发表机构
AI Quant Researcher（AI量化研究员）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文提出Halo方法，通过为现有深度预测器增加尺度估计输出并采用负对数似然训练，在电力价格预测中显著提升点估计精度，且无需重新调参。
AI 中文摘要
异方差预测，即网络在估计位置参数的同时估计尺度参数，通常以不确定性量化作为动机。本文表明，它还能改进点估计，这与时间序列之外异方差估计的负面结果报道形成对比。Halo 是一种修改方法，它重用现有深度预测器的架构，为其隐含分布的尺度提供第二个输出，并在匹配的负对数似然下进行训练。在三种最先进的模型——Transformer、图网络与变分自编码器配对、以及单层卷积网络——上，在高斯和拉普拉斯损失下进行适配，均展示了这一现象。在标准预测基准的五个电力价格市场上，Halo 在30个模型-市场-指标比较中的28个中改善了MSE和MAE，平均MSE降低2.6%至16.5%，平均MAE降低1.7%至11.0%。两个发现浮现：（1）尺度估计来自第二个投影头还是完整的并行网络，其重要性远低于网络是否估计尺度；（2）在已为点估计基线调优的超参数下，改进仍然成立，因此重新调优是可选的。
英文摘要
Heteroscedastic forecasting, where a network estimates a scale parameter alongside a location parameter, is normally motivated by uncertainty quantification. This paper shows it also improves the point estimate, in contrast to reported negative results for heteroscedastic estimation outside time series. Halo is a modification that reuses an existing deep forecaster's architecture, giving it a second output for the scale of its implied distribution and training it under the matching negative log likelihood. Adapting three state-of-the-art models --- a transformer, a graph network paired with a variational autoencoder, and a single-layer convolutional network --- under both Gaussian and Laplacian losses demonstrates the phenomenon. On the five electricity price markets of a standard forecasting benchmark, Halo improves MSE and MAE in 28 of 30 model-market-metric comparisons, cutting average MSE by 2.6% to 16.5% and average MAE by 1.7% to 11.0%. Two findings emerge: (1) whether the scale estimate comes from a second projection head or from a full parallel network matters far less than whether the network estimates scale, and (2) the improvement holds under the hyperparameters already tuned for the point-estimate baseline, so retuning is optional.
