Near-optimal Nonmyopic Value of Information in Graphical Models
This addresses a fundamental issue in real-world systems like sensor networks for selecting optimal observations, though it appears to be an incremental advance in algorithmic theory for graphical models.
The paper tackles the problem of nonmyopically selecting the most informative subset of variables in graphical models to reduce uncertainty, presenting the first efficient randomized algorithm that achieves a constant factor (1-1/e-epsilon) approximation guarantee with high confidence and proving a hardness result that no polynomial-time algorithm can do better than (1-1/e) unless P = NP.
A fundamental issue in real-world systems, such as sensor networks, is the selection of observations which most effectively reduce uncertainty. More specifically, we address the long standing problem of nonmyopically selecting the most informative subset of variables in a graphical model. We present the first efficient randomized algorithm providing a constant factor (1-1/e-epsilon) approximation guarantee for any epsilon > 0 with high confidence. The algorithm leverages the theory of submodular functions, in combination with a polynomial bound on sample complexity. We furthermore prove that no polynomial time algorithm can provide a constant factor approximation better than (1 - 1/e) unless P = NP. Finally, we provide extensive evidence of the effectiveness of our method on two complex real-world datasets.