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In contemporary industrial settings, the loss of collected data is a common issue, frequently caused by sensor degradation, adverse working conditions, electrical interference during motor startup, and network malfunctions. Consequently, the robust imputation of missing time-series data is a crucial component of any data-driven application. However, a significant gap exists as many state-of-the-art imputation methods are noncausal, leveraging future information to interpolate missing values. This characteristic renders them unsuitable for real-time industrial online monitoring, which demands strict adherence to temporal causality. To address this challenge, this article introduces CondVS4, a novel causal generative model specifically designed for online imputation. CondVS4 guarantees causality by performing posterior inference for missing variables conditioned solely on historical and current observations. Through extensive experiments on three real-world industrial datasets under various missingness patterns, CondVS4 demonstrates superior performance compared to a wide range of baseline methods. Furthermore, we show that our model substantially enhances the reliability of a downstream soft-sensing task, proving its effectiveness and practical value for online industrial applications.
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Li et al. (2026) studied this question.
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