  Feature interactions can contribute to a large proportion of variation in
many prediction models. In the era of big data, the coexistence of high
dimensionality in both responses and covariates poses unprecedented challenges
in identifying important interactions. In this paper, we suggest a two-stage
interaction identification method, called the interaction pursuit via distance
correlation (IPDC), in the setting of high-dimensional multi-response
interaction models that exploits feature screening applied to transformed
variables with distance correlation followed by feature selection. Such a
procedure is computationally efficient, generally applicable beyond the
heredity assumption, and effective even when the number of responses diverges
with the sample size. Under mild regularity conditions, we show that this
method enjoys nice theoretical properties including the sure screening
property, support union recovery, and oracle inequalities in prediction and
estimation for both interactions and main effects. The advantages of our method
are supported by several simulation studies and real data analysis.
