Directed graphical models such as Bayesian nets are often used to implement intelligent tutoring systems able to interact in real-time with learners in a purely automatic way. When coping with such models, keeping a bound on the number of parameters might be important for multiple reasons. First, as these models are typically based on expert knowledge, a huge number of parameters to elicit might discourage practitioners from adopting them. Moreover, the number of model parameters affects the complexity of the inferences, while a fast computation of the queries is needed for real-time feedback. We advocate logical gates with uncertainty for a compact parametrization of the conditional probability tables in the underlying Bayesian net used by tutoring systems. We discuss the semantics of the model parameters to elicit and the assumptions required to apply such approach in this domain. We also derive a dedicated inference scheme to speed up computations.

This paper presents a new approach for computing posterior probabilities in Bayesian nets, which sidesteps the triangulation problem. The current state of art is the clique tree propagation approach. When the underlying graph of a Bayesian net is triangulated, this approach arranges its cliques into a tree and computes posterior probabilities by appropriately passing around messages in that tree. The computation in each clique is simply direct marginalization. When the underlying graph is not triangulated, one has to first triangulated it by adding edges. Referred to as the triangulation problem, the problem of finding an optimal or even a ?good? triangulation proves to be difficult. In this paper, we propose to first decompose a Bayesian net into smaller components by making use of Tarjan's algorithm for decomposing an undirected graph at all its minimal complete separators. Then, the components are arranged into a tree and posterior probabilities are computed by appropriately passing around messages in that tree. The computation in each component is carried out by repeating the whole procedure from the beginning. Thus the triangulation problem is sidestepped.

The Quick Medical Reference (QMR) is a compendium of statistical knowledge connecting diseases to findings (symptoms). The information in QMR can be represented as a Bayesian network. The inference problem (or, in more medical language, giving a diagnosis) for the QMR is to, given some findings, find the probability of each disease. Rejection sampling and likelihood weighted sampling (a.k.a. likelihood weighting) are two simple algorithms for making approximate inferences from an arbitrary Bayesian net (and from the QMR Bayesian net in particular). Heretofore, the samples for these two algorithms have been obtained with a conventional "classical computer". In this paper, we will show that two analogous algorithms exist for the QMR Bayesian net, where the samples are obtained with a quantum computer. We expect that these two algorithms, implemented on a quantum computer, can also be used to make inferences (and predictions) with other Bayesian nets.