Near-optimal Nonmyopic Value of Information in Graphical Models

TL;DR

This paper introduces an efficient randomized algorithm for nonmyopically selecting the most informative variables in graphical models, achieving near-optimal approximation guarantees and validated on real-world datasets.

Contribution

It presents the first polynomial-time algorithm with a constant factor approximation guarantee for nonmyopic information gathering in graphical models.

Findings

Algorithm achieves (1-1/e-epsilon) approximation with high confidence.

No polynomial-time algorithm can surpass the (1-1/e) approximation barrier unless P=NP.

Extensive experiments demonstrate the method's effectiveness on real-world data.

Abstract

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.