$\clubsuit$ CLOVER $\clubsuit$: Probabilistic Forecasting with Coherent Learning Objective Reparameterization

Obtaining accurate probabilistic forecasts is an operational challenge in many applications, such as energy management, climate forecasting, supply chain planning, and resource allocation. Many of these applications present a natural hierarchical structure over the forecasted quantities; and forecasting systems that adhere to this hierarchical structure are said to be coherent. Furthermore, operational planning benefits from the accuracy at all levels of the aggregation hierarchy. However, building accurate and coherent forecasting systems is challenging: classic multivariate time series tools and neural network methods are still being adapted for this purpose. In this paper, we augment an MQForecaster neural network architecture with a modified multivariate Gaussian factor model that achieves coherence by construction. The factor model samples can be differentiated with respect to the model parameters, allowing optimization on arbitrary differentiable learning objectives that align with the forecasting system's goals, including quantile loss and the scaled Continuous Ranked Probability Score (CRPS). We call our method the Coherent Learning Objective Reparametrization Neural Network (CLOVER). In comparison to state-of-the-art coherent forecasting methods, CLOVER achieves significant improvements in scaled CRPS forecast accuracy, with average gains of 15%, as measured on six publicly-available datasets.