Hagemann, Paul;
Hertrich, Johannes;
Casfor, Maren;
Heidenreich, Sebastian;
Steidl, Gabriele;
(2024)
Mixed noise and posterior estimation with conditional deepGEM.
Machine Learning: Science and Technology
, 5
(3)
, Article 035001. 10.1088/2632-2153/ad5926.
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Abstract
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.
| Type: | Article |
|---|---|
| Title: | Mixed noise and posterior estimation with conditional deepGEM |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.1088/2632-2153/ad5926 |
| Publisher version: | https://doi.org/10.1088/2632-2153/ad5926 |
| Language: | English |
| Additional information: | Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 license (http://creativecommons.org/licenses/by/4.0/). Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI. |
| Keywords: | normalizing flow, inverse problem, posterior, expectation maximization |
| UCL classification: | UCL UCL > Provost and Vice Provost Offices > UCL BEAMS UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science |
| URI: | https://discovery.ucl.ac.uk/id/eprint/10194672 |
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