A new method for learning pseudo-Boolean functions with applications in terrorists profiling

In this paper, we present a new framework for learning pseudo-Boolean functions from training data. The new learning framework is based on the observation that the training data can be seen as constraints on the possible candidate pseudo-Boolean functions and that, without any additional information, any of the pseudo-Boolean functions satisfying these constraints is equally likely. We define two types of learning from a training data set: one is to learn to predict the probability that the target function value f*(x₀) falls within an interval [a, b]; and the other is to learn a specific pseudo-Boolean function f as an approximation of the target function f*. Efficient algorithms for both learning tasks are presented. We relate our approach to the Bayesian classifier method. We argue that the new learning framework is suitable for applications in which the training data is rather limited and yet one would like to make useful and reliable predictions on the future data points. Applications in terrorist detection and classification clearly present such a situation where training data for terrorists are rather scarce.