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Abstract:
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Given a dataset (X,Y), consider testing the null that Y is independent of X_j given the other variables. Conditional independence testing without assumptions is known to be impossible, but the recent “Model-X assumption" alleviates this issue by assuming that the distribution of X is known. Testing conditional independence hypotheses in the model-X framework has been the subject active methodological research, especially in the context of model-X knockoffs and their successful application to genome-wide association studies. However, the theoretical aspects of the conditional independence testing problem under model-X have not received as much attention. In this talk, I examine this question by establishing various theoretical properties of the conditional randomization test.
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