FROM POINT ESTIMATES TO PREDICTIVE DISTRIBUTIONS IN MACHINE LEARNING MODELS - A STATISTICAL IMPORTANCE SAMPLING FRAMEWORK

In this thesis, we leverage powerful statistical frameworks for optimal sequential estimation and tracking in non-linear and non-Gaussian dynamical models, which enjoy proven (asymptotic) optimality properties. Initially, we build upon our previous work, which employed first-order Taylor series approximation to propagate the first two predictive moments, to derive Bayesian encoder-decoder networks. This work introduced the notion of dense, pixel-level uncertainty map that is crucial in fields, such as autonomous vehicles and medical segmentation. We then extended the Bayesian framework to an ensembling scheme based on ensemble Kalman Filtering (EnKF). While EnKF represents the predictive distribution with an ensemble of draws, it implicitly assumes a Gaussian model. Finally, we derived an advanced sequential importance sampling (SIS) technique to sequentially propagate random samples from the density through the model layers. The proposed importance sampling framework is able to approximate any density, not only Gaussians, has established performance guarantees and can be implemented in parallel. We demonstrate that propagating full distributions delivers significantly increased robustness to noise and adversarial attacks. Moreover, the second moment is a reliable metric to measure the model\u27s confidence under various distributional shifts. Another notable characteristic of the model is its ability to self-assess its decisions, especially in situations where it generates inaccurate predictions. This feature represents a step towards the development of self-aware machines