Predictive Uncertainty Quantification with Missing Covariates

Predictive uncertainty quantification is crucial in decision-making problems, in order to communicate the limits of predictive performance. We investigate how to adequately quantify predictive uncertainty when the covariates can be missing. A bottleneck is that missing values induce heteroskedasticity on the response's predictive distribution given the observed covariates. 

In this talk, we first introduce in details Conformal Prediction, a theoretically grounded framework for constructing prediction sets with finite sample distribution-free marginal coverage guarantee for any underlying machine learning model. We will highlight CP's limitations and current active research directions. 

Then, we focus on building predictive sets for the response that are valid conditionally on the missing values pattern. After discussing why this goal is hard, we provide principled methodological ideas that can be leveraged to achieve validity conditional on the missing values pattern.