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

Abstract

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. Such hierarchical structures are said to be coherent when values at different scales are equal when brought to the same level, else would need to be reconciled. 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, granting decision-makers a common view of the future serving aligned decision-making. The method is evaluated on two different case studies to predict building electrical loads across spatial, temporal, and spatio-temporal hierarchies, benchmarked against base and multi-task regressors. Although the regressor natively profits from computationally efficient learning thanks to the unification of independent forecasts into a global multi-task model, 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. Particularly, investigating reduced number of model weights and varying native multi-output regressors can tackle the two preeminent challenges that are the curse of dimensionality and coherency-learning complications from scaled trees respectively. Overall, the paper expands and unites traditionally disjointed hierarchical forecasting methods providing a fertile route toward a novel generation of forecasting regressors.

Structural hierarchical learning for energy networks

“…Thereby, recent work suggested bridging forecasting with the coherency requirements of the reconciliation phase [21]. The approach proposes (i) a unique hierarchical forecasting model, providing a global overview of information across the hierarchy to the regressor, while (ii) including coherency requirements within its learning process.…”

“…The more recently proposed hierarchical learning method [21] intended to unify hierarchical forecasts together while exploiting the coherency requirement of produced predictions. The approach builds on the presented formulations of optimal reconciliation, see Eq.…”

“…To propose a regressor that is robust to scale differences and avoids normalization requirements and its subsequent identified faulty-coherency learning [21], we leverage the Mean Structurally-Scaled Square Error (MS3E) defined in Ref. [21] for the definition of the learning loss function.…”

“…To propose a regressor that is robust to scale differences and avoids normalization requirements and its subsequent identified faulty-coherency learning [21], we leverage the Mean Structurally-Scaled Square Error (MS3E) defined in Ref. [21] for the definition of the learning loss function. Structurally scaled errors must, indeed, be considered in hierarchical forecasting as produced predictions will possess major scale differences inherent to hierarchical structures.…”

“…Designing hierarchical loss functions notably differentiates itself in this way from the scaled multi-output regressors of Ref. [21]. To avoid a biased learning process favoring the top levels of the aggregation, where predicted values possess larger magnitudes, such structural scale differences must be adjusted.…”