Gaussian Graphical Model Selection from Size Constrained Measurements

In this paper, we introduce the problem of learning graphical models from size constrained measurements. This is inspired by a wide range of problems where one is unable to measure all the variables involved simultaneously. We propose notions of data requirement for this setting and then begin by considering an extreme case where one is allowed to only measure pairs of variables. For this setting we propose a simple algorithm and provide guarantees on its behavior. We then generalize to the case where one is allowed to measure up to r variables simultaneously, and draw connections to the field of combinatorial designs. Finally, we propose an interactive version of the proposed algorithm that is guaranteed to have significantly better data requirement on a wide range of realistic settings.