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FDS Colloquium: Aaditya Ramdas (CMU), “The numeraire e-variable and reverse information projection”

Wednesday, March 27, 2024    
11:30AM – 1:00PM
Yale Institute for Foundations of Data Science
Kline Tower 13th Floor, Room 1327
New Haven, CT 06511

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Speaker: Aaditya Ramdas
Assistant Professor, Department of Statistics & Data Science (75%),
Machine Learning Department (25%),
Carnegie Mellon University

Wednesday, March 27, 2024
Lunch: 11:30 am (Kitchen)
Talk: 12:00 pm (Seminar Room #1327)
at the Yale institute for Foundations of Data Science, Kline Tower, 13th Floor

Title: The numeraire e-variable and reverse information projection

Abstract: In an excellent 1999 Yale PhD thesis, Jonathan Li proposed and defined a critical concept that he called the reverse information projection (RIPr), which is akin to a KL projection of a distribution onto a set of probability measures. This concept has gained prominence recently in game-theoretic statistics and sequential testing by betting, because it characterizes the log-optimal bet/e-variable of a point alternative hypothesis against a composite null hypothesis. However, it required assumptions of convexity of the set of distributions and a common reference measure to define densities. In this talk, we will show how to fully and completely generalize the theory underlying the RIPr, showing that it is always well defined, without any assumptions on the distributions involved. Further, a strong duality result identifies it as the dual to an optimal bet/e-variable called the numeraire, which is unique and also always exists without assumptions. This fully generalizes Kelly betting to composite nulls, and also results by Grunwald and coauthors on safe testing. The talk will not assume any prior knowledge on these topics.

This is joint work with Martin Larsson and Johannes Ruf (

Bio: Aaditya Ramdas (PhD, 2015) is an assistant professor at Carnegie Mellon University, in the Departments of Statistics and Machine Learning. His research interests include game-theoretic statistics and sequential anytime-valid inference, multiple testing and post-selection inference, and uncertainty quantification for machine learning (conformal prediction, calibration). His applied areas of interest include neuroscience, genetics and auditing (real-estate, finance, elections). Aaditya received the IMS Peter Gavin Hall Early Career Prize, the COPSS Emerging Leader Award, the Bernoulli New Researcher Award, the NSF CAREER Award, the Sloan fellowship in Mathematics, and faculty research awards from Adobe and Google. He also spends 20% of his time at Amazon working on causality and sequential experimentation.


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