Speaker: Kacper Chwiałkowski
This is work in progress. Most of non-parametric conditional independence tests, if not all of them, require some assumptions on random variables being tested (e.g. smooth density or being able to estimate density). This is in contrast to non-parametric two sample tests or independence tests, which are consistent regardless of underlying distributions. Is conditional independence testing more difficult then those two other problems or have we just not found the right test yet? I'll show that there is no U-statistic based test for conditional independence and then I'll discuss a following general conjecture: If a test for conditional independence controls type one error on level alpha, then its power is less or equal to alpha. If time permits we will discuss a specific, U-statistic based test, which requires weak assumptions on random variables (by weak I mean: relaxing them further might enlarge space of distribution so much that it's impossible to conduct a U-statistics based test).