Simulator-Based Inference with WALDO: Confidence Regions by Leveraging Prediction Algorithms and Posterior Estimators for Inverse Problems
Simulator-Based Inference with WALDO: Confidence Regions by Leveraging Prediction Algorithms and Posterior Estimators for Inverse Problems
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发表时间：
2022-05
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通讯作者：
Luca Masserano;T. Dorigo;Rafael Izbicki;Mikael Kuusela;Ann B. Lee
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作者：
Luca Masserano;T. Dorigo;Rafael Izbicki;Mikael Kuusela;Ann B. Lee
预测算法，如深度神经网络（dnn），在许多科学领域被用于直接估计基于模拟器的模型中感兴趣的内部参数，特别是在观察包括图像或复杂高维数据的设置中。同时，现代神经密度估计，如归一化流，在不确定性量化中越来越受欢迎，特别是当参数和观测值都是高维的时候。然而，参数推理是一个逆问题，而不是一个预测任务；因此，一个公开的挑战是构建有条件有效和精确的置信区域，保证覆盖数据生成过程的真实参数的概率，无论（未知）参数值是什么，并且不依赖于大样本理论。许多基于模拟器的推理（SBI）方法确实已知会产生有偏差或过于自信的参数区域，从而产生误导性的不确定性估计。本文提出了WALDO，一种利用目前在SBI中广泛采用的预测算法或后验估计来构建有限样本条件有效性置信区域的新方法。WALDO重构了著名的Wald检验统计量，并使用了一种计算效率很高的基于回归的机制来进行经典的假设检验的内曼反演。我们将我们的方法应用于最近的一个高能物理问题，在这个问题上，使用dnn进行预测之前会导致带有预测偏差的估计。我们还说明了我们的方法如何可以纠正过度自信的后验区域计算归一化流。
Prediction algorithms, such as deep neural networks (DNNs), are used in many domain sciences to directly estimate internal parameters of interest in simulator-based models, especially in settings where the observations include images or complex high-dimensional data. In parallel, modern neural density estimators, such as normalizing flows, are becoming increasingly popular for uncertainty quantification, especially when both parameters and observations are high-dimensional. However, parameter inference is an inverse problem and not a prediction task; thus, an open challenge is to construct conditionally valid and precise confidence regions, with a guaranteed probability of covering the true parameters of the data-generating process, no matter what the (unknown) parameter values are, and without relying on large-sample theory. Many simulator-based inference (SBI) methods are indeed known to produce biased or overly confident parameter regions, yielding misleading uncertainty estimates. This paper presents WALDO, a novel method to construct confidence regions with finite-sample conditional validity by leveraging prediction algorithms or posterior estimators that are currently widely adopted in SBI. WALDO reframes the well-known Wald test statistic, and uses a computationally efficient regression-based machinery for classical Neyman inversion of hypothesis tests. We apply our method to a recent high-energy physics problem, where prediction with DNNs has previously led to estimates with prediction bias. We also illustrate how our approach can correct overly confident posterior regions computed with normalizing flows.