离散时间更新过程的信息与因果结构
Informational and Causal Architecture of Discrete-Time Renewal Processes
AI总结：
本文研究离散时间更新过程的信息与因果结构，确定其预测的最小充分统计量，推导统计复杂度、excess熵等的计算公式，定义有限因果状态的更新过程子类，并以Simple Nonunifilar Source为例验证，为分析无限统计复杂度的过程奠定基础。
摘要：
更新过程被广泛用于建模由孤立事件与静止期交替构成的随机行为，静止期的持续时间由给定的概率规律确定。本文确定了用于预测更新过程的最小充分统计量（即因果状态集合），计算了存储这些状态所需的历史记忆容量（统计复杂度），界定了可预测的信息量（ excess 熵），并将单次测量的熵分解为与过去共享、与未来共享或与两者共享的部分。因果状态等价关系定义了一类新的更新过程子类——尽管事件间计数分布无界，但其因果状态数量有限。我们利用这些公式分析了参数化Simple Nonunifilar Source（简单非单源）的输出，该源由简单的两状态隐马尔可夫模型生成，但具有无限状态的ε机表示。总体而言，这些结果为分析具有无限统计复杂度和无限excess熵的过程奠定了基础。
英文摘要：
Renewal processes are broadly used to model stochastic behavior consisting of isolated events separated by periods of quiescence, whose durations are specified by a given probability law. Here, we identify the minimal sufficient statistic for their prediction (the set of causal states), calculate the historical memory capacity required to store those states (statistical complexity), delineate what information is predictable (excess entropy), and decompose the entropy of a single measurement into that shared with the past, future, or both. The causal state equivalence relation defines a new subclass of renewal processes with a finite number of causal states despite having an unbounded interevent count distribution. We use these formulae to analyze the output of the parametrized Simple Nonunifilar Source, generated by a simple two-state hidden Markov model, but with an infinite-state epsilon-machine presentation. All in all, the results lay the groundwork for analyzing processes with infinite statistical complexity and infinite excess entropy.
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。
