Probabilistic hierarchical time-series forecasting is an important variant of
time-series forecasting, where the goal is to model and forecast multivariate
time-series that have underlying hierarchical relations. Most methods focus on
point predictions and do not provide well-calibrated probabilistic forecasts
distributions. Recent state-of-art probabilistic forecasting methods also
impose hierarchical relations on point predictions and samples of distribution
which does not account for coherency of forecast distributions. Previous works
also silently assume that datasets are always consistent with given
hierarchical relations and do not adapt to real-world datasets that show
deviation from this assumption. We close both these gaps and propose PROFHIT,
which is a fully probabilistic hierarchical forecasting model that jointly
models forecast distribution of entire hierarchy. PROFHIT uses a flexible
probabilistic Bayesian approach and introduces a novel Distributional Coherency
regularization to learn from hierarchical relations for entire forecast
distribution that enables robust and calibrated forecasts as well as adapt to
datasets of varying hierarchical consistency. On evaluating PROFHIT over wide
range of datasets, we observed 41-88% better performance in accuracy and
calibration. Due to modeling the coherency over full distribution, we observed
that PROFHIT can robustly provide reliable forecasts even if up to 10% of input
time-series data is missing where other methods' performance severely degrade
by over 70%.

PROFHIT 提出了一种全概率层次预测模型，它通过引入 Distributional Coherency 正则化来从层次关系中学习完整预测分布，从而实现鲁棒和校准的预测，能够适应变化的层次一致性，并在广泛的数据集上获得了比其他方法高达 41-88％的准确性和校准性能提升，在数据缺失时仍能提供可靠的预测。