Can we break the dependency in distributed detection?

We consider a distributed detection problem where sensors observe dependent observations. We ask, if we can allow the sensors to locally exchange a few bits with each other, whether we can use these bits to "break" the dependency of the sensor observations, and thus reduce the dependent detection problem to the much better-studied and understood case of conditionally independent observations. To this end, we propose an optimization problem that we prove is equivalent to minimizing the dependency between the sensor observations. This problem is in general NP-hard, however, we show that for at least some cases of Gaussian distributions it can be solved efficiently. For general distributions, we propose to use alternating minimization and derive a constant factor approximation algorithm. Numerical evaluations indicate that our approach can offer significant improvement in detection accuracy over alternative schemes.