We present and evaluate the Fast (conditional) Independence Test (FIT) -- a
nonparametric conditional independence test. The test is based on the idea that
when P(X∣Y,Z)=P(X∣Y), Z is not useful as a feature to predict
X, as long as Y is also a regressor. On the contrary, if P(X∣Y,Z)=P(X∣Y), Z might improve prediction results. FIT applies to
thousand-dimensional random variables with a hundred thousand samples in a
fraction of the time required by alternative methods. We provide an extensive
evaluation that compares FIT to six extant nonparametric independence tests.
The evaluation shows that FIT has low probability of making both Type I and
Type II errors compared to other tests, especially as the number of available
samples grows. Our implementation of FIT is publicly available