Source-linked AI summary
Modeling spatio-temporal locality in multi-step forecasting of geo-referenced time series
Annunziata D'Aversa, Gianvito Pio, Michelangelo Ceci
TL;DR
Forecasting distributed-sensor measurements must account for dependencies among nearby locations, while existing methods generally model spatial information globally. SPALT uses linear model trees to model spatial relationships among similar-trend time series and evaluates this approach for multi-step renewable-energy forecasting, where it generally outperforms competing tree-based and neural methods.
Problem
Existing approaches generally model spatial information globally, despite dependencies among nearby geo-referenced sensors and the relevance of multi-step forecasts.
Method
SPALT extends linear model trees by grouping similar-trend time series and selectively injecting spatial features, with locality-aware Reduced Error Pruning.
Results
SPALT almost always outperforms the considered competitors across three datasets and forecasting horizons, with statistically significant advantages over SPALT-NP-NS for all measures and node count at α = 0.001.
Takeaways & Limitations
SPALT provides advantages in predictive errors and model complexity for multi-step predictions from geo-distributed sensors.
Takeaways & Limitations
The evaluation focuses on renewable-energy data, with other application domains left for future work.
Abstract
from arXiv · showhide
Forecasting future measurements from geographically distributed sensors is essential across many domains. However, the spatial distribution of these sensors raises multiple challenges, primarily due to spatial autocorrelation phenomena, that introduce inter-dependencies among nearby locations, that cannot therefore be treated independently. While some existing approaches can capture such phenomena, they generally model the spatial dimension globally across all locations. On the other hand, the method we propose in this paper, called SPALT, focuses on capturing spatial relationships among time series with similar trends, even if they occur at different times, thus modeling the spatio-temporal locality. SPALT leverages linear model trees, which allow us to consider the spatial autocorrelation locally: during the tree-building process, the adopted heuristics group time series exhibiting similar trends into the same node, on which additional features considering the spatial dimension are selectively injected. Additionally, we propose a new pruning strategy, based on Reduced Error Pruning, that also considers the spatio-temporal locality during the tree simplification. Designed for a multi-step setting, SPALT provides forecasts for multiple future time steps across multiple sensors simultaneously. The characteristics exhibited by SPALT can provide significant benefits in different domains, where measurements come from distributed sensors. In this paper, we focus on data produced by sensors located in multiple renewable power plants measuring their energy production at regular, short intervals. Experiments on 3 real-world datasets demonstrate the effectiveness of SPALT in forecasting the production of energy at different time horizons, and its superior performance in comparison with tree-based models and state-of-the-art neural networks that incorporate both temporal and spatial dimensions.
1 Introduction
Forecasting geo-referenced sensor measurements matters for operational planning, but spatial autocorrelation and mixed local trends complicate modeling. SPALT addresses these challenges by modeling spatio-temporal locality in multi-step renewable-energy forecasting.
- Motivation: Renewable-energy forecasting supports network-intervention planning and energy-distribution optimization.
- Motivation: Spatial autocorrelation creates dependencies among nearby sensor observations, making independent treatment inappropriate.Spatial proximity can influence measurements, consistent with Tobler’s first law of geography.
- Motivation: Nearby sensors may exhibit different linear and non-linear trends because of localized conditions such as mountain-versus-valley weather.
- Method: SPALT groups time series with similar trends and selectively models their spatial relationships within linear model trees.Unlike global spatial modeling, it captures spatio-temporal locality among similar-trend instances.
- Application: SPALT targets multi-step forecasting of 6, 12, or 18 future energy-production values at 5-to-15-minute resolution.
- Method: The paper adds a Reduced Error Pruning strategy that incorporates spatio-temporal locality into tree simplification.Its contributions include evaluation of locality modeling and pruning effects on forecasting errors and model complexity.
2 Related work
Prior forecasting methods model temporal and spatial dependencies across domains, including energy applications, but the reviewed approaches model spatial information globally rather than spatio-temporal locality.
- Spatio-temporal forecasting: Related work includes hybrid CNN-LSTM architectures and networks combining temporal, spatial, and semantic views.Examples include precipitation nowcasting and taxi-demand prediction.
- Spatio-temporal forecasting: Existing neural approaches can use spatial information but are described as unable to model spatio-temporal locality.D2STGNN is identified as an initial attempt toward this direction.
- Energy forecasting: Energy-sector studies apply spatial information to multi-step photovoltaic, consumption, wind-power, and broader energy forecasting.Reported horizons include 24 hourly predictions, 12 monthly predictions, and 16 values at 15-minute intervals.
- Energy forecasting: Sparse VAR methods capture spatial co-dependencies but cannot capture complex non-linear dependencies among variables.
- Energy forecasting: GCN-LSTM methods model spatial information throughout time-series processing to extract complex spatio-temporal patterns.GAP-LSTM is applied to renewable energy, air pollution, and traffic forecasting.
- Research gap: The reviewed methods model spatial information globally across locations rather than spatio-temporal locality.
