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TEMPER introduces a novel probabilistic forecasting architecture that integrates temporal autoencoders with differentiable masked neural decision forests to improve uncertainty calibration. While it outperforms naive baselines on specific metrics like median absolute error, the study highlights that simple calibration adjustments often yield comparable or superior results for interval coverage. This work offers valuable insights into balancing complex model components against practical tuning strategies for time-series applications.
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TEMPER: Temporal Encoder-Masked Probabilistic Ensemble Regressor for Time-Series Forecasting

arXiv3 min read

arXiv:2609.23701v1 Announce Type: cross Abstract: Probabilistic forecasting requires accurate central predictions and calibrated uncertainty estimates. This paper presents TEMPER, the Temporal Encoder-Masked Probabilistic Ensemble Regressor, a univariate time-series forecasting algorithm that combines a temporal autoencoder, a differentiable masked neural decision forest, continuous ranked probability score (CRPS) training, and Gaussian-mixture post-processing. The R implementation is built on torch for R and returns horizon-wise density, distribution, quantile, and sampler functions. We evaluate TEMPER on three deterministic synthetic level series with trend, periodic, regime-switching, nonlinear-threshold, and heteroskedastic components. Across 96 rolling-origin forecasts at horizons t + 1, t + 5, t + 20, and t + 60, TEMPER obtains 2.824% mean CRPS normalized by origin level, 3.635% median absolute error, and 68.8% empirical 90% interval coverage after training with a 300-epoch cap and early-stopping patience of 100. A naive persistence bootstrap has the best aggregate CRPS, 2.763%, while TEMPER has the best median absolute error and the best CRPS at t+1 and t+5. The ablation study uses matched series-origin-horizon cells, horizon-wise CRPS deltas, endpoint sensitivity summaries, and a calibration-specific interval study. Relaxing the learned mask improves average CRPS by 0.472 percentage points on the ablation subset, mainly through long-horizon gains. A twofold interval inflation improves held-out coverage from 54.2% to 91.7% and gives the best 90% interval score among tested calibration rules. The results identify calibration, horizon-specific tuning, and component selection as the central research priorities.

Abstract:Probabilistic forecasting requires accurate central predictions and calibrated uncertainty estimates. This paper presents TEMPER, the Temporal Encoder-Masked Probabilistic Ensemble Regressor, a univariate time-series forecasting algorithm that combines a temporal autoencoder, a differentiable masked neural decision forest, continuous ranked probability score (CRPS) training, and Gaussian-mixture post-processing. The R implementation is built on torch for R and returns horizon-wise density, distribution, quantile, and sampler functions. We evaluate TEMPER on three deterministic synthetic level series with trend, periodic, regime-switching, nonlinear-threshold, and heteroskedastic components. Across 96 rolling-origin forecasts at horizons t + 1, t + 5, t + 20, and t + 60, TEMPER obtains 2.824% mean CRPS normalized by origin level, 3.635% median absolute error, and 68.8% empirical 90% interval coverage after training with a 300-epoch cap and early-stopping patience of 100. A naive persistence bootstrap has the best aggregate CRPS, 2.763%, while TEMPER has the best median absolute error and the best CRPS at t+1 and t+5. The ablation study uses matched series-origin-horizon cells, horizon-wise CRPS deltas, endpoint sensitivity summaries, and a calibration-specific interval study. Relaxing the learned mask improves average CRPS by 0.472 percentage points on the ablation subset, mainly through long-horizon gains. A twofold interval inflation improves held-out coverage from 54.2% to 91.7% and gives the best 90% interval score among tested calibration rules. The results identify calibration, horizon-specific tuning, and component selection as the central research priorities.

Machine Learning (stat.ML); Machine Learning (cs.LG)

arXiv:2609.23701 [stat.ML]

(or arXiv:2609.23701v1 [stat.ML] for this version)

https://doi.org/10.48550/arXiv.2609.23701 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

results/ablation_summary.csv

results/benchmark_summary.csv

results/calibration_ablation_by_horizon.csv

results/calibration_ablation_detail.csv

results/calibration_ablation_summary.csv

results/component_ablation_by_horizon.csv

results/component_ablation_paired.csv

results/crps_by_horizon.csv

results/extended_analysis_metadata.txt

results/raw_forecast_metrics.csv

results/run_metadata.txt

results/sensitivity_summary.csv

results/synthetic_series.csv

scripts/build_analysis_outputs.R

scripts/generate_temper_figures.R

scripts/rebuild_tables_from_raw.R

scripts/run_temper_experiments.R

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