[STAT/AP] Paulo Serra: Uncertainty quantification in sparse quantile regression

In statistics we often want to discover (or account for) structure in observed data, and dimension plays a crucial role in this task. For instance, high-dimensional data sometimes live in a lower dimensional space and sparse models are a popular way to account for this.

Sparse quantile regression combined with appropriate penalties produces sparse, robust estimators. In this talk I will share some results pertaining to advantages of sparse quantile regression over mean-based estimators, particularly in terms of robustness. We study the performance of these estimators under a very general model, allowing for correlation in the data, asymmetric distributions, sub-gaussian but also heavier data distributions. We obtain local (also minimax) rates for prediction and estimation, and share the current state of the results on uncertainty quantification.

This is joint work with Alexandra Vegelien, Eduard Belitser VU Amsterdam.