Title: Low priced lunch in conditional independence testing
Authors: Jonas Peters - University of Copenhagen (Denmark) [presenting]
Rajen D Shah - University of Cambridge (United Kingdom)
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.