Probabilistic Forecasting with Coherent Aggregation
Geoffrey Négiar Ruijun Ma O. Nangba Meetei Mengfei Cao Michael W. Mahoney
Obtaining accurate probabilistic forecasts while respecting hierarchical
information is an important operational challenge in many applications, perhaps
most obviously in energy management, supply chain planning, and resource
allocation. The basic challenge, especially for multivariate forecasting, is
that forecasts are often required to be coherent with respect to the
hierarchical structure. In this paper, we propose a new model which leverages a
factor model structure to produce coherent forecasts by construction. This is a
consequence of a simple (exchangeability) observation: permuting
\textit{}base-level series in the hierarchy does not change their aggregates.
Our model uses a convolutional neural network to produce parameters for the
factors, their loadings and base-level distributions; it produces samples which
can be differentiated with respect to the model's parameters; and it can
therefore optimize for any sample-based loss function, including the Continuous
Ranked Probability Score and quantile losses. We can choose arbitrary
continuous distributions for the factor and the base-level distributions. We
compare our method to two previous methods which can be optimized end-to-end,
while enforcing coherent aggregation. Our model achieves significant
improvements: between $11.8-41.4\%$ on three hierarchical forecasting datasets.
We also analyze the influence of parameters in our model with respect to
base-level distribution and number of factors.