Halo: Improving forecast accuracy through heteroscedastic estimation

The work introduces a modification that augments an existing deep forecaster with an output for distributional scale and trains it using the corresponding likelihood objective.

Source: [4]

The proposed modification is intended to reuse the underlying forecasting architecture rather than require architecture-specific redesign.

Source: [22]

The modified forecaster produces location estimates together with positive scale estimates.

Source: [9]

The implementation compares a shared-representation dual-output design with a parallel design that uses separate network copies for location and scale.

Source: [2], [10]

The experiments adapt a transformer, a graph-based model paired with a variational autoencoder, and a shallow convolutional model.

Source: [19]

The adaptations use distributional choices aligned with the original squared-error and absolute-error training objectives.

Source: [19]

All models use series standardization, and the modified outputs are transformed back using the input-series scale, with the location also restored using its mean.

Source: [7], [8], [15], [18]

Evaluation uses an electricity-price forecasting benchmark spanning several market datasets.

Source: [21]

The comparison baseline retains each original forecasting model and reuses its previously tuned settings for the relevant model and market.

Source: [21]

Modified variants are evaluated against those baselines, including validation-based tuning experiments for the modified models.

Source: [16]

Accuracy is assessed with squared-error and absolute-error measures, aggregated over the forecast horizon.

Source: [14], [20]

Tuning uses a validation holdout, while reported evaluation uses a separate test holdout reached after tuning.

Source: [12]

Reported experiments show improvement on both accuracy measures across most model-market-metric comparisons.

Source: [4]

The reported average reductions span a range for both squared-error and absolute-error measures, varying by model.

Source: [6]

In the architecture comparisons, estimating scale appears more consequential for accuracy than choosing between the dual-output and parallel designs.

Source: [13]

The reported improvement generally remains when the modified model uses settings already tuned for the point-estimate baseline, while retuning has mixed effects.

Source: [13]

The tested setting withholds future exogenous inputs, assumes a single endogenous channel, and aligns exogenous and endogenous lookback windows.

Source: [3], [5], [17]

The heteroscedastic distributions considered use a location-and-scale parameterization.

Source: [3]

Training uses an adaptive optimizer, early stopping, a decaying learning-rate schedule, and seeds derived from a fixed base together with model and market identity.

Source: [12]

Experiments run on a unified-memory personal-computing system using a machine-learning framework and its platform graphics backend.

Source: [12]

Each reported result comes from a single training run, and variability across seeds is not reported.

Source: [12]

Testing on other benchmarks, forecast horizons, and seeds remains future work.

Source: [11]