Kernel partial correlation: a novel approach to capturing conditional independence in graphical models for noisy data

ABSTRACT

Graphical models capture the conditional independence structure among random variables via existence of edges among vertices. One way of inferring a graph is to identify zero partial correlation coefficients, which is an effective way of finding conditional independence under a multivariate Gaussian setting. For more general settings, we propose kernel partial correlation which extends partial correlation with a combination of two kernel methods. First, a nonparametric function estimation is employed to remove effects from other variables, and then the dependence between remaining random components is assessed through a nonparametric association measure. The proposed approach is not only flexible but also robust under high levels of noise owing to the robustness of the nonparametric approaches.

KEYWORDS:

• Conditional independence
• graphical model
• Hilbert–Schmidt independence criterion
• partial correlation coefficient
• reproducing kernel Hilbert space
• support vector regression

Acknowledgments

The authors would like to thank the members of the RWD research group for helpful discussions.

Disclosure statement

No potential conflict of interest was reported by the authors.

Methods

The R language package KPCor is available at: http://stat.purdue.edu/∼oh84.

Additional information

Funding

This paper is based upon research supported in part by the National Science Foundation under grant no. DMS1107025.