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.

不规则采样的多变量时间序列是各种应用领域中普遍存在的现象，本文提出了一种名为时间参数化卷积神经网络（TPCNN）的新型神经网络架构，特别适用于处理不规则时间序列数据，我们对 TPCNN 进行了插值和分类任务的实验评估并与其他最先进方法进行了比较，结果表明 TPCNN 模型不仅具有竞争性的性能，而且比其他方法更高效。同时，该架构利用可学习的时间函数的组合，提高了网络性能和序列输入的可解释性，在该领域中首次应用卷积操作。

基于时间参数化的卷积神经网络用于不规则采样的时间序列

Time-Parameterized Convolutional Neural Networks for Irregularly Sampled  Time Series

Irregularly sampled multivariate time series are ubiquitous in various
fields, particularly in healthcare, and exhibit two key characteristics:
intra-series irregularity and inter-series discrepancy. Intra-series
irregularity refers to the fact that time-series signals are often recorded at
irregular intervals, while inter-series discrepancy refers to the significant
variability in sampling rates among diverse series. However, recent advances in
irregular time series have primarily focused on addressing intra-series
irregularity, overlooking the issue of inter-series discrepancy. To bridge this
gap, we present Warpformer, a novel approach that fully considers these two
characteristics. In a nutshell, Warpformer has several crucial designs,
including a specific input representation that explicitly characterizes both
intra-series irregularity and inter-series discrepancy, a warping module that
adaptively unifies irregular time series in a given scale, and a customized
attention module for representation learning. Additionally, we stack multiple
warping and attention modules to learn at different scales, producing
multi-scale representations that balance coarse-grained and fine-grained
signals for downstream tasks. We conduct extensive experiments on widely used
datasets and a new large-scale benchmark built from clinical databases. The
results demonstrate the superiority of Warpformer over existing
state-of-the-art approaches.

Warpformer 是一种全新的方法，考虑了多元时间序列的内部不规则性和不同序列之间的差异，通过设计特殊的输入表示，变形模块和注意力模块，生成多尺度表示，用于各种下游任务。