Irregularly sampled multivariate time series are ubiquitous in several application domains, leading to sparse, not fully-observed and non-aligned observations across different variables. Standard sequential neural network architectures, such as recurrent neural networks (RNNs) and convolutional neural networks (CNNs), consider regular spacing between observation times, posing significant challenges to irregular time series modeling. While most of the proposed architectures incorporate RNN variants to handle irregular time intervals, convolutional neural networks have not been adequately studied in the irregular sampling setting. In this paper, we parameterize convolutional layers by employing time-explicitly initialized kernels. Such general functions of time enhance the learning process of continuous-time hidden dynamics and can be efficiently incorporated into convolutional kernel weights. We, thus, propose the time-parameterized convolutional neural network (TPCNN), which shares similar properties with vanilla convolutions but is carefully designed for irregularly sampled time series. We evaluate TPCNN on both interpolation and classification tasks involving real-world irregularly sampled multivariate time series datasets. Our experimental results indicate the competitive performance of the proposed TPCNN model which is also significantly more efficient than other state-of-the-art methods. At the same time, the proposed architecture allows the interpretability of the input series by leveraging the combination of learnable time functions that improve the network performance in subsequent tasks and expedite the inaugural application of convolutions in this field.

翻译：非均匀采样的多元时间序列在多个应用领域中普遍存在，导致不同变量间出现稀疏、未完全观测及非对齐的观测数据。标准的序列神经网络架构（如循环神经网络（RNN）和卷积神经网络（CNN））假设观测时间间隔固定，这给非均匀时间序列建模带来了重大挑战。尽管多数现有架构采用RNN变体处理不规则时间间隔，但卷积神经网络在非均匀采样场景下的研究尚不充分。本文通过采用时间显式初始化的核函数对卷积层进行参数化。这种通用时间函数可增强连续时间隐态动力学学习过程，并能高效集成至卷积核权重中。由此，我们提出时序参数化卷积神经网络（TPCNN），该模型虽与标准卷积具有相似特性，但专为非均匀采样时间序列设计。我们在涉及真实世界非均匀采样多元时间序列数据集的内插与分类任务上评估TPCNN。实验结果表明，所提出的TPCNN模型性能具有竞争力，且显著优于当前其他先进方法。同时，该架构通过整合可学习时间函数组合增强输入序列的可解释性，既提升了后续任务的网络性能，也推动了卷积神经网络在该领域的首次应用。