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The Hardness of Conditional Independence Testing

Presented by: 
Jonas Peters University of Copenhagen
Date: 
Monday 15th January 2018 - 11:55 to 12:40
Venue: 
INI Seminar Room 1
Abstract: 
Testing for conditional independence between continuous random variables is considered to be a hard statistical problem. We provide a formalization of this result and show that a test with correct size does not have power against any alternative. It is thus impossible to obtain any guarantee if the relationships between the random variables can be arbitrarily complex. We propose a practical test that achieves the correct size if the conditional expectations are smooth enough such that they can be estimated from data. This is joint work with Rajen Shah.
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University of Cambridge Research Councils UK
    Clay Mathematics Institute London Mathematical Society NM Rothschild and Sons