We study conditions that allow accurate graphical model selection from non-stationary data. The observed data is modelled as a vector-valued zero-mean Gaussian random process whose samples are uncorrelated but have different covariance matrices. This model contains as special cases the standard setting of i.i.d. samples as well as the case of samples forming a stationary time series. More generally, our approach applies to any data for which efficient decorrelation transforms, such as the Fourier transform for stationary time series, are available. By analyzing a conceptually simple model selection method, we derive a sufficient condition on the required sample size for accurate graphical model selection based on non-stationary data.

中文翻译：

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从非平稳样本中选择图形模型的样本复杂度

我们研究允许从非平稳数据中准确选择图形模型的条件。观察到的数据被建模为向量值零均值高斯随机过程，其样本不相关但具有不同的协方差矩阵。该模型包含作为特殊情况的 iid 样本的标准设置以及样本形成平稳时间序列的情况。更一般地说，我们的方法适用于任何可以使用有效去相关变换（例如固定时间序列的傅立叶变换）的数据。通过分析概念上简单的模型选择方法，我们推导出了基于非平稳数据进行精确图形模型选择所需样本量的充分条件。