利用条件 deepGEM 进行混合噪声和后验估计

IF 6.3 2区物理与天体物理 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE

Machine Learning Science and Technology Pub Date : 2024-07-01 DOI:10.1088/2632-2153/ad5926

Paul Hagemann, Johannes Hertrich, Maren Casfor, Sebastian Heidenreich and Gabriele Steidl

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引用次数: 0

摘要

我们开发了一种在贝叶斯逆问题中联合估计后验参数和噪声参数的算法，该算法的动机来自于采用混合噪声模型的纳米计量学的间接测量和应用。我们建议用期望最大化（EM）算法来解决这个问题。基于当前的噪声参数，我们在 E 步中学习一个近似后验的条件归一化流。在 M 步中，我们建议通过 EM 算法再次找到噪声参数更新，该算法具有解析公式。我们将条件归一化流的训练与正向和反向库尔贝克-莱布勒发散进行了比较，结果表明，与以往的方法不同，我们的模型能够纳入来自许多测量的信息。

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Mixed noise and posterior estimation with conditional deepGEM

We develop an algorithm for jointly estimating the posterior and the noise parameters in Bayesian inverse problems, which is motivated by indirect measurements and applications from nanometrology with a mixed noise model. We propose to solve the problem by an expectation maximization (EM) algorithm. Based on the current noise parameters, we learn in the E-step a conditional normalizing flow that approximates the posterior. In the M-step, we propose to find the noise parameter updates again by an EM algorithm, which has analytical formulas. We compare the training of the conditional normalizing flow with the forward and reverse Kullback–Leibler divergence, and show that our model is able to incorporate information from many measurements, unlike previous approaches.

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来源期刊

Machine Learning Science and Technology Computer Science-Artificial Intelligence

CiteScore

9.10

自引率

4.40%

发文量

审稿时长

5 weeks

期刊介绍： Machine Learning Science and Technology is a multidisciplinary open access journal that bridges the application of machine learning across the sciences with advances in machine learning methods and theory as motivated by physical insights. Specifically, articles must fall into one of the following categories: advance the state of machine learning-driven applications in the sciences or make conceptual, methodological or theoretical advances in machine learning with applications to, inspiration from, or motivated by scientific problems.