  Change-points are a routine feature of 'big data' observed in the form of
high-dimensional data streams. In many such data streams, the component series
possess group structures and it is natural to assume that changes only occur in
a small number of all groups. We propose a new change point procedure, called
'groupInspect', that exploits the group sparsity structure to estimate a
projection direction so as to aggregate information across the component series
to successfully estimate the change-point in the mean structure of the series.
We prove that the estimated projection direction is minimax optimal, up to
logarithmic factors, when all group sizes are of comparable order. Moreover,
our theory provide strong guarantees on the rate of convergence of the
change-point location estimator. Numerical studies demonstrates the competitive
performance of groupInspect in a wide range of settings and a real data example
confirms the practical usefulness of our procedure.
