马尔可夫订单估计器
On a Class of Markov Order Estimators Based on PPM and Other Universal Codes
论文作者
论文摘要
我们研究了马尔可夫订单的一系列估计量的固定梯形过程，这些过程对梅尔哈夫，古特曼和ZIV以及1989年以及ryabko，astola，astola和Malyutov在2006年和2016年进行的构建略有修改。 平等的。但是，我们称之为通用马尔可夫订单的修改满足了一些有吸引力的属性，而提到的作者对其原始结构没有显示。首先，马尔可夫命令几乎肯定是一致的，而没有任何限制。其次，它们是由弦长的对数除以熵速率的对数渐近界限。第三，如果我们通过部分匹配（ppm）选择预测作为通用代码，那么长度的不同长度等于通用马尔可夫顺序的数量构成了块互信息的上限。因此，通用马尔可夫订单也可以间接用于量化长期记忆以进行厄贡过程。
We investigate a class of estimators of the Markov order for stationary ergodic processes which form a slight modification of the constructions by Merhav, Gutman, and Ziv in 1989 as well as by Ryabko, Astola, and Malyutov in 2006 and 2016. All the considered estimators compare the estimate of the entropy rate given by a universal code with the empirical conditional entropy of a string and return the order for which the two quantities are approximately equal. However, our modification, which we call universal Markov orders, satisfies a few attractive properties, not shown by the mentioned authors for their original constructions. Firstly, the universal Markov orders are almost surely consistent, without any restrictions. Secondly, they are upper bounded asymptotically by the logarithm of the string length divided by the entropy rate. Thirdly, if we choose the Prediction by Partial Matching (PPM) as the universal code then the number of distinct substrings of the length equal to the universal Markov order constitutes an upper bound for the block mutual information. Thus universal Markov orders can be also used indirectly for quantification of long memory for an ergodic process.
