Distributed Detection with Empirically Observed Statistics. We consider a binary distributed detection problem in which the distributions of the sensor observations are unknown and only empirically observed statistics are available to the fusion center. The source (test) sequences are transmitted through different channels to the fusion center, which also observes noisy versions of labelled training sequences generated independently from the two underlying distributions. The fusion center decides which distribution the source sequence is sampled from based on the observed statistics, i.e., the noisy training data. We derive the optimal typeII error exponent given that the typeI error decays exponentially fast. We further maximize the typeII error exponent over the proportions of channels for both source and training sequences and conclude that as the ratio of the lengths of training to test sequences tends to infinity, using only one channel is optimal. Finally, we relate our results to the distributed detection problem studied by Tsitsiklis.

New Results on Testing Against Independence with RateLimited Constraints This work studies error exponent limits in hypothesis testing (HT) in a distributed scenario with partial communication constraints. We derive general conditions on the Type I error restriction under which the error exponent of the optimal Type II error has a closedform characterization for the task of testing against independence. We show that the error exponent is preserved for a family of decreasing Type I error restrictions. Complementing this analysis, new expressions are derived to bound the optimal Type II error probability for a finite number of observations. These bounds shed light about the velocity at which error exponent limits are attained with the number of samples.