  This paper studies graphical model selection, i.e., the problem of estimating
a graph of statistical relationships among a collection of random variables.
Conventional graphical model selection algorithms are passive, i.e., they
require all the measurements to have been collected before processing begins.
We propose an active learning algorithm that uses junction tree representations
to adapt future measurements based on the information gathered from prior
measurements. We prove that, under certain conditions, our active learning
algorithm requires fewer scalar measurements than any passive algorithm to
reliably estimate a graph. A range of numerical results validate our theory and
demonstrates the benefits of active learning.
