  High-dimensional variable selection is an important issue in many scientific
fields, such as genomics. In this paper, we develop a sure independence feature
screening pro- cedure based on kernel canonical correlation analysis (KCCA-SIS,
for short). KCCA- SIS is easy to be implemented and applied. Compared to the
sure independence screen- ing procedure based on the Pearson correlation (SIS,
for short) developed by Fan and Lv [2008], KCCA-SIS can handle nonlinear
dependencies among variables. Compared to the sure independence screening
procedure based on the distance correlation (DC- SIS, for short) proposed by Li
et al. [2012], KCCA-SIS is scale free, distribution free and has better
approximation results based on the universal characteristic of Gaussian Kernel
(Micchelli et al. [2006]). KCCA-SIS is more general than SIS and DC-SIS in the
sense that SIS and DC-SIS correspond to certain choice of kernels. Compared to
supremum of Hilbert Schmidt independence criterion-Sure independence screening
(sup-HSIC-SIS, for short) developed by Balasubramanian et al. [2013], KCCA-SIS
is scale free removing the marginal variation of features and response
variables. No model assumption is needed between response and predictors to
apply KCCA-SIS and it can be used in ultrahigh dimensional data analysis.
Similar to DC-SIS and sup- HSIC-SIS, KCCA-SIS can also be used directly to
screen grouped predictors and for multivariate response variables. We show that
KCCA-SIS has the sure screening prop- erty, and has better performance through
simulation studies. We applied KCCA-SIS to study Autism genes in a
spatiotemporal gene expression dataset for human brain development, and
obtained better results based on gene ontology enrichment analysis comparing to
the other existing methods.

Methodology