Kernel Partial Correlation with an Application to Single Cell Sequencing Data Analysis

• Activity Number: 547
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 10:30 AM to 12:20 PM
• Sponsor: Section on Statistical Learning and Data Mining
• Author(s): Ji Hwan Oh* and Hyonho Chun and Faye Zheng and Rebecca Doerge
• Companies: Purdue University and and Purdue University and Purdue University
• Keywords: Graphical Models ; Reproducing Kernel Hilbert Space ; Single-Cell Analysis ; Non-parametric Model ; Conditional Independence ; Partial Correlation

Abstract

Graphical models are designed to capture conditional independencies among multiple variables by existences of edges. Under the assumption of a multivariate normality, de- tection of the conditional independence is equivalent to the identification of a zero partial correlation coefficient. As a generalization, we propose a new measure, kernel partial corre- lation, which is estimated by the combination of two statistical methods; in the first part of which we use a nonparametric regression for conditioning, and then in the second part we check the nonparametric association to detect the independence. Our approach does not rely on distributional assumptions, so that it can be used in situations where the level of noise is high, many outliers exist, and associations involve nonlinearity. We show that our method performs better than well-known previously developed approaches in the simulated datasets which mimic characteristics of real single cell sequencing data. Then we apply our method to a real single cell sequencing data analysis and compare with other graphical models.