AutoPQ: Automating Quantile estimation from Point forecasts in the context of sustainability

TL;DR

AutoPQ addresses the key challenges of probabilistic forecasting in smart grids by automatically converting point forecasts into quantile forecasts through a conditional invertible neural network (cINN). It automates both the selection of the underlying point forecasting method and hyperparameters, and, in the HPC variant, jointly optimizes point-forecast configurations with latent-space sampling via CASH, using hierarchical, PK-informed hyperparameter optimization and successive halving to manage computational budgets. The approach demonstrates strong probabilistic performance gains (CRPS improvements averaging over 9–15% across datasets) while explicitly reporting electricity consumption and monetary costs to assess environmental impact. This makes AutoPQ a scalable, sustainable solution for uncertainty quantification in smart grids, with configurable defaults for general systems and advanced settings for high-stakes, computation-heavy tasks. The work also provides a framework for energy-aware benchmarking and identifies avenues for further improvements in configuration space design and integration of forecast-value metrics.

Abstract

Optimizing smart grid operations relies on critical decision-making informed by uncertainty quantification, making probabilistic forecasting a vital tool. Designing such forecasting models involves three key challenges: accurate and unbiased uncertainty quantification, workload reduction for data scientists during the design process, and limitation of the environmental impact of model training. In order to address these challenges, we introduce AutoPQ, a novel method designed to automate and optimize probabilistic forecasting for smart grid applications. AutoPQ enhances forecast uncertainty quantification by generating quantile forecasts from an existing point forecast by using a conditional Invertible Neural Network (cINN). AutoPQ also automates the selection of the underlying point forecasting method and the optimization of hyperparameters, ensuring that the best model and configuration is chosen for each application. For flexible adaptation to various performance needs and available computing power, AutoPQ comes with a default and an advanced configuration, making it suitable for a wide range of smart grid applications. Additionally, AutoPQ provides transparency regarding the electricity consumption required for performance improvements. We show that AutoPQ outperforms state-of-the-art probabilistic forecasting methods while effectively limiting computational effort and hence environmental impact. Additionally and in the context of sustainability, we quantify the electricity consumption required for performance improvements.

Figures (9)

• Figure 1: Overview of AutoPQ: Lag features, seasonal features, and exogenous features are selected and used as inputs by a point forecasting model to generate a point forecast in an unknown distribution. This point forecast and the features are combined in a cINN, resulting in a representation of the forecast in a known and tractable distribution. The neighborhood of this representation is analyzed to determine how to include uncertainty information. Finally, with the backward pass through the cINN, the uncertainty is mapped back to the unknown distribution to generate the probabilistic forecast. Automation methods are highlighted in green.
• Figure 2: Comparison of the average computational effort in terms of runtime across the six datasets used in the evaluation: effort for training a point forecasting model with configuration $\uplambda_\text{p}$ and effort for generating a quantile forecast based on the point forecast using the cINN with $\boldsymbol{\uplambda}_\text{q}$. Due to the significantly smaller computational effort of generating the quantile forecast, it is worthwhile to evaluate several $\uplambda_\text{q}$ for one $\boldsymbol{\uplambda}_\text{p}$ to properly balance the efforts. Note that for ETS, SVR, and XGB the standard deviation is higher than the mean value.
• Figure 3: Estimated BO prior distribution and its utilization in the HPO of the sampling hyperparameter.
• Figure 4: Exemplary $40%$, $70%$, and $98%$PI for the Mobility dataset. The probabilistic forecasts of AutoPQ-/advanced (a-c) are generated based on the point forecasting methods ETS (SM), XGB (ML), and TFT (DL), respectively, showing different performance. Note that AutoPQ-/advanced automatically optimizes the hyperparameters and selects the best-/performing method for each dataset, i. e., TFT for Mobility. The probabilistic benchmarks (d-i) can be categorized into direct probabilistic methods (DeepAR, NNQF, QRNN) and point forecast-/based probabilistic methods (Gaussian PI, Empirical PI, Conformal PI based on a TFT forecaster).
• Figure 5: Comparison of the convergence of \ref{['alg:autopq_combined-smart']} and \ref{['alg:autopq_combined-dumb']} (ablation) for the HPO of the MLP and NHiTS on the two exemplary datasets. The thick solid line represents the mean value, and the opaque area is the standard deviation over five runs.