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 gap 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
significantly better 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 是一种完全概率性的分层预测模型，通过灵活的概率贝叶斯方法和引入新颖的分布一致性正则化，能够从分层关系中学习整个预测分布，从而实现鲁棒和校准的预测，并适应具有不同分层一致性的数据集。评估结果显示，PROFHiT 在准确性方面表现出了 41-88% 的改进，并且具有更好的校准性。此外，由于对整个分布的一致性建模，当输入时间序列数据缺失 10% 时，PROFHiT 仍然能够提供可靠的预测，而其他方法的性能会下降超过 70%。

刚性的伤害：概率层次时间序列预测的软一致性正则化

When Rigidity Hurts: Soft Consistency Regularization for Probabilistic  Hierarchical Time Series Forecasting

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。