Efficient Observation Selection in Probabilistic Graphical Models Using Bayesian Lower Bounds

Real-world data often includes rich relational information, which can be leveraged to help predict unknown variables using a small amount of observed variables via a propagation effect. We consider the problem of selecting the best subset of variables to observe to maximize the overall prediction accuracy. Under the Bayesian framework, the optimal subset should be chosen to minimize the Bayesian optimal error rate, which, unfortunately, is critically challenging to calculate when the variables follow complex and high dimensional probabilistic distributions such as graphical models. In this paper, we propose to use a class of Bayesian lower bounds, including Bayesian Cramér Rao bounds as well as a novel extension of it to discrete graphical models, as surrogate criteria for optimal subset selection, providing a set of computationally efficient algorithms. Extensive experiments are presented to demonstrate our algorithm on both simulated and real-world datasets.