Jonas Peters, Department of Mathematical Sciences, University of Copenhagen

Invariant Causal Prediction

Abstract: Why are we interested in the causal structure of a process? In classical prediction tasks as regression, for example, it seems that no causal knowledge is required. In many situations, however, we want to understand how a system reacts under interventions, e.g., in gene knock-out experiments. Here, causal models become important because they are usually considered invariant under those changes. A causal prediction uses only direct causes of the target variable as predictors; it remains valid even if we intervene on predictor variables or change the whole experimental setting. In this talk, we show how we can exploit this invariance principle to estimate causal structure from data. We apply the methodology to data sets from biology, epidemiology, and finance. The talk does not require any knowledge about causal concepts.

David Ginsbourger, Idiap Research Institute and University of Bern, http://www.ginsbourger.ch
Quantifying and reducing uncertainties on sets under Gaussian Process priors

Abstract: Gaussian Process models have been used in a number of problems where an objective function f needs to be studied based on a drastically limited number of evaluations.

Global optimization algorithms based on Gaussian Process models have been investigated for several decades, and have become quite popular notably in design of computer experiments. Also, further classes of problems involving the estimation of sets implicitly defined by f, e.g. sets of excursion above a given threshold, have inspired multiple research developments.

In this talk, we will give an overview of recent results and challenges pertaining to the estimation of sets under Gaussian Process priors, with a particular interest for to the quantification and the sequential reduction of associated uncertainties.

Based on a series of joint works primarily with Dario Azzimonti, François Bachoc, Julien Bect, Mickaël Binois, Clément Chevalier, Ilya Molchanov, Victor Picheny, Yann Richet and Emmanuel Vazquez.