文章背景与核心概要

概率性长期时间序列预测（LTSF）通常依赖于复杂的深度学习模型训练。现有的免训练共形预测方法虽然能够提供预测区间，但往往缺乏完整的预测分布，且在长跨度预测中容易受到反馈延迟的影响。

本文提出的 KReF 框架通过检索历史数据中的“回溯-未来”对，构建出查询局部的经验预测分布。该方法无需基于梯度的模型训练，通过稳健的预处理、轻量级嵌入技术以及基于验证集缩放率的概率积分变换映射，实现了卓越的预测不确定性量化和稳健的点预测效果。

KReF：用于长期时间序列预测与预测不确定性的免训练检索框架

摘要

Probabilistic long-term time-series forecasting (LTSF) traditionally relies on heavily trained models or training-free conformal methods that lack a complete predictive distribution. This paper introduces KReF, a novel training-free retrieval framework that leverages historical lookback-future pairs to construct query-local empirical predictive distributions. By employing robust preprocessing, lightweight embedding techniques, and probability-integral-transform maps with validation-selected scaling rates, KReF delivers state-of-the-art predictive uncertainty and robust point forecasts without gradient-based model training.

概率性长期时间序列预测通常依赖于经过训练的模型。免训练的共形方法通常围绕现有的点预测器构建区间，无法原生表示完整的预测分布；其序列变体在长跨度预测中还会遭受反馈延迟日益严重的问题。

Probabilistic long-term time-series forecasting commonly relies on trained models. Training-free conformal methods typically construct intervals around a pre-existing point forecaster and do not natively represent a complete predictive distribution; sequential variants additionally suffer from increasingly delayed feedback at long horizons.

我们提出了 KReF，这是一个免训练的检索框架，它将检索到的历史未来数据视为查询局部的经验预测分布。经过稳健的预处理后，KReF 使用手工统计特征或冻结的随机傅里叶特征对每个回溯窗口进行嵌入，并检索相似的历史“回溯-未来”对。它们的相似度权重直接定义了预测概率质量、分位数、CRPS 以及加权平均点预测。KReF 进一步利用观测到的查询回溯窗口构建概率积分变换映射，并应用验证集选择的扩张和收缩率来调整区间边界。

We propose KReF, a training-free retrieval framework that treats retrieved historical futures as a query-local empirical predictive distribution. After robust preprocessing, KReF embeds each lookback using handcrafted statistics or frozen random Fourier features and retrieves similar historical lookback-future pairs. Their similarity weights directly define predictive masses, quantiles, CRPS, and a weighted-mean point forecast. KReF further uses the observed query lookback to construct a probability-integral-transform map and applies validation-selected expansion and shrinkage rates to adapt interval boundaries.

在六个 LTSF 基准测试和四个预测跨度上，KReF 在所有 12 种数据集-嵌入设置中均获得了最低的 CRPS，并在 9 种设置中获得了最低的 IS90。在无需基于梯度的拟合的情况下，其点预测在六个数据集中的两个上达到了或超过了经过训练的基准模型。归档预言机（archive-oracle）分析进一步揭示了在更细粒度的跨度和通道路由下，该方法仍有巨大的提升空间。这些结果确立了检索作为一种在 LTSF 中有用且尚未被充分探索的归纳偏置。

Across six LTSF benchmarks and four horizons, KReF obtains the lowest CRPS in all 12 dataset-embedding settings and the lowest IS90 in 9 settings. Without gradient-based fitting, its point forecasts also match or surpass trained baselines on two of six datasets. An archive-oracle analysis further reveals substantial headroom under finer horizon- and channel-wise routing. These results establish retrieval as a useful and underexplored inductive bias for LTSF.

元数据

arXiv ID: arXiv:2608.06748 [cs.LG]
作者: Yang Zhang, Rui Su
提交日期: 2026年8月7日
主要学科: 机器学习 (cs.LG)
次要学科: 人工智能 (cs.AI)
全文链接: 查看 PDF | DOI

arXiv ID: arXiv:2608.06748 [cs.LG]

Authors: Yang Zhang, Rui Su

Submitted On: August 7, 2026

Primary Subject: Machine Learning (cs.LG)

Secondary Subjects: Artificial Intelligence (cs.AI)

Full-Text Links: View PDF | DOI