Adaptive estimation in weighted group testing

We consider a generalization of the problem of estimating the support size of a hidden subset S of a universe U from samples. This framework falls under the group testing [1] and the conditional sampling models [2, 3]. In group testing, for a query set, we are told if it intersects with the set S. We propose a generalization of this problem, where each element has a non-negative weight, and the objective is to estimate the total weight of the universe. In contrast to the regular group testing, we consider stronger access models, where each query outputs an element (with an appropriate probability), and reveals its weight. We show that in this natural generalization of the problem can be solved with only polylogarithmically many queries, and also discuss some lower bounds for the problem.