  We consider offline detection of a single changepoint in binary and count
time-series. We compare exact tests based on the cumulative sum (CUSUM) and the
likelihood ratio (LR) statistics, and a new proposal that combines exact
two-sample conditional tests with multiplicity correction, against standard
asymptotic tests based on the Brownian bridge approximation to the CUSUM
statistic. We see empirically that the exact tests are much more powerful in
situations where normal approximations driving asymptotic tests are not
trustworthy: (i) small sample settings; (ii) sparse parametric settings; (iii)
time-series with changepoint near the boundary.
  We also consider a multichannel version of the problem, where channels can
have different changepoints. Controlling the False Discovery Rate (FDR), we
simultaneously detect changes in multiple channels. This "local" approach is
shown to be more advantageous than multivariate global testing approaches when
the number of channels with changepoints is much smaller than the total number
of channels.
  As a natural application, we consider network-valued time-series and use our
approach with (a) edges as binary channels and (b) node-degrees or other local
subgraph statistics as count channels. The local testing approach is seen to be
much more informative than global network changepoint algorithms.
