Event Date
Speaker: Nicolai Amann, Visiting Assistant Professor, Statistics, UC Davis
Title: "Uncertainty quantification in high dimensions"
Abstract: Recently, there has been substantial interest in uncertainty quantification for statistical learning, in particular, in high-dimensional settings that arise in modern data science. Our goal is to construct prediction sets PIα whose coverage probability is close to its nominal level 1−α in large samples. These guarantees should hold under minimal assumptions on the data-generating process that include the high-dimensional framework and conditional on the training data, because numerous predictions are usually computed based on one and the same training sample.
In my talk, I will compare three procedures for creating prediction sets: Cross-validation (CV), CV+, and full conformal prediction. For each method, I will establish conditions under which it provides training-conditionally valid prediction sets asymptotically. All three methods crucially rely on a stability condition that ensures the predictor or conformity scores do not heavily rely on a small fraction of the training data. Furthermore, I will discuss the necessity of this condition and show a close connection between the conditional
coverage probabilities of CV and CV+ under stability.
Finally, I will introduce a computationally efficient shortcut formula that allows to approximate full conformal prediction sets while having the same conditional coverage guarantees asymptotically under stability. For a specific conformity score, this shortcut formula coincides with the symmetrized Jackknife, thereby providing a connection between CV and full conformal prediction.
This is part of the STA 290 Seminar Series