Efficient Test Selection in Active Diagnosis via Entropy Approximation
  We consider the problem of diagnosing faults in a system represented by a
Bayesian network, where diagnosis corresponds to recovering the most likely
state of unobserved nodes given the outcomes of tests (observed nodes). Finding
an optimal subset of tests in this setting is intractable in general. We show
that it is difficult even to compute the next most-informative test using
greedy test selection, as it involves several entropy terms whose exact
computation is intractable. We propose an approximate approach that utilizes
the loopy belief propagation infrastructure to simultaneously compute
approximations of marginal and conditional entropies on multiple subsets of
nodes. We apply our method to fault diagnosis in computer networks, and show
the algorithm to be very effective on realistic Internet-like topologies. We
also provide theoretical justification for the greedy test selection approach,
along with some performance guarantees.
