Discovering Constrained Substructures in Bayesian Trees Using the E.M. Algorithm

In this paper, we present an Expectation-Maximization learning algorithm (E.M.) for estimating parameters of partially-constrained Bayesian trees. The Bayesian trees considered here consist of an unconstrained subtree and a set of constrained subtrees. In this tree structure, constraints are imposed on some of the parameters of the parametrized conditional distributions, such that all conditional distributions within the same subtree share the same constraint. We propose a learning method that uses the unconstrained subtree to guide the process of discovering a set of relevant constrained substructures. This substructure discovery procedure is accomplished simultaneously as the constraints are enforced in the Expectation-step of the E.M.-based algorithm. Additionally, we show how our method can be applied to the problem of learning representative pose models from a set of unsegmented video sequences. Finally, our experiments demonstrate the potential of the resulting learned model for human motion classification.