Fast Conditional Independence Test for Vector Variables with Large Sample Sizes

By Krzysztof Chalupka, Pietro Perona, Frederick Eberhardt. 2018

37 citations recorded by the source corpus.

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.

Subfields: Artificial Intelligence, Statistics and Probability, Statistical Learning Theory

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Artificial Intelligence

1. Yoshua Bengio
2. Bernhard Schölkopf
3. Anirudh Goyal
4. Stefan Bauer
5. Nan Rosemary Ke
6. Francesco Locatello
7. Kyunghyun Cho
8. Quoc V. Le

In Statistics and Probability

1. Anirudh Goyal
2. Stefan Bauer
3. Yoshua Bengio
4. Francesco Locatello
5. Nan Rosemary Ke
6. Nal Kalchbrenner
7. Bernhard Schölkopf
8. Arthur Gretton

In Statistical Learning Theory

1. Yoshua Bengio
2. Stefan Bauer
3. Francesco Locatello
4. Nal Kalchbrenner
5. Nan Rosemary Ke
6. Anirudh Goyal
7. Bernhard Schölkopf
8. Arthur Gretton

Citations in the corpus

• Toward Causal Representation Learning (2021, background): “Recent progress in (conditional) independence testing heavily relies on kernel function classes to represent probability distributions in reproducing kernel Hilbert spaces [43], [61], [74], [91], [92], [193], [280].”
• Towards Causal Representation Learning (2021, positive): “progress in (conditional) independence testing heavily relies on kernel function classes to represent probability distributions in reproducing kernel Hilbert spaces [90, 91, 73, 278, 60, 191, 42].”
• Causality for Machine Learning (2019, methodology): “Recent progress in (conditional) independence testing heavily relies on kernel function classes to represent probability distributions in reproducing kernel Hilbert spaces (Gretton et al., 2005a,b; Fukumizu et al., 2008; Zhang et al., 2011; Pfister et al., 2018b; Chalupka et al., 2018).”