Abstract

Most learning algorithms assume that a training dataset is given initially. We address the common situation where data is not available initially, but can be obtained, at a cost. We focus on learning Bayesian belief networks (BNs) over discrete variables. As such BNs are models of probabilistic distributions, we consider the “generative” challenge of learning the parameters for a fixed structure, that best match the true distribution. We focus on the budgeted learning setting, where there is a known fixed cost ci for acquiring the value of the ith feature for any specified instance, and a known total budget to spend acquiring all information. After formally defining this problem from a Bayesian perspective, we first consider non-sequential algorithms that must decide, before seeing any results, which features of which instances to probe. We show this is NP-hard, even if all variables are independent, then prove that the greedy allocation algorithm iga is optimal here when the costs are uniform, but can otherwise be sub-optimal. We then show that general (sequential) policies perform better than non-sequential, and explore the challenges of learning the parameters for general belief networks in this sequential setting, describing conditions for when the obvious round-robin algorithm will, versus will not, work optimally. We also explore the effectiveness of this and various other heuristic algorithms. Appearing in Proceedings of the 27 th International Confeence on Machine Learning, Haifa, Israel, 2010. Copyright 2010 by the author(s)/owner(s).