Abstract :

Although most deep learning models provide probabilistic distributions as a predictive output, their evaluation often relies mainly on raw performance metrics (e.g. accuracy for classification) insensitive to the uncertainty expressed by these distributions. Yet, the inherent restrictions on the generalization ability of these models make them extremely unlikely to reach flawless performance on new data, hence advocating for the importance of examining the confidence of the predictions. In this regard, the field of model calibration has recently gained considerable attention in the deep learning community, with the aim of encouraging reliable predictions. Meanwhile, the development of models like Bayesian neural networks, deep ensemble or evidential deep models has made it possible to estimate the level of epistemic uncertainty, inherent to the learning process, in complement to the aleatoric uncertainty already estimated by standard models. While the quality of predictive/aleatoric uncertainty can be measured by well-established calibration methods, the same cannot be said about epistemic uncertainty. Since the latter is considered the ideal score in a range of applications, it is therefore of utmost importance to explore its calibration properties, which has rarely been addressed in the literature. When attempting to define epistemic calibration, more challenges arise on how to formalize this calibration, assuming its existence. For instance, it may be worth considering whether it is feasible to study it similarly to model calibration, or at the very least, based on fundamental principles. Throughout this thesis, we have attempted to overcome these challenges by conducting work of both a theoretical and experimental nature in the specific context of deep classifiers. After reviewing the state of the art to quantifying probabilistic uncertainty, especially in the field of deep models, and given the difficulty of quantitatively calibrating epistemic uncertainty, we first define formally two elementary principles that epistemic uncertainty should ideally satisfy to our view: data-related and model-related principles. Indeed, as epistemic uncertainty is associated with knowledge in the model, it should decrease with the amount of available data and increase with the expressivity/complexity of the model. Empirically, and on a variety of datasets, we show that commonly used Bayesian models or alternatives do not fully verify these fundamental principles. Therefore, we argue that these models lack epistemic calibration, and we refer to this phenomenon as the epistemic uncertainty hole. Considering the critical role that the prior plays in shaping epistemic uncertainty, we investigate how much this failure of the tested models is due to an inadequate choice of prior. To this end, we introduce Conflictual loss, a loss function that favors diversity of the outputs thanks to the use of an uninformative prior. We then experimentally show that Conflictual loss leads to a better calibrated epistemic uncertainty and does not suffer from the epistemic uncertainty hole. Additionally, special inputs were investigated, which were either noisy samples or drawn from the test set, to understand the evolution of different sources of uncertainties. Furthermore, we analyze the specificities of the conflictual diversity in the parameters space and highlight the differences with deep ensembles. Building on the findings of this analysis, a compact version of the model was formalized, further emphasizing the benefits of the uninformative prior. Finally, the models were evaluated on popular applications such as out-of-distribution (OOD) detection and Bayesian active learning.