# Dynamic Combination of Heterogeneous Models for Hierarchical Time Series

arXiv: https://arxiv.org/abs/2112.11669 · HTML: https://mlsanity.com/paper/2112.11669/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 43 references that are in the map.
- First posted on arXiv 22 Dec 2021.

## Builds on (most cited first, 9 of 9)

- [Outrageously Large Neural Networks: The Sparsely-Gated Mixture-of-Experts Layer](https://mlsanity.com/paper/1701.06538/) (2017)
- [DeepAR: Probabilistic Forecasting with Autoregressive Recurrent Networks](https://mlsanity.com/paper/1704.04110/) (2017)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Neural Spline Flows](https://mlsanity.com/paper/1906.04032/) (2019)
- [Functional Variational Bayesian Neural Networks](https://mlsanity.com/paper/1903.05779/) (2019)
- [Merlion: A Machine Learning Library for Time Series](https://mlsanity.com/paper/2109.09265/) (2021)
- [Simultaneously Reconciled Quantile Forecasting of Hierarchically Related Time Series](https://mlsanity.com/paper/2102.12612/) (2021)
- [Autoregressive Quantile Flows for Predictive Uncertainty Estimation](https://mlsanity.com/paper/2112.04643/) (2021)
- [Improving Output Uncertainty Estimation and Generalization in Deep Learning via Neural Network Gaussian Processes](https://mlsanity.com/paper/1707.05922/) (2017)

## Built on by (most cited first, 3 of 3)

- [Massively Multimodal Foundation Models: A Framework for Capturing Interactions with Specialized Mixture-of-Experts](https://mlsanity.com/paper/2509.25678/) (2025)
- [Let Experts Feel Uncertainty: A Multi-Expert Label Distribution Approach to Probabilistic Time Series Forecasting](https://mlsanity.com/paper/2602.04678/) (2026)
- [Hierarchical Industrial Demand Forecasting with Temporal and Uncertainty Explanations](https://mlsanity.com/paper/2603.06555/) (2026)

## Abstract (arXiv)

We introduce a framework to dynamically combine heterogeneous models called textttDYCHEM, which forecasts a set of time series that are related through an aggregation hierarchy. Different types of forecasting models can be employed as individual ``experts'' so that each model is tailored to the nature of the corresponding time series. textttDYCHEM learns hierarchical structures during the training stage to help generalize better across all the time series being modeled and also mitigates coherency issues that arise due to constraints imposed by the hierarchy. To improve the reliability of forecasts, we construct quantile estimations based on the point forecasts obtained from combined heterogeneous models. The resulting quantile forecasts are coherent and independent of the choice of forecasting models. We conduct a comprehensive evaluation of both point and quantile forecasts for hierarchical time series (HTS), including public data and user records from a large financial software company. In general, our method is robust, adaptive to datasets with different properties, and highly configurable and efficient for large-scale forecasting pipelines.