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Matey NEYKOV (Northwestern University) Some insights in Nonparametric Conditional Independence Testing
Statistical Seminar: Every Monday at 2:00 pm.
Time: 3:00 pm – 4:15 pm
Date: 18th September 2023
Matey NEYKOV (Northwestern University) – Some insights in Nonparametric Conditional Independence Testing
In this talk we discuss some recent developments in nonparametric conditional independence testing. Specifically if X, Y, Z are three real valued random variables, of bounded support, with Z being continuous, we develop a minimax optimal test which determines whether X is independent of Y given Z under certain smoothness assumptions. Unfortunately, the minimax optimal test which is based on binning Z, depends on unknown constants. In order to calibrate it we propose a local permutation procedure which permutes samples whose corresponding Z values fall into the same bin. Despite its simplicity and empirical support, the theoretical underpinnings of the local permutation test are unclear. To that end we establish theoretical foundations of local permutation tests with a particular focus on binning-based statistics. In particular we derive some sufficient conditions under which the type I error of our test is controlled below a desired level and we show that in some cases our test calibrated through local permutation can achieve minimax optimal power.
Cristina BUTUCEA (CREST), Alexandre TSYBAKOV (CREST), Karim LOUNICI (CMAP) , Jaouad MOURTADA (CREST)