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

TL;DR

This paper introduces DILATE, a novel loss function for training deep neural networks in time series forecasting, especially for non-stationary signals, improving shape and temporal change prediction over traditional methods.

Contribution

The paper proposes DILATE, a new differentiable loss function that enhances deep time series forecasting by explicitly modeling shape and time distortions, with a custom back-propagation implementation.

Findings

DILATE outperforms standard MSE and DTW-based losses on non-stationary datasets.

It improves shape and temporal change detection in forecasts.

Applicable to various neural network architectures, including recurrent and fully connected models.

Abstract

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 DILATE (DIstortion Loss including shApe and TimE), a new objective function for training deep neural networks. DILATE 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 DILATE, 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 DILATE compared to models trained with the standard Mean Squared Error (MSE) loss function, and also to DTW and variants. DILATE 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.