Fast Conditional Independence Test for Vector Variables with Large Sample Sizes
This provides a faster and more accurate nonparametric conditional independence test for researchers and practitioners dealing with large-scale data, though it is incremental as it builds on existing prediction-based ideas.
The paper tackles the problem of efficiently testing conditional independence for high-dimensional data with large sample sizes, presenting the Fast (conditional) Independence Test (FIT) that achieves low Type I and Type II errors compared to existing methods, handling thousand-dimensional variables and hundred thousand samples quickly.
We present and evaluate the Fast (conditional) Independence Test (FIT) -- a nonparametric conditional independence test. The test is based on the idea that when $P(X \mid Y, Z) = P(X \mid Y)$, $Z$ is not useful as a feature to predict $X$, as long as $Y$ is also a regressor. On the contrary, if $P(X \mid Y, Z) \neq P(X \mid Y)$, $Z$ 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.