  We consider change-point estimation in a sequence of high-dimensional signals
given noisy observations. Classical approaches to this problem such as the
filtered derivative method are useful for sequences of scalar-valued signals,
but they have undesirable scaling behavior in the high-dimensional setting.
However, many high-dimensional signals encountered in practice frequently
possess latent low-dimensional structure. Motivated by this observation, we
propose a technique for high-dimensional change-point estimation that combines
the filtered derivative approach from previous work with convex optimization
methods based on atomic norm regularization, which are useful for exploiting
structure in high-dimensional data. Our algorithm is applicable in online
settings as it operates on small portions of the sequence of observations at a
time, and it is well-suited to the high-dimensional setting both in terms of
computational scalability and of statistical efficiency. The main result of
this paper shows that our method performs change-point estimation reliably as
long as the product of the smallest-sized change (the Euclidean-norm-squared of
the difference between signals at a change-point) and the smallest distance
between change-points (number of time instances) is larger than a Gaussian
width parameter that characterizes the low-dimensional complexity of the
underlying signal sequence.
