**Date: **Wednesday, January 27th, 2021

9:00 am – 10:00 am Pacific Time

12:00 pm – 1:00 pm Eastern Time

**Location: **Weekly Seminar, Zoom

### Title: Online Multivalid Learning: Means, Moments, and Prediction Intervals

### Abstract:

We present a general, efficient technique for providing contextual predictions that are “multivalid” in various senses, against an online sequence of adversarially chosen examples (x,y). This means that the resulting estimates correctly predict various statistics of the labels y not just marginally — as averaged over the sequence of examples — but also conditionally on x \in G for any G belonging to an arbitrary intersecting collection of groups.

We provide three instantiations of this framework. The first is mean prediction, which corresponds to an online algorithm satisfying the notion of multicalibration from Hebert-Johnson et al.. The second is variance and higher moment predictions, which corresponds to an online algorithm satisfying the notion of mean-conditioned moment multicalibration from Jung et al. Finally, we define a new notion of prediction interval multivalidity, and give an algorithm for finding prediction intervals which satisfy it. Because our algorithms handle adversarially chosen examples, they can equally well be used to predict statistics of the residuals of arbitrary point prediction methods, giving rise to very general techniques for quantifying the uncertainty of predictions of black box algorithms, even in an online adversarial setting. When instantiated for prediction intervals, this solves a similar problem as conformal prediction, but in an adversarial environment and with multivalidity guarantees stronger than simple marginal coverage guarantees.

This talk is based on a paper that is joint work with Varun Gupta, Christopher Jung, Georgy Noarov, and Mallesh Pai.

### Bio:

Aaron Roth is a professor of Computer and Information Sciences at the University of Pennsylvania, affiliated with the Warren Center for Network and Data Science, and co-director of the Networked and Social Systems Engineering (NETS) program. He is also an Amazon Scholar at Amazon AWS. He is the recipient of a Presidential Early Career Award for Scientists and Engineers (PECASE) awarded by President Obama in 2016, an Alfred P. Sloan Research Fellowship, an NSF CAREER award, and research awards from Yahoo, Amazon, and Google. His research focuses on the algorithmic foundations of data privacy, algorithmic fairness, game theory, and machine learning. Together with Cynthia Dwork, he is the author of the book “The Algorithmic Foundations of Differential Privacy.” Together with Michael Kearns, he is the author of “The Ethical Algorithm”.