Irregularly sampled time series forecasting, characterized by non-uniform intervals, is prevalent in practical applications. However, previous research have been focused on regular time series forecasting, typically relying on transformer architectures. To extend transformers to handle irregular time series, we tackle the positional embedding which represents the temporal information of the data. We propose CTLPE, a method learning a continuous linear function for encoding temporal information. The two challenges of irregular time series, inconsistent observation patterns and irregular time gaps, are solved by learning a continuous-time function and concise representation of position. Additionally, the linear continuous function is empirically shown superior to other continuous functions by learning a neural controlled differential equation-based positional embedding, and theoretically supported with properties of ideal positional embedding. CTLPE outperforms existing techniques across various irregularly-sampled time series datasets, showcasing its enhanced efficacy.

本研究解决了不规则采样时间序列预测中存在的间隔不均问题，建立了更加有效的模型。提出的CTLPE方法通过学习连续线性函数来编码时间信息，成功应对观察模式不一致和时间间隔不规则的挑战。实验结果表明，CTLPE在多个不规则采样时间序列数据集上表现优越，具有重要的实际应用潜力。

不规则时间序列预测的连续时间线性位置嵌入