Mixed Noise and Posterior Estimation with Conditional DeepGEM
This work addresses challenges in nanometrology and indirect measurements by enabling more accurate posterior and noise estimation, though it appears incremental as it builds on existing EM and normalizing flow methods.
The paper tackles the problem of jointly estimating posterior distributions and noise parameters in Bayesian inverse problems with mixed noise, proposing an expectation maximization algorithm that uses conditional normalizing flows for approximation and achieves analytical updates for noise parameters.
Motivated by indirect measurements and applications from nanometrology with a mixed noise model, we develop a novel algorithm for jointly estimating the posterior and the noise parameters in Bayesian inverse problems. 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 KL, and show that our model is able to incorporate information from many measurements, unlike previous approaches.