发表机构
University of Hamburg; Graduate School of Mathematical Sciences, University of Tokyo; CREST, Japan Science and Technology Agency; European Centre for Algorithmic Transparency（汉堡大学; 东京大学大学院数学系研究科; 日本科学技术振兴机构 CREST; 欧洲算法透明中心）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对小噪声高维网络随机微分方程，提出最小距离估计框架，分解误差并给出非渐近界，结合自适应Lasso实现一致图恢复。
AI 中文摘要
我们考虑在小噪声、高维情形下的网络随机微分方程推断，其中扩散系数随 $\ep\to0$ 消失，而网络规模和参数维度可能发散。我们基于一个确定性测量模型建立最小距离估计框架，该模型可省略漂移中的干扰项，并推导出一个非渐近误差界，将估计误差分解为随机波动、干扰差异和可辨识性项。对于重复测量下的线性参数化交互模型，我们以图连通性和噪声水平给出了干扰差异和可辨识性间隙的显式非渐近界。在适当的混合和平衡条件下，这导出了估计量的一致性和收敛速率。我们进一步通过自适应Lasso研究图恢复。惩罚估计量被证明继承了初步估计量的速率，并一致地恢复真实的交互图。这些结果为具有干扰漂移分量的高维网络随机微分方程中的参数估计和边选择提供了理论基础。
英文摘要
We consider inference for network stochastic differential equations in a small-noise, high-dimensional regime, where the diffusion coefficient vanishes with $\ep\to0$ while the network size and parameter dimension may diverge. We develop a minimum-distance estimation framework based on a deterministic measurement model that may omit nuisance terms in the drift, and derive a non-asymptotic error bound decomposing the estimation error into stochastic fluctuation, nuisance discrepancy, and identifiability terms. For a linearly parametrized interaction model under repeated measurements, we obtain explicit non-asymptotic bounds on the nuisance discrepancy and the identifiability gap in terms of graph connectivity and noise level. Under suitable mixing and balance conditions, this yields consistency and convergence rates for the estimator. We further study graph recovery via adaptive Lasso. The penalized estimator is shown to inherit the rate of the preliminary estimator and to recover the true interaction graph consistently. These results provide a theoretical basis for parameter estimation and edge selection in high-dimensional network SDEs with nuisance drift components.
