Efficient Test Selection in Active Diagnosis via Entropy Approximation
This work addresses the challenge of efficient fault diagnosis in systems like computer networks, though it is incremental as it builds on existing greedy selection and approximation techniques.
The paper tackles the intractable problem of selecting optimal tests for fault diagnosis in Bayesian networks by proposing an approximate method using loopy belief propagation to compute entropy terms, and demonstrates its effectiveness on realistic Internet-like topologies.
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.