论文标题
马尔可夫链和网络模型中的状态聚集
State aggregations in Markov chains and block models of networks
论文作者
论文摘要
我们从信息理论的角度考虑了马尔可夫链的国家聚集方案。具体而言，我们考虑汇总Markov链的状态，以便最大化按T时间步骤隔开的汇总状态的相互信息。我们表明，对于T = 1，此方法将作为特定情况恢复了学位校正的随机块模型的最大样品估计量，从而使我们能够从动力学镜头中解释此流行的生成网络模型的可能性景观的某些特征。我们进一步强调了如何使用合成流量和现实世界洋流的相干，远程动力学模块，考虑到时间尺度t >> 1是必不可少的，我们能够恢复海洋表面电流的基本特征。
We consider state-aggregation schemes for Markov chains from an information-theoretic perspective. Specifically, we consider aggregating the states of a Markov chain such that the mutual information of the aggregated states separated by T time steps is maximized. We show that for T = 1 this approach recovers the maximum-likelihood estimator of the degree-corrected stochastic block model as a particular case, thereby enabling us to explain certain features of the likelihood landscape of this popular generative network model from a dynamical lens. We further highlight how we can uncover coherent, long-range dynamical modules for which considering a time-scale T >> 1 is essential, using synthetic flows and real-world ocean currents, where we are able to recover the fundamental features of the surface currents of the oceans.
