时间Wasserstein插补：一种通用的时间序列插补方法
Temporal Wasserstein Imputation: A Versatile Method for Time Series Imputation
AI总结：
本文提出了一种完全非参数化的时间Wasserstein插补方法，用于处理具有任意非系统性缺失模式的时间序列，能够减轻分布偏差并支持下游统计分析，理论和数值实验验证了其有效性和实用性。
摘要：
缺失数据会显著阻碍标准时间序列分析，但它们在实际应用中频繁发生。在本文中，我们介绍了时间Wasserstein插补，这是一种用于插补时间序列中缺失数据的新方法。与大多数现有技术不同，我们的方法是完全非参数化的，避免了在插补前进行模型设定的需要，使其即使对于具有非线性动态的经验应用也很适用。其有原则的算法实现能够无缝处理具有任何非系统性缺失模式的单变量或多变量时间序列。此外，缺失条目的合理范围和辅助信息（如box constraints）可以轻松纳入。另外，我们的方法减轻了许多现有方法中常见的分布偏差，确保使用插补后的序列进行更可靠的下游统计分析。我们建立了交替最小化算法向临界点的收敛性。我们还提供了可以识别底层时间序列边际分布的条件。包括涵盖线性和非线性时间序列的广泛模拟以及对现实世界地下水数据集的分析在内的数值实验，证实了所提出方法的实用性。
英文摘要：
Missing data can significantly hamper standard time series analysis, yet they occur frequently in applications. In this paper, we introduce temporal Wasserstein imputation, a novel method for imputing missing data in time series. Unlike most existing techniques, our approach is fully nonparametric, circumventing the need for model specification prior to imputation, making it suitable for empirical applications even with nonlinear dynamics. Its principled algorithmic implementation can seamlessly handle univariate or multivariate time series with any non-systematic missing pattern. In addition, the plausible range and side information of the missing entries (such as box constraints) can easily be incorporated. Furthermore, our method mitigates the distributional bias common among many existing approaches, ensuring more reliable downstream statistical analysis using the imputed series. We establish the convergence of an alternating minimization algorithm to critical points. We also provide conditions under which the marginal distributions of the underlying time series can be identified. Numerical experiments, including extensive simulations covering both linear and nonlinear time series and an analysis on a real-world groundwater dataset, corroborate the practical usefulness of the proposed method.
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