arXiv：cs.LG· Yangwen Zhang, Shiwei Ni, Xiaoping Zhang, Xiaofei Guan, Lili Ju·· 5 小时前AI 评分30
AECSF：面向高维非线性数据同化的自适应集成条件分数滤波
AECSF: Adaptive Ensemble Conditional Score Filtering for High-Dimensional Nonlinear Data Assimilation
AI 导读
研究者提出免训练的自适应集成条件分数滤波方法 AECSF，基于条件 Tweedie 恒等式构建可解析求解的分数估计器，将含噪后验分数估计转化为条件均值估计。该方法采用共享自适应加权提议集成，利用反向粒子信息在同一轮反向扩散中更新，无需单独采样即可为每个含噪反向粒子给出估计。数值实验显示，AECSF 在预报集成规模有限的高维问题中提升了后验采样与非线性滤波精度。
正文
Abstract:Bayesian state estimation for high-dimensional nonlinear dynamical systems entails a fundamental tension between statistical fidelity and computational tractability, as particle weights can collapse, while Gaussian ensemble updates can miss non-Gaussian posterior structure. Score-based diffusion filters offer a sampling-based alternative, but existing training-free score filters often rely on heuristic likelihood corrections, which can compromise posterior accuracy by neglecting uncertainty about the system state associated with each noisy reverse particle. To address these issues, we propose AECSF, a training-free adaptive ensemble conditional score filter. AECSF constructs an analytically tractable score estimator from the conditional Tweedie identity, which recasts noisy posterior score estimation as estimating the conditional mean of the system state given a noisy reverse particle and the observation. To estimate these conditional means efficiently, AECSF employs a shared adaptive weighted proposal ensemble, while particle-specific conditional weights yield an estimate for each noisy reverse particle without separate proposal sampling. The proposal ensemble is updated using reverse-particle information within the same reverse-diffusion run to improve conditional-mean estimation. Theoretically, we characterize when a fixed weighted proposal measure yields the exact noisy posterior score. Under stated assumptions, we establish a bound relating conditional-mean estimation errors to reverse-sampling endpoint error. Numerical experiments demonstrate that AECSF improves the accuracy of posterior sampling and nonlinear filtering in high-dimensional problems with limited forecast ensembles.
| Subjects: | Machine Learning (stat.ML); Machine Learning (cs.LG); Numerical Analysis (math.NA) |
| Cite as: | arXiv:2609.32411 [stat.ML] |
| (or arXiv:2609.32411v2 [stat.ML] for this version) | |
| https://doi.org/10.48550/arXiv.2609.32411 arXiv-issued DOI via DataCite |
Submission history
From: Xiaofei Guan [view email]
[v1]
Sat, 26 Sep 2026 09:37:52 UTC (149 KB)
[v2]
Fri, 2 Oct 2026 02:30:54 UTC (149 KB)
来源：arXiv：cs.LG · arxiv.org