  We address the problem of detecting changes in multivariate datastreams, and
we investigate the intrinsic difficulty that change-detection methods have to
face when the data dimension scales. In particular, we consider a general
approach where changes are detected by comparing the distribution of the
log-likelihood of the datastream over different time windows. Despite the fact
that this approach constitutes the frame of several change-detection methods,
its effectiveness when data dimension scales has never been investigated, which
is indeed the goal of our paper. We show that the magnitude of the change can
be naturally measured by the symmetric Kullback-Leibler divergence between the
pre- and post-change distributions, and that the detectability of a change of a
given magnitude worsens when the data dimension increases. This problem, which
we refer to as \emph{detectability loss}, is due to the linear relationship
between the variance of the log-likelihood and the data dimension. We
analytically derive the detectability loss on Gaussian-distributed datastreams,
and empirically demonstrate that this problem holds also on real-world datasets
and that can be harmful even at low data-dimensions (say, 10).
