Diepe Credal Neurale Netwerken voor Onzekerheidskwantificatie

In recent years, neural networks have shown great promise and remarkable advancements across various scientific domains. However, their predictive performance tends to degrade in uncertain scenarios, particularly when encountering inputs that deviate from the training distribution or under conditions that include observational noise, natural perturbations, adversarial corruption, and missing data, among others. As a result, effectively estimating the uncertainty associated with neural network predictions and properly distinguishing between its two main forms - aleatoric and epistemic uncertainty - remains essential for improving the robustness, reliability, and trustworthiness of machine learning models. Such advancements are particularly beneficial for downstream decision-based tasks, including selective prediction, out-of-distribution (OOD) detection, and active learning, and are essential in safety-critical applications such as autonomous driving and medical image analysis. Focusing on quantifying uncertainties in neural network predictions, aleatoric uncertainty refers to the inherent randomness in the relationship between an input and an output—that is, an estimation of the ground-truth conditional probability p(output | input). In contrast, epistemic uncertainty represents the ignorance associated with the estimation of the ground-truth conditional probability p(output | input)-that is, the uncertainty about the NN's probability prediction itself. Traditionally, standard neural networks (SNNs) are employed, whose weights and biases are estimated as exact and fixed values. In cases in which SNNs provide specific point predictions, they express pure certainty, as neither epistemic nor aleatoric uncertainty is captured. When their prediction is of a probabilistic nature, e.g., a softmax-based categorical probability in classification, the SNN estimates the underlying conditional probability, p(output|input). In this context, the uncertainty captured by such predictions is purely aleatoric. The reason for failing to capture epistemic uncertainty lies in using a single probability distribution to model the non-deterministic relationship between predictions and input data while assuming precise knowledge of this dependency. As a further confirmation of this, the uncertainty associated with SNN parameters is disregarded, implicitly suggesting complete certainty regarding the ground-truth model. To account for epistemic uncertainty in predictions, it is desirable for a neural network to adopt a second-order representation in the output space to express the uncertainty about a prediction's uncertainty itself - the imprecision associated with the estimate of the underlying conditional probability p(output|input). The primary objective of this dissertation is to advance the uncertainty quantification (UQ) in neural network classifiers for improving their robustness, reliability, and trustworthiness. The core innovations lie in the development of novel deep credal neural networks that predict a credal set—a convex set of probability distributions—as the second-order representation, designed to accommodate diverse perspectives and application scenarios.