Invited Talk 1: Computing with Ignorance: a possibilistic view of uncertainty in machine learning (Jeremie Houssineau)

Probability is the default language for uncertainty in machine learning, but it is a demanding one: it asks for a full distribution even when the evidence is less precise. Outer probability measures relax that demand, they keep a measure-theoretic framework while letting ignorance be expressed directly, rather than being forced into a prior probability. Where probability integrates, possibility theory takes suprema, so the operations of summarising, updating and propagating a belief become optimisation problems instead of often-intractable integrals. I will only assume knowledge of the familiar aleatoric/epistemic distinction, and then show how possibility theory can be implemented in general via a maxitive analogue of the Donsker-Varadhan formula that recasts inference as optimisation, leading to a drop-in replacement for the cross-entropy loss that gives deep classifiers a sense of when to abstain.