A rank-based approach to active diagnosis

The problem of active diagnosis arises in several applications such as disease diagnosis and fault diagnosis in computer networks, where the goal is to rapidly identify the binary states of a set of objects (e.g., faulty or working) by sequentially selecting, and observing, potentially noisy responses to binary valued queries. Previous work in this area chooses queries sequentially based on Information gain, and the object states are inferred by maximum a posteriori (MAP) estimation. In this work, rather than MAP estimation, we aim to rank objects according to their posterior fault probability. We propose a greedy algorithm to choose queries sequentially by maximizing the area under the ROC curve associated with the ranked list. The proposed algorithm overcomes limitations of existing work. When multiple faults may be present, the proposed algorithm does not rely on belief propagation, making it feasible for large scale networks with little loss in performance. When a single fault is present, the proposed algorithm can be implemented without knowledge of the underlying query noise distribution, making it robust to any misspecification of these noise parameters. We demonstrate the performance of the proposed algorithm through experiments on computer networks, a toxic chemical database, and synthetic datasets.