# Hierarchical learning, forecasting coherent spatio-temporal individual and aggregated building loads

arXiv: https://arxiv.org/abs/2301.12967 · HTML: https://mlsanity.com/paper/2301.12967/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 9 of its 53 references that are in the map.
- First posted on arXiv 30 Jan 2023.

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

- [Constrained Convolutional Neural Networks for Weakly Supervised Segmentation](https://mlsanity.com/paper/1506.03648/) (2015)
- [Forecast Evaluation for Data Scientists: Common Pitfalls and Best Practices](https://mlsanity.com/paper/2203.10716/) (2022)
- [Constrained Deep Weak Supervision for Histopathology Image Segmentation](https://mlsanity.com/paper/1701.00794/) (2017)
- [Imposing Hard Constraints on Deep Networks: Promises and Limitations](https://mlsanity.com/paper/1706.02025/) (2017)
- [Physics-constrained Deep Learning of Multi-zone Building Thermal Dynamics](https://mlsanity.com/paper/2011.05987/) (2020)
- [A machine learning approach for forecasting hierarchical time series](https://mlsanity.com/paper/2006.00630/) (2020)
- [Hierarchical forecast reconciliation with machine learning](https://mlsanity.com/paper/2006.02043/) (2020)
- [Cross-temporal forecast reconciliation: Optimal combination method and heuristic alternatives](https://mlsanity.com/paper/2006.08570/) (2020)
- [Convex Banding of the Covariance Matrix](https://mlsanity.com/paper/1405.6210/) (2014)

## Built on by (most cited first, 2 of 2)

- [Forecasting time series with constraints](https://mlsanity.com/paper/2502.10485/) (2025)
- [Structural hierarchical learning for energy networks](https://mlsanity.com/paper/2302.03978/) (2023)

## Abstract (arXiv)

Optimal decision-making compels us to anticipate the future at different horizons. However, in many domains connecting together predictions from multiple time horizons and abstractions levels across their organization becomes all the more important, else decision-makers would be planning using separate and possibly conflicting views of the future. This notably applies to smart grid operation. To optimally manage energy flows in such systems, accurate and coherent predictions must be made across varying aggregation levels and horizons. With this work, we propose a novel multi-dimensional hierarchical forecasting method built upon structurally-informed machine-learning regressors and established hierarchical reconciliation taxonomy. A generic formulation of multi-dimensional hierarchies, reconciling spatial and temporal hierarchies under a common frame is initially defined. Next, a coherency-informed hierarchical learner is developed built upon a custom loss function leveraging optimal reconciliation methods. Coherency of the produced hierarchical forecasts is then secured using similar reconciliation technics. The outcome is a unified and coherent forecast across all examined dimensions. The method is evaluated on two different case studies to predict building electrical loads across spatial, temporal, and spatio-temporal hierarchies. Although the regressor natively profits from computationally efficient learning, results displayed disparate performances, demonstrating the value of hierarchical-coherent learning in only one setting. Yet, supported by a comprehensive result analysis, existing obstacles were clearly delineated, presenting distinct pathways for future work. Overall, the paper expands and unites traditionally disjointed hierarchical forecasting methods providing a fertile route toward a novel generation of forecasting regressors.