Learning the influence graph G of a high-dimensional Markov process is central to many application domains, including social networks, neuroscience, and financial risk analysis. However, in many of these applications, future states of the process are occasionally and unpredictably influenced by a distant past state, thus destroying the Markovianity. To study this practical issue, we propose the past influence model (PIM), which captures the occasional "random resets to past" by modifying the Markovian dynamics in [1], which, in turn, is a non-linear generalization of the dynamics studied in [2], [3]. The recursive greedy algorithm proposed in this paper recovers any bounded degree $G$ when the number of ``jumps back in time" is order-wise smaller than the total number of samples, and the algorithm does not require memory.

翻译：学习高维马尔可夫过程的影响图G是社交网络、神经科学和金融风险分析等众多应用领域的核心问题。然而，在许多此类应用中，过程的未来状态偶尔会不可预测地受到遥远过去状态的影响，从而破坏马尔可夫性。为研究这一实际问题，我们提出过去影响模型（PIM），该模型通过修改文献[1]中的马尔可夫动力学来捕捉偶尔发生的“随机重置至过去”现象，而文献[1]本身又是对文献[2]、[3]所研究动力学的非线性推广。本文提出的递归贪心算法能在“时间回溯跳跃”次数量级小于总样本数时恢复任意有界度图G，且该算法无需记忆存储。