Abstract:
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We introduce an additive partial correlation operator as an extension of partial correlation to the nonlinear setting, and use it to develop a new estimator of nonparametric graphical models. Our graphical models are based on additive conditional independence (ACI), a new statistical relation introduced recently by Li, Chun, and Zhao (2014) that captures the spirit of conditional independence but resorting to high-dimensional kernels for its estimation. Additive partial correlation operator completely characterizes ACI, and has the additional advantage of putting marginal variations in appropriate scales when evaluating inter-dependence, which leads to enhanced accuracy. We establish the consistency of the new estimator. Through simulation experiments and analysis of a Dream4 Challenge data set, we demonstrate that our method performs better than existing methods when the joint distribution is deviated from normality, and the better scaling further enhances its performance.
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