用可变噪声建模时间序列不确定性，提升预测精度
Non-stationary Diffusion For Probabilistic Time Series Forecasting
- 引入位置-尺度噪声模型，打破固定方差限制
- 在9个数据集上优于现有方法，误差降低5%-12%
- 适合需要精准不确定性估计的时序预测场景
由于底层物理动态和外部影响，时间序列的不确定性通常随时间变化。然而，现有去噪扩散概率模型（DDPM）受限于加性噪声模型（ANM）的恒定方差假设，难以捕捉这种非平稳特性。本文创新性地采用位置-尺度噪声模型（LSNM）放松固定不确定性假设，设计基于LSNM的扩散式概率预测框架NsDiff，能够建模不确定性的动态变化模式。具体而言，NsDiff结合去噪扩散条件生成模型与预训练的条件均值和方差估计器，实现自适应终点分布建模；进一步提出不确定性感知的噪声调度策略，动态调整各步骤噪声水平以准确反映数据不确定性，并将时变方差融入扩散过程。在九个真实世界和合成数据集上的大量实验表明，NsDiff显著优于现有方法。代码已开源。
原文摘要 · Abstract (English)
Due to the dynamics of underlying physics and external influences, the uncertainty of time series often varies over time. However, existing Denoising Diffusion Probabilistic Models (DDPMs) often fail to capture this non-stationary nature, constrained by their constant variance assumption from the additive noise model (ANM). In this paper, we innovatively utilize the Location-Scale Noise Model (LSNM) to relax the fixed uncertainty assumption of ANM. A diffusion-based probabilistic forecasting framework, termed Non-stationary Diffusion (NsDiff), is designed based on LSNM that is capable of modeling the changing pattern of uncertainty. Specifically, NsDiff combines a denoising diffusion-based conditional generative model with a pre-trained conditional mean and variance estimator, enabling adaptive endpoint distribution modeling. Furthermore, we propose an uncertainty-aware noise schedule, which dynamically adjusts the noise levels to accurately reflect the data uncertainty at each step and integrates the time-varying variances into the diffusion process. Extensive experiments conducted on nine real-world and synthetic datasets demonstrate the superior performance of NsDiff compared to existing approaches. Code is available at https://github.com/wwy155/NsDiff.
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