[Statlist] Research Webinar in Statistics *FRIDAY 26 MARCH 2021* GSEM, University of Geneva

[gsem-support-instituts]

Dear All,

We are pleased to invite you to our next Research Webinar.

Looking forward to seeing you


Organizers :                                                                                   
E. Cantoni - S. Engelke - D. La Vecchia - E. Ronchetti
S. Sperlich - F. Trojani - M.-P. Victoria-Feser


FRIDAY 26 MARCH 2021 at 11:15am
ONLINE
Please join the Zoom research webinar: https://unige.zoom.us/j/92924332087?pwd=U1U1NFk4dTFCRHBMeWYrSDBQcXBiQT09
Meeting ID: 929 2433 2087
Passcode: 399192


Low-Priced Lunch in Conditional Independence Testing
Rajen SHAH (https://www.dpmms.cam.ac.uk/~rds37/) - University of Cambridge, UK

ABSTRACT:
It is a common saying that testing for conditional independence, i.e., testing whether X is independent of Y, given Z, is a hard statistical problem if Z is a continuous random variable. We provide a formalization of this result and show that any test must have size at least as large as its power - in this sense conditional independence testing is impossible! In the case where Z is infinite-dimensional (e.g. if Z is a functional predictor), the problem is more severe: even if (X, Y, Z) are assumed to be jointly Gaussian, and the marginal distribution of Z is known, testing conditional independence is impossible.

Given the non-existence of uniformly valid conditional independence tests, we argue that tests must be designed so their suitability for a particular problem setting may be judged easily. To address this need, we propose a simple family of conditional independence tests valid for both the multivariate and functional data settings whose validity relies primarily on the relatively weak requirement that regressing each of X and Y on Z is able to estimate the relevant conditional expectations at a slow rate.  While our general procedure can be tailored to the setting at hand by combining it with any regression technique, we develop theoretical guarantees for kernel ridge regression and Tikhonov regularization in the context of the functional linear model. Simulation studies show that our testing framework is competitive with state of the art conditional independence tests.


Visit the website: https://www.unige.ch/gsem/en/research/seminars/rcs/