[Turing-Southampton] S3RI seminar: Rajen Shah, Thursday 2-3pm

[Helen Ogden]

Dear all,

On Thursday (8 November) at 2pm in 54 / 7035 (7B), we have an S3RI 
seminar from Rajen Shah (University of Cambridge) on "Low-priced lunch 
in conditional independence testing". Details are given below.

The seminar will also be available via a live web-cast at
https://coursecast.soton.ac.uk/Panopto/Pages/Viewer.aspx?id=a28870b9-7e02-4981-b631-a98f008d9aa8

The talk will be followed by tea and cake in the staff reading room on 
level 4 of building 54.

Also, a reminder of the S3RI special seminar from Jonathan Rougier on 
Wednesday at 5pm in 58/1067: see attached flyer, and register at:
https://s3r1-special-seminar-nov18.eventbrite.co.uk/

Best wishes,
Helen

Low-priced lunch in conditional independence testing

Rajen Shah, University of Cambridge

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 formalisation 
of this result and show that a test with correct size does not have 
power against any alternative.

Given the non-existence of a uniformly valid conditional independence 
test, 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 to nonlinearly regress X on Z, and Y on Z and then compute a 
test statistic based on the sample covariance between the residuals, 
which we call the generalised covariance measure (GCM). We prove that 
validity of this form of test relies almost entirely on the weak 
requirement that the regression procedures are able to estimate the 
conditional means X given Z, and Y given Z, 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 the theoretical guarantees for 
kernel ridge regression. A simulation study shows that the test based on 
GCM is competitive with state of the art conditional independence tests.


For the current schedule of S3RI seminars, see 
https://tinyurl.com/s3riseminar

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