选举模型过程的动力学与推理
Dynamics and Inference for Voter Model Processes
摘要：
我们考虑一组节点上的离散时间选举模型过程，每个节点处于两种状态之一，0或1。在每个时间步中，每个节点根据采样概率采用随机采样的邻居的状态，称为节点交互参数。我们研究的极大似然估计的节点相互作用参数从观察到的节点状态的选举模型过程的实现给定的数量。与以前的工作网络自回归过程的参数估计，其长期的行为是根据一个平稳的随机过程，选举模型是一个吸收随机过程，最终达到共识状态。这就需要开发一个框架，用于从观测中导出参数估计误差界，该观测由选举模型过程的几个实现组成。我们目前的参数估计误差界解释的观察数据，根据一个扩展的选民过程，包括周期，每个对应于实现的选举模型的过程，直到吸收到一个共识状态。为了获得这些结果，选举模型过程的共识时间起着重要作用。我们提出了新的界限，所有的时刻和一个约束，具有任何给定的概率共识时间，这可能是独立的利益。与大多数现有的工作相比，我们的结果产生了一个共识的时间范围，具有很高的概率。我们还提出了一个采样复杂性下界的参数估计在规定的误差容限的局部稳定估计类。
英文摘要：
We consider a discrete-time voter model process on a set of nodes, each being in one of two states, either 0 or 1. In each time step, each node adopts the state of a randomly sampled neighbor according to sampling probabilities, referred to as node interaction parameters. We study the maximum likelihood estimation of the node interaction parameters from observed node states for a given number of realizations of the voter model process. In contrast to previous work on parameter estimation of network autoregressive processes, whose long-run behavior is according to a stationary stochastic process, the voter model is an absorbing stochastic process that eventually reaches a consensus state. This requires developing a framework for deriving parameter estimation error bounds from observations consisting of several realizations of a voter model process. We present parameter estimation error bounds by interpreting the observation data as being generated according to an extended voter process that consists of cycles, each corresponding to a realization of the voter model process until absorption to a consensus state. In order to obtain these results, consensus time of a voter model process plays an important role. We present new bounds for all moments and a bound that holds with any given probability for consensus time, which may be of independent interest. In contrast to most existing work, our results yield a consensus time bound that holds with high probability. We also present a sampling complexity lower bound for parameter estimation within a prescribed error tolerance for the class of locally stable estimators.
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