Sensor Selection for Hypothesis Testing: Complexity and Greedy Algorithms

In this paper, we consider sensor selection for (binary) hypothesis testing. Given a pair of hypotheses and a set of candidate sensors to measure (detect) the signals generated under the hypotheses, we aim to select a subset of the sensors (under a budget constraint) that yields the optimal signal detection performance. In particular, we consider the Neyman-Pearson detector based on measurements of the chosen sensors. The goal is to minimize (resp., maximize) the miss probability (resp., detection probability) of the Neyman-Pearson detector, while satisfying the budget constraint. We first show that the sensor selection for the Neyman-Pearson detector problem is NP-hard. We then characterize the performance of greedy algorithms for solving the sensor selection problem when we consider a surrogate to the miss probability as an optimization metric, which is based on the Kullback-Leibler distance. By leveraging the notion of submodularity ratio, we provide a bound on the performance of greedy algorithms.