概率有根树的再研究
Rooted Trees with Probabilities Revisited
摘要：
带概率的根树可以方便地表示一类带记忆的随机过程。它们允许描述和分析变长码用于数据压缩和分布匹配。在这项工作中，叶平均节点和交换定理（LANSIT）和著名的应用程序的路径长度和叶熵重申。然后将LANSIT应用于信息发散。接下来，微分LANSIT的推导，它允许写归一化的泛函的叶分布作为一个平均值的泛函的分支分布。随机变量的联合分布和相应的条件分布是叶分布和分枝分布的特殊情况。利用微分Lansit，Pinsker不等式的根树的概率制定，与应用产品分布的近似。特别是，它表明，如果一个分布和产品分布的归一化信息散度接近零，那么熵率接近产品分布的熵率。
英文摘要：
Rooted trees with probabilities are convenient to represent a class of random processes with memory. They allow to describe and analyze variable length codes for data compression and distribution matching. In this work, the Leaf-Average Node-Sum Interchange Theorem (LANSIT) and the well-known applications to path length and leaf entropy are re-stated. The LANSIT is then applied to informational divergence. Next, the differential LANSIT is derived, which allows to write normalized functionals of leaf distributions as an average of functionals of branching distributions. Joint distributions of random variables and the corresponding conditional distributions are special cases of leaf distributions and branching distributions. Using the differential LANSIT, Pinsker's inequality is formulated for rooted trees with probabilities, with an application to the approximation of product distributions. In particular, it is shown that if the normalized informational divergence of a distribution and a product distribution approaches zero, then the entropy rate approaches the entropy rate of the product distribution.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
