Motonobu Kanagawa (Max Planck Institute for Intelligent Systems)
Title
Why Uncertainty Matters in Deterministic Computations? A Decision Theoretic Perspective
Abstract
Probabilistic numerical methods have recently become an active area of research, for the purpose of quantifying uncertainty in deterministic computations such as numerical integration,
optimisation, numerical linear algebra and solutions for differential equations.
Such uncertainty, which is epistemic rather than stochastic, is caused by limited computational budgets in solving numerical tasks in practice,
and arises as discretisation error in approximating continuous objects.
In the literature, several motivations have been given for probabilistic numerical methods, including propagation of uncertainty in a pipeline of numerical methods,
aiming at the assessment of the resulting scientific conclusions, or at the optimal allocation of computational resources in the pipeline.
In this talk, I will argue that another important motivation is provided by decision problems,
where one is required to choose an optimal action from given candidate actions associated with possible losses.
I will discuss how probabilistic numerical methods can play fundamental roles in such decision problems, showcasing several motivating examples.
