Shape and Time Distortion Loss for Training Deep Time Series Forecasting Models
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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.
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