提出一种可高效计算的马尔可夫转移矩阵距离度量，适用于医疗流程等场景建模比较。
A distance function for stochastic matrices
- 基于马尔可夫链序列的Bhattacharyya角定义新距离函数
- 该度量具闭式解，且与遍历链的混合时间收敛性相关
- 适合用于医疗等实际场景中不同马尔可夫模型的对比分析
受信息几何启发，本文倡导在随机矩阵空间上定义一种距离函数。从马尔可夫链序列出发，提出使用Bhattacharyya角作为比较短期与长期马尔可夫链运行的自然工具。推导了该距离与混合时间收敛性的界。为实现不同马尔可夫链模型的比较，尤其在医疗流程场景中，提出一种新的随机矩阵距离度量。该度量为真正距离，具有闭式表达，数值计算高效。对于遍历马尔可夫链，证明了对马尔可夫序列使用Bhattacharyya角或使用新提出的随机矩阵距离，所得模型间距离一致。
原文摘要 · Abstract (English)
Motivated by information geometry, a distance function on the space of stochastic matrices is advocated. Starting with sequences of Markov chains the Bhattacharyya angle is advocated as the natural tool for comparing both short and long term Markov chain runs. Bounds on the convergence of the distance and mixing times are derived. Guided by the desire to compare different Markov chain models, especially in the setting of healthcare processes, a new distance function on the space of stochastic matrices is presented. It is a true distance measure which has a closed form and is efficient to implement for numerical evaluation. In the case of ergodic Markov chains, it is shown that considering either the Bhattacharyya angle on Markov sequences or the new stochastic matrix distance leads to the same distance between models.
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