Prize-Collecting Data Fusion for Cost-Performance Tradeoff in Distributed Inference

A novel formulation for optimal sensor selection and in-network fusion for distributed inference known as the prize-collecting data fusion (PCDF) is proposed in terms of optimal tradeoff between the costs of aggregating the selected set of sensor measurements and the resulting inference performance at the fusion center. For i.i.d. measurements, PCDF reduces to the prize-collecting Steiner tree (PCST) with the single-letter Kullback-Leibler divergence as the penalty at each node, as the number of nodes goes to infinity. PCDF is then analyzed under a correlation model specified by a Markov random field (MRF) with a given dependency graph. For a special class of dependency graphs, a constrained version of the PCDF reduces to the PCST on an augmented graph. In this case, an approximation algorithm is given with the approximation ratio depending only on the number of profitable cliques in the dependency graph. Based on these results, two heuristics are proposed for node selection under general correlation structure, and their performance is studied via simulations.