A new canonical correlation (CC) based interaction screening procedure called CCIS is suggested for the ultrahigh dimensional interaction model with a multivariate response. The CCIS procedure consists of two steps: First, it selects a set of candidate features which has a large CC with the squared response; Then it recovers the influential main effects and interactions simultaneously from the reduced interaction model built by the features selected in the first step. CCIS has a ranking statistic with a simple structure, thus it can be calculated very quickly. More importantly, CCIS is powerful to detect the features which have a linear relationship with the response. Both theoretical results and numerical studies are provided to illustrate the effectiveness of CCIS.
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