Self-Discrepancy Conditional Independence Test

Sanghack Lee, Vasant Honavar
Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence, PMLR R15:691-700, 2017.

Abstract

Tests of conditional independence (CI) of ran- dom variables play an important role in ma- chine learning and causal inference. Of partic- ular interest are kernel-based CI tests which allow us to test for independence among ran- dom variables with complex distribution func- tions. The efficacy of a CI test is measured in terms of its power and its calibratedness. We show that the Kernel CI Permutation Test (KCIPT) suffers from a loss of calibratedness as its power is increased by increasing the number of bootstraps. To address this limita- tion, we propose a novel CI test, called Self- Discrepancy Conditional Independence Test (SDCIT). SDCIT uses a test statistic that is a modified unbiased estimate of maximum mean discrepancy (MMD), the largest difference in the means of features of the given sample and its permuted counterpart in the kernel-induced Hilbert space. We present results of experi- ments that demonstrate SDCIT is, relative to the other methods: (i) competitive in terms of its power and calibratedness, outperforming other methods when the number of condition- ing variables is large; (ii) more robust with re- spect to the choice of the kernel function; and (iii) competitive in run time.

Cite this Paper

BibTeX
@InProceedings{pmlr-vR15-lee17b, title = {Self-Discrepancy Conditional Independence Test}, author = {Lee, Sanghack and Honavar, Vasant}, booktitle = {Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence}, pages = {691--700}, year = {2017}, editor = {Elidan, Gal and Kersting, Kristian}, volume = {R15}, series = {Proceedings of Machine Learning Research}, month = {11--15 Aug}, publisher = {PMLR}, pdf = {https://raw.githubusercontent.com/mlresearch/r15/main/assets/lee17b/lee17b.pdf}, url = {https://proceedings.mlr.press/r15/lee17b.html}, abstract = {Tests of conditional independence (CI) of ran- dom variables play an important role in ma- chine learning and causal inference. Of partic- ular interest are kernel-based CI tests which allow us to test for independence among ran- dom variables with complex distribution func- tions. The efficacy of a CI test is measured in terms of its power and its calibratedness. We show that the Kernel CI Permutation Test (KCIPT) suffers from a loss of calibratedness as its power is increased by increasing the number of bootstraps. To address this limita- tion, we propose a novel CI test, called Self- Discrepancy Conditional Independence Test (SDCIT). SDCIT uses a test statistic that is a modified unbiased estimate of maximum mean discrepancy (MMD), the largest difference in the means of features of the given sample and its permuted counterpart in the kernel-induced Hilbert space. We present results of experi- ments that demonstrate SDCIT is, relative to the other methods: (i) competitive in terms of its power and calibratedness, outperforming other methods when the number of condition- ing variables is large; (ii) more robust with re- spect to the choice of the kernel function; and (iii) competitive in run time.}, note = {Reissued by PMLR on 04 October 2026.} }
Endnote
%0 Conference Paper %T Self-Discrepancy Conditional Independence Test %A Sanghack Lee %A Vasant Honavar %B Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence %C Proceedings of Machine Learning Research %D 2017 %E Gal Elidan %E Kristian Kersting %F pmlr-vR15-lee17b %I PMLR %P 691--700 %U https://proceedings.mlr.press/r15/lee17b.html %V R15 %X Tests of conditional independence (CI) of ran- dom variables play an important role in ma- chine learning and causal inference. Of partic- ular interest are kernel-based CI tests which allow us to test for independence among ran- dom variables with complex distribution func- tions. The efficacy of a CI test is measured in terms of its power and its calibratedness. We show that the Kernel CI Permutation Test (KCIPT) suffers from a loss of calibratedness as its power is increased by increasing the number of bootstraps. To address this limita- tion, we propose a novel CI test, called Self- Discrepancy Conditional Independence Test (SDCIT). SDCIT uses a test statistic that is a modified unbiased estimate of maximum mean discrepancy (MMD), the largest difference in the means of features of the given sample and its permuted counterpart in the kernel-induced Hilbert space. We present results of experi- ments that demonstrate SDCIT is, relative to the other methods: (i) competitive in terms of its power and calibratedness, outperforming other methods when the number of condition- ing variables is large; (ii) more robust with re- spect to the choice of the kernel function; and (iii) competitive in run time. %Z Reissued by PMLR on 04 October 2026.
APA
Lee, S. & Honavar, V.. (2017). Self-Discrepancy Conditional Independence Test. Proceedings of the 33rd Conference on Uncertainty in Artificial Intelligence, in Proceedings of Machine Learning Research R15:691-700 Available from https://proceedings.mlr.press/r15/lee17b.html. Reissued by PMLR on 04 October 2026.

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