Probabilistic forecasting consists in predicting a distribution of possible future outcomes. In this paper, we address this problem for non-stationary time series, which is very challenging yet crucially important. We introduce the STRIPE model for representing structured diversity based on shape and time features, ensuring both probable predictions while being sharp and accurate. STRIPE is agnostic to the forecasting model, and we equip it with a diversification mechanism relying on determinantal point processes (DPP). We introduce two DPP kernels for modelling diverse trajectories in terms of shape and time, which are both differentiable and proved to be positive semi-definite. To have an explicit control on the diversity structure, we also design an iterative sampling mechanism to disentangle shape and time representations in the latent space. Experiments carried out on synthetic datasets show that STRIPE significantly outperforms baseline methods for representing diversity, while maintaining accuracy of the forecasting model. We also highlight the relevance of the iterative sampling scheme and the importance to use different criteria for measuring quality and diversity. Finally, experiments on real datasets illustrate that STRIPE is able to outperform state-of-the-art probabilistic forecasting approaches in the best sample prediction.

Summary and Contributions: In this paper, the authors deal with the time-series forecasting problem, particularly focusing on the probabilistic setting where multiple future outcomes are estimated. In the introduction they clearly present the main drawbacks of methods available in the literature: deep learning-based models are accurate and can capture sharp variations w.r.t. the groundtruth, but they are not able to propose multiple and diverse outcomes for a given input time-series; probabilistic methods can effectively solve the diversity issue but lose the sharpness of the predicted outcomes, and do not have control over the diversity. The authors introduce a method, called STRIPE, to overcome these problems: they use a loss function based on determinantal point processes (DPP) which exploits two kernels (K_shape and K_time) purposefully designed for controlling the shape and temporal diversity; moreover since K_shape and K_time can not be simply added and optimized jointly, the authors introduce an iterative process to model independently the variations in shape and time. Then, they consider the DILATE quality loss and perform an ablation study of various diversity losses, and finally they perform a comparison with state-of-the-art techniques on both synthetic and real world datasets.