Imputing missing data in Building Internet of Things (BIoT) poses a significant challenge due to the complex multi-dimensional variations and the inevitable occurrence of long-span missing gaps during maintenance or repair periods. In this paper, we introduce ODE-MI, a novel neural ODE-guided Multiple Imputation framework tailored for BIoT time series with high missing gaps. ODE-MI integrates shapelet-wise convolution, node embeddings, and dynamic graph embeddings with transfer delay to capture compound spatio-temporal (ST) volatilities, trends, and high-order impact transfer. Our contributions include the design of a multi-faceted backbone network capable of capturing long-distance ST characteristics in BIoT, and the development of the ODE-MI framework to handle long-term missing data within networked dynamic attributes. Empirical assessments using open datasets demonstrate that ODE-MI outperforms existing imputation methods, especially in scenarios involving continuous long-span missing gaps.

An acyclic model, often depicted as a directed acyclic graph (DAG), has been widely employed to represent directional causal relations among collected nodes. In this article, we propose an efficient method to learn linear non-Gaussian DAG in high dimensional cases, where the noises can be of any continuous non-Gaussian distribution. The proposed method leverages the concept of topological layer to facilitate the DAG learning, and its theoretical justification in terms of exact DAG recovery is also established under mild conditions. Particularly, we show that the topological layers can be exactly reconstructed in a bottom-up fashion, and the parent-child relations among nodes can also be consistently established. The established asymptotic DAG recovery is in sharp contrast to that of many existing learning methods assuming parental faithfulness or ordered noise variances. The advantage of the proposed method is also supported by the numerical comparison against some popular competitors in various simulated examples as well as a real application on the global spread of COVID-19.