This talk will address questions and challenges regarding the representation and adequate handling of (predictive) uncertainty in (supervised) machine learning. A particular focus will be put on the distinction between two important types of uncertainty, often referred to as aleatoric and epistemic, and how to quantify these uncertainties in terms of appropriate numerical measures. Roughly speaking, while aleatoric uncertainty is due to the randomness inherent in the data generating process, epistemic uncertainty is caused by the learner's ignorance of the true underlying model. Some conceptual and theoretical issues of existing methods will identified, showing the challenging nature of uncertainty quantification in general and the disentanglement of aleatoric and epistemic uncertainty in particular. We also address recent criticism of the aleatoric-epistemic dichotomy in the context of machine learning and generative AI.

For machine learning tasks, say, prediction, uncertainty quantification usually means one of two things: the assignment of data-driven degrees of belief to relevant hypotheses or the construction of confidence sets.  Reliability in these two contexts also has different meanings, so there's really no common ground on which these can be compared.  Towards resolving this dichotomy, I consider the assignment of data-driven degrees of belief that are valid in the sense that the output is calibrated: roughly, degrees of belief assigned to true/false hypotheses tend to be large/small.  This begs the question: what kind of degrees of belief are valid in this sense?  To answer this, I'll give a generalization of the false confidence theorem in statistical inference to the context of prediction, establishing that no precise probability distribution offers valid uncertainty quantification; hence the title claim that imprecision is imperative for valid uncertainty quantification.  To keep the "IM" wordplay going, I'll argue that the imperative imprecision isn't impossible to implement.  Indeed, those methods that are reliable in the usual frequentist sense, such as conformal prediction, can easily be transformed into an imprecise probability with a special consonant form, thereby offering valid uncertainty quantification for machine learning.  

In the real world, the test data rarely matches the training data. In this talk, we first distinguish common paradigms used to develop and evaluate methods for out-of-distribution generalization in the presence of multiple training environments. We then focus on robust, i.e. worst-case, generalization methods based on invariant causal mechanisms and advocate for evaluating them in more realistic settings where the robust risk is only partially identifiable by the source distributions. In particular, we illustrate on specific examples and real data, how in this misspecified robust generalization setting, the ranking of invariant-based methods may change drastically. 

The Epistemic AI is an approach which proposes the use of second-order uncertainty measures for quantifying epistemic uncertainty in artificial intelligence. A mathematical framework which generalises the concept of random variable, random sets, for instance, enable a more flexible and expressive approach to uncertainty modeling. We discuss ways in which the random sets and credal sets formalisms can model classification uncertainty over both the target and parameter spaces of a machine learning model (e.g., a neural network), outperforming Bayesian, ensemble and evidential baselines. We show how the principle can be extended to generative AI, in particular large language models less prone to hallucination, as well as diffusion processes and generative adversarial networks. Exciting applications to large concept models and visual language models as well as neural operators, scientific machine learning and neurosymbolic reasoning are discussed.