Observations made in continuous time are often irregular and contain the missing values across different channels. One approach to handle the missing data is imputing it using splines, by fitting the piecewise polynomials to the observed values. We propose using the splines as an input to a neural network, in particular, applying the transformations on the interpolating function directly, instead of sampling the points on a grid. To do that, we design the layers that can operate on splines and which are analogous to their discrete counterparts. This allows us to represent the irregular sequence compactly and use this representation in the downstream tasks such as classification and forecasting. Our model offers competitive performance compared to the existing methods both in terms of the accuracy and computation efficiency.
翻译:连续时间进行的观测往往不规则,并包含不同渠道缺失的值。处理缺失数据的一种方法是使用样条对数据进行估算,将片断的多数值与观察到的值相匹配。我们提议使用样条作为神经网络的一种输入,特别是直接对内插功能进行转换,而不是对网格上的点进行取样。为了做到这一点,我们设计了可以在样条上运行的层,这些层与其离散的对等层相似。这样,我们就能够集中代表不规则的序列,并在分类和预测等下游任务中使用这种代表。我们的模型在准确性和计算效率两方面都与现有方法相比具有竞争性的性能。