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SUMMARY:Model-X and doubly robust conditional independence testing - Eugen
 e Katsevich (University of Pennsylvania)
DTSTART:20230428T143000Z
DTEND:20230428T160000Z
UID:TALK199957@talks.cam.ac.uk
CONTACT:97804
DESCRIPTION:Model-X approaches to testing conditional independence between
  a predictor and an outcome variable given a vector of covariates usually 
 assume exact knowledge of the conditional distribution of the predictor gi
 ven the covariates. Nevertheless\, model-X methodologies are often deploye
 d with this conditional distribution learned in sample. We investigate the
  consequences of this choice through the lens of the distilled conditional
  randomization test (dCRT). We find that Type-I error control is still pos
 sible\, but only if the mean of the outcome variable given the covariates 
 is estimated well enough. This demonstrates that the dCRT is doubly robust
 \, and motivates a comparison to the generalized covariance measure (GCM) 
 test\, another doubly robust conditional independence test. We prove that 
 these two tests are asymptotically equivalent\, and show that the GCM test
  is in fact optimal against (generalized) partially linear alternatives by
  leveraging semiparametric efficiency theory. In an extensive simulation s
 tudy\, we compare the dCRT to the GCM test. We find that the GCM test and 
 the dCRT are quite similar in terms of both Type-I error and power\, and t
 hat post-lasso based test statistics (as compared to lasso based statistic
 s) can dramatically improve Type-I error control for both methods.
LOCATION:https://maths-cam-ac-uk.zoom.us/j/93998865836?pwd=VzVzN1VFQ0xjS3V
 DdlY0enBVckY5dz09
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