Differentiable Expectation-Maximisation and Applications to Gaussian Mixture Model Optimal Transport
The work develops methods to make Expectation-Maximisation (EM), usually treated as a black box, differentiable using Mixture Wasserstein distance (MW2) for Gaussian Mixture Models (GMMs). It explores different gradient calculation strategies, including full automatic differentiation and approximate implicit gradients, providing stability results for MW2 loss functions in imaging and machine learning.