Maximum-entropy remote sampling

We consider the “remote-sampling” problem of choosing a subset S, with |S|= s, from a set N of observable random variables, so as to obtain as much information as possible about a set T of target random variables which are not directly observable. Our criterion is that of minimizing the entropy of T conditioned on S. We con ne our attention to the case in which the random variables have a joint Gaussian distribution. We demonstrate that the problem is NP-complete. We provide two methods for calculating lower bounds on the entropy: (i) a spectral method, and (ii) a continuous nonlinear relaxation. We employ these bounds in a branch-and-bound scheme to solve problem instances to optimality. ? 2001 Elsevier Science B.V. All rights reserved.