Gaussian graphical model selection is usually studied under independent sampling, but in many applications observations arise from dependent dynamics. We study structure learning when the data consist of a single trajectory of Gaussian Glauber dynamics. We develop two complementary approaches. The first is a local edge-testing estimator based on an appropriately designed correlation test that reveals edges. This estimator does not require waiting for the chain to mix and admits an embarrassingly parallel edgewise implementation. The second is a burn-in/thinning reduction: under a Dobrushin contraction condition, we prove that a suitably subsampled Gaussian Gibbs trajectory is close in total variation to an i.i.d. product sample, allowing standard i.i.d. Gaussian graphical model learners to be used as black boxes. The key technical ingredient, which may be of independent interest, is a high-dimensional total-variation bound for random-scan Gaussian Gibbs samplers, obtained by combining Wasserstein contraction with an approximate Lipschitz smoothing argument. We prove finite-sample recovery guarantees for both approaches, establish information-theoretic lower bounds on the observation time, and empirically compare the resulting sample-computation tradeoffs.

翻译：高斯图模型选择通常在独立采样条件下研究，但许多实际应用中的观测数据源自依赖动力学过程。我们针对单条高斯Glauber动力学轨迹构成的数据展开结构学习研究，并开发了两种互补方法。第一种是基于恰当设计的相关性检验来揭示边结构的局部边估计器，该估计器无需等待链混合即可工作，并支持极其高效的并行逐边实现。第二种方法采用预热/稀释简化策略：在Dobrushin收缩条件下，我们证明适当子采样的高斯Gibbs轨迹在全变差距离上接近独立同分布乘积样本，从而允许将标准独立同分布高斯图模型学习器作为黑箱使用。本文的关键技术贡献（可能具有独立研究价值）是通过结合Wasserstein收缩与近似Lipschitz平滑论证，推导出随机扫描高斯Gibbs采样器的高维全变差界。我们证明了两种方法的有限样本恢复保证，建立了观测时间的信息论下界，并实证比较了由此产生的样本-计算权衡关系。