This paper addresses the problem of time series forecasting for non-stationary signals and multiple future steps prediction. To handle this challenging task, we introduce the Shape and Time Distortion Loss (STDL), a new objective function dedicated to training deep neural networks. STDL aims at accurately predicting sudden changes, and explicitly incorporates two terms supporting precise shape and temporal change detection. We introduce a differentiable loss function suitable for training deep neural nets, and provide a custom back-prop implementation for speeding up optimization. We also introduce a variant of STDL, which provides a smooth generalization of temporally-constrained Dynamic Time Warping (DTW). Experiments carried out on various non-stationary datasets reveal the very good behaviour of STDL compared to models trained with the standard Mean Squared Error (MSE) loss function, and also to DTW and variants. STDL is also agnostic to the choice of the model, and we highlight its benefit for training fully connected networks as well as specialized recurrent architectures, showing its capacity to improve over state-of-the-art trajectory forecasting approaches.

本文提出一种针对非平稳信号和多个未来时间步长预测的时间序列预测方法DILATE，改进了深度神经网络训练的目标函数，支持精确形状和时间变化检测，并提供了用于加速优化的自定义反向传播实现，证明了DILATE相较于标准的均方误差(MSE)损失函数和DTW模型的优异性能。

训练深度时间序列预测模型时的 形状与时间畸变损失

训练深度时间序列预测模型时的形状与时间畸变损失