AI 中文总结
该研究提出随机块奥恩斯坦-乌伦贝克（SBOU）过程模型，开发出一种社区检测算法，在特定渐近 regime 下可实现一致的社区恢复，并通过 RE-Europe 风电容量数据集验证了方法的有效性。
AI 中文摘要
我们提出了随机块奥恩斯坦-乌伦贝克（SBOU）过程，这是一种连续时间多元模型，其漂移矩阵编码了各成分之间的潜在群体结构。我们的主要贡献是一种社区检测算法，在结合了密集采样、长跨度和高维渐近的 regime 中，其错误分类比例收敛到零。据我们所知，这是离散观测的连续时间多元模型中潜在群体恢复的首个此类一致性结果。作为关键中间结果，我们在相同 regime 中建立了离散观测的漂移矩阵最大似然估计量的一致性，从而扩展了高维 Lévy 驱动奥恩斯坦-乌伦贝克的文献。对于实际应用，我们开发了一种可行的模型选择程序，用于估计漂移矩阵的支撑集，该程序支持数据驱动选择潜在群体的数量。SBOU 框架可视为离散时间随机块 VAR 模型的连续时间推广，允许组间存在正负动态交互，而非仅正交互。我们在 RE-Europe 风电容量数据集上说明了该方法，并恢复了与地理基准一致的国家层面分组。
英文摘要
We propose the stochastic block Ornstein-Uhlenbeck (SBOU) process, a continuous-time multivariate model in which the drift matrix encodes a latent group structure among its components. Our main contribution is a community-detection algorithm whose misclassification proportion converges to zero in a regime combining infill, long-span, and high-dimensional asymptotics. To our knowledge, this is the first consistency result of this kind for latent group recovery in a discretely observed continuous-time multivariate model. As a key intermediate result, we establish consistency of the discretely observed maximum likelihood estimator of the drift matrix in the same regime, thereby extending the high-dimensional Lévy-driven Ornstein-Uhlenbeck literature. For practical implementation, we develop a feasible model-selection procedure for estimating the support of the drift matrix, which enables data-driven selection of the number of latent groups. The SBOU framework can be viewed as a continuous-time generalisation of the discrete-time stochastic-block VAR model, allowing for both positive and negative dynamic interactions between groups as opposed to only positive. We illustrate the methodology on the RE-Europe wind-capacity dataset and recover a country-level grouping consistent with the geographic benchmark.
CommentsNN pages, 9 figures
