不训练的简单区间竟成概率预测最强基线。
Report the Floor: A Training-Free Conformal Interval Is a Mandatory Baseline for Probabilistic Time-Series Forecasting
- 用最新值加分位数构造无参数区间，无需训练
- 在2217个真实时间序列上胜过多数现有方法
- 适合评估新模型时作为必须对比的基准
尽管概率预测模型日益复杂，但其对比基线却常弱或缺失。我们发现，最简单的共形区间——将最后一个观测值包裹在有限样本分裂共形残差分位数中，无参数、无训练——远比近期研究中几乎被忽略的强度更强。在一阶在线预测中，覆盖来自九个公开数据集（Monash、LOTSA、LTSF交通/电力/天气套件、METR-LA、BOOM、nips/probts）的2217个真实序列，该方法显著优于朴素值-分位数基线、整个NPTS家族（NPTS 73%、SeasonalNPTS 64%）、以及已发表的共形季节池（CSP，71%的序列，95%置信区间[69,73]，配对威尔科克斯检验p≈7.6e-135）；其性能与更简单的学习型共形预测器（RCI、分位数回归）相当，仅略逊于自适应在线与集成方法（SPCI、ACI、AgACI），后者因追踪分布变化而领先9-33%相对温克勒宽度。此外，它在六大数据集上校准性优于训练过的神经网络（如DeepNPTS）：名义95%覆盖率下，平凡下界覆盖真值84-85%，而DeepNPTS仅66%。多步季节性预测中情况反转：随机游走下界最差，季节池（CSP）最优，本文明确划定此边界。最后提出ConformalNaive+，一个一行代码、无需训练、可自适应时序的筛选器，在每个时序上选择更优下界并恢复覆盖率。我们认为，匹配的共形朴素下界应在任何声称性能提升的学习型概率预测器中成为强制基线。
原文摘要 · Abstract (English)
Probabilistic forecasters are increasingly learned, yet the baselines they are compared against are often weak or omitted. We show that the simplest possible conformal interval - a last-value point forecast wrapped in a finite-sample split-conformal residual quantile, with no parameters and no training - is a far stronger baseline than its near-total absence from recent learned-forecasting and conformal-time-series comparisons would suggest. In one-step-ahead online forecasting across 2,217 real series from nine public sources (Monash, LOTSA, the LTSF traffic/electricity/weather suites, METR-LA, BOOM, nips/probts), this ConformalNaive interval decisively beats the naive value-quantile baselines, the entire NPTS family (NPTS 73%, SeasonalNPTS 64% of series), and the published Conformal Seasonal Pools (CSP) method (71% of series, bootstrap 95% CI [69,73], paired Wilcoxon p approx 7.6e-135); it is on par with the simpler learned conformal predictors (RCI, quantile regression; median relative Winkler within 2%) and is beaten only by the adaptive-online and ensemble methods (SPCI, ACI, AgACI), which track distribution shift and lead by 9-33% relative Winkler. It is also better calibrated than a trained neural forecaster: on the six datasets that introduced DeepNPTS, the trivial floors cover the truth 84-85% of the time at a nominal 95%, versus DeepNPTS's 66%. At multi-step seasonal horizons the picture inverts: the random-walk floor is the weakest method and the seasonal pool (CSP) wins - a boundary we map. Finally we give ConformalNaive+, a one-line, training-free, horizon-adaptive selector that attains the better of two complementary floors at every horizon with restored coverage. We argue the matching conformal naive floor must be a mandatory baseline whenever a learned probabilistic forecaster claims gains.
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