Gaussian graphical model selection is an important paradigm with numerous applications, including biological network modeling, financial network modeling, and social network analysis. Traditional approaches assume access to independent and identically distributed (i.i.d) samples, which is often impractical in real-world scenarios. In this paper, we address Gaussian graphical model selection under observations from a more realistic dependent stochastic process known as Glauber dynamics. Glauber dynamics, also called the Gibbs sampler, is a Markov chain that sequentially updates the variables of the underlying model based on the statistics of the remaining model. Such models, aside from frequently being employed to generate samples from complex multivariate distributions, naturally arise in various settings, such as opinion consensus in social networks and clearing/stock-price dynamics in financial networks. In contrast to the extensive body of existing work, we present the first algorithm for Gaussian graphical model selection when data are sampled according to the Glauber dynamics. We provide theoretical guarantees on the computational and statistical complexity of the proposed algorithm's structure learning performance. Additionally, we provide information-theoretic lower bounds on the statistical complexity and show that our algorithm is nearly minimax optimal for a broad class of problems.

翻译：高斯图模型选择是一个重要的研究范式，在生物网络建模、金融网络建模以及社交网络分析等诸多领域具有广泛应用。传统方法通常假设观测数据为独立同分布样本，而这在实际场景中往往难以满足。本文针对一种更为现实的依赖随机过程——Glauber动力学——的观测数据，研究高斯图模型选择问题。Glauber动力学（亦称Gibbs采样器）是一种马尔可夫链，它依据剩余模型的统计特性顺序更新底层模型的变量。此类模型除了常被用于从复杂多元分布中生成样本外，也自然出现在多种实际场景中，例如社交网络中的意见共识形成以及金融网络中的清算/股价动态。与现有大量研究不同，我们首次提出了针对Glauber动力学采样数据的高斯图模型选择算法。我们为所提算法的结构学习性能提供了计算复杂度与统计复杂度的理论保证。此外，我们给出了统计复杂度的信息论下界，并证明该算法对一大类问题具有近乎极小极大最优性。