用少量校准数据修正仿真推断中的模型偏差,提升参数估计准确性。
Flow Matching Calibration for Simulation-Based Inference under Model Misspecification
- 基于流匹配思想,用校准样本微调已有后验估计器。
- 在合成与真实数据上均显著降低模型误设带来的偏差。
- 无需知道错误来源,适合复杂模型的稳健推断任务。
模拟推断(SBI)正推动实验科学变革,使复杂非线性模型的参数估计成为可能。然而,模型误设仍是长期挑战:在贝叶斯框架下,模拟器、噪声或先验建模的近似误差可能导致后验分布偏差或过度自信。为此,本文提出流匹配校准后验估计(FMCPE),利用流匹配范式,通过少量校准样本对训练好的后验估计器进行修正。该方法分两步:首先在大量模拟数据上训练后验逼近器;其次,通过流匹配将预测结果映射至由校准观测支撑的真实后验。该设计无需知晓误设形式或具体受影响的模型组件,即可实现从大规模仿真中获取可扩展性,同时具备对分布偏移的鲁棒性。在合成基准和真实数据集上的实验表明,相比标准SBI基线,本方法能持续缓解误设影响,显著提升推断精度与不确定性量化能力,且计算效率保持良好。
原文摘要 · Abstract (English)
Simulation-based inference (SBI) is transforming experimental sciences by enabling parameter estimation in complex non-linear models from simulated data. A persistent challenge, however, is model misspecification. In a Bayesian setting, targeting posterior distributions, errors may arise from the simulator, the noise or prior modelling. These model components are only approximations of reality, and severe mismatches can yield biased or overconfident posteriors. We address this issue by introducing Flow Matching Corrected Posterior Estimation (FMCPE), a framework that leverages the flow matching paradigm to refine simulation-trained posterior estimators using a small set of calibration samples. Our approach proceeds in two stages: first, a posterior approximator is trained on abundant simulated data; second, flow matching transports its predictions toward the true posterior supported by calibration observations. We rely on the later to guide the correction, without requiring explicit knowledge of the misspecification form or of which model components are affected. This design enables FMCPE to combine the scalability of SBI with robustness to distributional shift. Across synthetic benchmarks and real-world datasets, we show that our proposal consistently mitigates the effects of misspecification, delivering improved inference accuracy and uncertainty quantification compared to standard SBI baselines, while remaining computationally efficient.
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