3 The proposed method
SPALT combines linear model trees with local spatio-temporal features and pruning for multi-step forecasting across geo-referenced time series. Its design captures linear and nonlinear dependencies while selectively modeling spatial relationships among instances with similar trends.
- SPALT overview: SPALT learns linear model trees for geo-referenced time series, aiming to capture linear and nonlinear dependencies while modeling spatio-temporal locality.The method focuses on spatial relationships among instances with similar trends rather than modeling spatial information globally.
- Multi-step forecasting: SPALT uses the MIMO strategy to return the whole vector of predictions for multiple future time steps simultaneously.Each leaf learns a multivariate linear function mapping w historical values to h future values.
- Tree construction: During tree construction, SPALT evaluates candidate splits on historical values using quantile binning and a multi-step MSE heuristic.Quantile binning reduces the thresholds considered per feature to a constant b, while split quality accounts for all h future time steps.
- Spatio-temporal locality: After tree construction, SPALT computes spatially weighted historical features from other locations represented in each leaf node.These features are generated for instances in leaves containing multiple locations and use spatial closeness between locations.
- Pruning and complexity: SPALT extends Reduced Error Pruning to consider spatio-temporal locality while simplifying the learned tree.The pruning strategy is intended to reduce overfitting and model complexity, and the added locality computations preserve the underlying linear model tree’s time complexity.
4 Experiments
Experiments on three renewable-energy datasets evaluate SPALT across multi-step horizons and show strong predictive performance, compact models, and effective spatio-temporal locality.
- Predictive performance: SPALT almost always outperforms the competitors across datasets, horizons, and MAE, RMSE, and RSE, with comparable results in most exceptions.STAEformer achieves significantly lower MAE and RMSE on WPP, but SPALT and HSTGNN obtain the best WPP RSE.
- Predictive performance: Average-rank differences favoring SPALT are close to 3 at h = 6 and close to 2 at h = 12 or h = 18, with α = 0.001 significance against XGB and XGB+PCNM.The comparisons use 3 datasets and 8 randomly selected runs per dataset for each horizon.
- Computational efficiency: SPALT runs faster than RF and all considered neural networks, while its running time appears to depend almost linearly on the number of instances.RT and XGB run faster but have significantly worse predictive errors.
- Model complexity: 23%–35% fewer nodes make SPALT trees more compact and interpretable across the reported dataset–horizon settings.The reduction ranges from about 23% on SDWPF and WPP with h = 6 to about 35% on UKPV with h = 6 and SDWPF with h = 12.
- Ablation study: Ignoring spatio-temporal locality worsens every considered measure across all horizons and datasets, with differences significant at α = 0.001, including number of nodes.SPALT selectively injects locality features when they improve validation performance; these features appear in roughly 64%–77% of leaf nodes.
- Ablation study: Pruning does not significantly change MAE, RMSE, or RSE, but significantly reduces the number of nodes at α = 0.001 without significantly affecting overall running time.The pruning strategy is therefore generally preferable because it produces less complex models without a measurable runtime penalty.
5 Conclusion
The paper introduces SPALT for multi-step forecasting of geo-distributed sensor time series and evaluates it on renewable-energy datasets. Experiments report effectiveness against tree-based and neural-network models, while ablations indicate benefits from spatio-temporal locality and pruning; broader application domains remain future work.
- 5 Conclusion: SPALT extends linear model trees to capture linear and non-linear dynamics in multi-step forecasting of geo-distributed sensor data.It enriches leaf-node models with historical-trend features from spatially proximate sensors exhibiting similar trends.
- 5 Conclusion: The proposed pruning strategy incorporates spatio-temporal locality into Reduced Error Pruning during tree simplification.
- 5 Conclusion: Experiments on three renewable-energy datasets compared SPALT with tree-based models and neural networks that model temporal and spatial dimensions.
- 5 Conclusion: Ablation results showed a statistically significant advantage for modeling spatio-temporal locality and reduced model complexity from pruning without affecting predictive accuracy.
- 5 Conclusion: Future work will evaluate SPALT beyond the energy domain and explore ensembles of linear model trees.
Authors and Affiliations
The paper is authored by Annunziata D’Aversa, Gianvito Pio, and Michelangelo Ceci, with affiliations spanning the University of Bari Aldo Moro, CINI, and the Jozef Stefan Institute.
- Authors and Affiliations: Annunziata D’Aversa, Gianvito Pio, and Michelangelo Ceci are the listed authors.
- Authors and Affiliations: The authors are affiliated with the Department of Computer Science at the University of Bari Aldo Moro in Bari, Italy.
- Authors and Affiliations: Gianvito Pio and Michelangelo Ceci are affiliated with the Data Science Lab of CINI in Rome, Italy.
- Authors and Affiliations: Michelangelo Ceci is affiliated with the Department of Knowledge Technologies at the Jozef Stefan Institute in Ljubljana, Slovenia.