The sure independence screening procedure by ranking the marginal Pear-
son correlation is well documented in literatures and works satisfactorily in the
ultra-high dimensional case. However, this marginal Person correlation learning would
easily miss the variable that is marginally uncorrelated with the response but corre-
lated with the response jointly with some other variables. This failure in missing an
important variable is due to the fact that the marginal Pearson correlation does not use
the joint information of the response and a set of covariates. In this paper, we intro-
duce a new screening method which leaves a variable into the active set if it jointly
with some other variables has a high canonical correlation with the response. This is

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• Sure screening by ranking the canonical correlations