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Activity Number: 548
Type: Contributed
Date/Time: Wednesday, August 12, 2015 : 10:30 AM to 12:20 PM
Sponsor: Section on Statistical Learning and Data Mining
Abstract #315962
Title: On Additive Partial Correlation Operator and Nonparametric Estimation of Graphical Models
Author(s): Kuang-Yao Lee* and Bing Li and Hongyu Zhao
Companies: Yale University and Penn State and Yale School of Public Health
Keywords: additive conditional independence ; reproducing kernel ; additive conditional covariance operator ; Gaussian graphical model ; partial correlation ; heterogeneity
Abstract:

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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