  The problem of detecting a few anomalous processes among a large number of
data streams is considered. At each time, aggregated observations can be taken
from a chosen subset of the processes, where the chosen subset conforms to a
given tree structure. The random observations are drawn from a general
distribution that may depend on the size of the chosen subset and the number of
anomalous processes in the subset. We propose a sequential search strategy by
devising an information-directed random walk (IRW) on the tree-structured
observation hierarchy. Subject to a reliability constraint, the proposed policy
is shown to be asymptotically optimal with respect to the detection accuracy.
Furthermore, it achieves the optimal logarithmic-order sample complexity with
respect to the size of the search space provided that the Kullback-Leibler
divergence between aggregated observations in the presence and the absence of
anomalous processes are bounded away from zero at all levels of the tree
structure as the size of the search space approaches infinity. Sufficient
conditions on the decaying rate of the aggregated observations to pure noise
under which a sublinear scaling in the size of the search space is preserved
are also identified for the Bernoulli case.
