  We consider online change detection of high dimensional data streams with
sparse changes, where only a subset of data streams can be observed at each
sensing time point due to limited sensing capacities. On the one hand, the
detection scheme should be able to deal with partially observable data and
meanwhile have efficient detection power for sparse changes. On the other, the
scheme should be able to adaptively and actively select the most important
variables to observe to maximize the detection power. To address these two
points, in this paper, we propose a novel detection scheme called CDSSD. In
particular, it describes the structure of high dimensional data with sparse
changes by smooth-sparse decomposition, whose parameters can be learned via
spike-slab variational Bayesian inference. Then the posterior Bayes factor,
which incorporates the learned parameters and sparse change information, is
formulated as a detection statistic. Finally, by formulating the statistic as
the reward of a combinatorial multi-armed bandit problem, an adaptive sampling
strategy based on Thompson sampling is proposed. The efficacy and applicability
of our method in practice are demonstrated with numerical studies and a real
case study.
