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

arXiv: https://arxiv.org/abs/2206.07940 · HTML: https://mlsanity.com/paper/2206.07940/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 36 references that are in the map.
- First posted on arXiv 16 Jun 2022.

## Builds on (most cited first, 12 of 12)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [On the Properties of Neural Machine Translation: Encoder-Decoder Approaches](https://mlsanity.com/paper/1409.1259/) (2014)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Accurate Uncertainties for Deep Learning Using Calibrated Regression](https://mlsanity.com/paper/1807.00263/) (2018)
- [Structured Inference Networks for Nonlinear State Space Models](https://mlsanity.com/paper/1609.09869/) (2016)
- [On a generalization of the Jensen-Shannon divergence and the JS-symmetrization of distances relying on abstract means](https://mlsanity.com/paper/1904.04017/) (2019)
- [The Functional Neural Process](https://mlsanity.com/paper/1906.08324/) (2019)
- [Learning Interpretable Deep State Space Model for Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2102.00397/) (2021)
- [Simultaneously Reconciled Quantile Forecasting of Hierarchically Related Time Series](https://mlsanity.com/paper/2102.12612/) (2021)
- [CAMul: Calibrated and Accurate Multi-view Time-Series Forecasting](https://mlsanity.com/paper/2109.07438/) (2021)
- [When in Doubt: Neural Non-Parametric Uncertainty Quantification for Epidemic Forecasting](https://mlsanity.com/paper/2106.03904/) (2021)
- [Probabilistic forecast reconciliation under the Gaussian framework](https://mlsanity.com/paper/2103.11128/) (2021)

## Built on by (most cited first, 4 of 4)

- [Large Scale Hierarchical Industrial Demand Time-Series Forecasting incorporating Sparsity](https://mlsanity.com/paper/2407.02657/) (2024)
- [Hierarchically Coherent Multivariate Mixture Networks](https://mlsanity.com/paper/2305.07089/) (2023)
- [Hierarchical Industrial Demand Forecasting with Temporal and Uncertainty Explanations](https://mlsanity.com/paper/2603.06555/) (2026)
- [Exactness Matters for Physical Rule Enforcement](https://mlsanity.com/paper/2605.08285/) (2026)

## Abstract (arXiv)

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%.