Input uncertainty propagation through trained neural networks
Paul Monchot,u00a0Loic Coquelin,u00a0Su00e9bastien Julien Petit,u00a0Su00e9bastien Marmin,u00a0Erwan Le Pennec,u00a0Nicolas Fischer
When physical sensors are involved, such as image sensors, the uncertainty over the input data is often a major component of the output uncertainty of machine learning models. In this work, we address the problem of input uncertainty propagation through trained neural networks. We do not rely on a Gaussian distribution assumption of the output or of any intermediate layer. We propagate instead a Gaussian Mixture Model (GMM) that offers much more flexibility, using the Split&Merge algorithm. This paperu2019s main contribution is the computation of a Wasserstein criterion to control the Gaussian splitting procedure for which theoretical guarantees of convergence on the output distribution estimates are derived. The methodology is tested against a wide range of datasets and networks. It shows robustness, and genericity and offers highly accurate output probability density function estimation while maintaining a reasonable computational cost compared with the standard Monte Carlo (MC) approach.
