BayOTIDE：基于函数分解的贝叶斯在线多元时间序列插补
BayOTIDE: Bayesian Online Multivariate Time series Imputation with functional decomposition
AI总结：
针对多元时间序列插补中局部建模、不规则采样和离线学习的局限性，提出BayOTIDE框架，利用高斯过程与随机微分方程进行函数分解，实现可扩展的在线推理，支持任意时间戳插补并提供不确定性量化。
摘要：
在交通和能源等现实场景中，大量带有缺失值和噪声的时间序列数据被广泛观察到，甚至是不规则采样。。尽管已提出许多插补方法，但大多数方法在局部时间范围上工作，这意味着模型通过将长序列分割为固定大小的块来训练。。这种局部时间范围会使模型忽略全局趋势或周期性模式。。更重要的是，几乎所有方法都假设观测值是在规则时间戳上采样的，无法处理由不同应用产生的复杂不规则采样时间序列（irregularly sampled time series）。第三，大多数现有方法以离线方式学习（learned in an offline manner），因此不适用于许多具有快速到达流数据的应用。。为克服这些局限性，我们提出了BayOTIDE：基于函数分解的贝叶斯在线多元时间序列插补（Bayesian Online Multivariate Time series Imputation with functional decomposition）。我们将多元时间序列视为具有不同模式的低秩时间因子组的加权组合（weighted combination of groups of low-rank temporal factors）。我们应用一组具有不同核函数作为函数先验的高斯过程来拟合这些因子。。为了提高计算效率，我们通过构造一个等价随机微分方程将GPs转换为状态空间先验，开发了一种可扩展的在线推理算法。。所提出的方法不仅能处理任意时间戳上的插补，还在下游应用中提供不确定性量化和可解释性（uncertainty quantification and interpretability）。我们在合成数据集和真实数据集上评估了我们的方法。。代码发布在https://github.com/xuangu-fang/BayOTIDE。
英文摘要：
In real-world scenarios like traffic and energy, massive time-series data with missing values and noises are widely observed, even sampled irregularly. While many imputation methods have been proposed, most of them work with a local horizon, which means models are trained by splitting the long sequence into batches of fit-sized patches. This local horizon can make models ignore global trends or periodic patterns. More importantly, almost all methods assume the observations are sampled at regular time stamps, and fail to handle complex irregular sampled time series arising from different applications. Thirdly, most existing methods are learned in an offline manner. Thus, it is not suitable for many applications with fast-arriving streaming data. To overcome these limitations, we propose BayOTIDE: Bayesian Online Multivariate Time series Imputation with functional decomposition. We treat the multivariate time series as the weighted combination of groups of low-rank temporal factors with different patterns. We apply a group of Gaussian Processes (GPs) with different kernels as functional priors to fit the factors. For computational efficiency, we further convert the GPs into a state-space prior by constructing an equivalent stochastic differential equation (SDE), and developing a scalable algorithm for online inference. The proposed method can not only handle imputation over arbitrary time stamps, but also offer uncertainty quantification and interpretability for the downstream application. We evaluate our method on both synthetic and real-world datasets.We release the code at {https://github.com/xuangu-fang/BayOTIDE}
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
