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We extend the differential approach to inference in Bayesian networks (BNs) (Darwiche, 2000) to handle specific problems that arise in the context of dynamic Bayesian networks (DBNs). We first summarize Darwiche's approach for BNs, which involves the representation of a BN in terms of a multivariate polynomial. We then show how procedures for the computation of corresponding polynomials for DBNs can be derived. These procedures permit not only an exact roll-up of old time slices but also a constant-space evaluation of DBNs. The method is applicable to both forward and backward propagation, and it does not presuppose that each time slice of the DBN has the same structure. It is compatible with approximative methods for roll-up and evaluation of DBNs. Finally, we discuss further ways of improving efficiency, referring as an example to a mobile system in which the computation is distributed over a normal workstation and a resource-limited mobile device.

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In this paper, we describe an interface consisting of a virtual showroom where a team of two highly realistic 3D agents presents product items in an entertaining and attractive way. The presentation flow adapts to users' attentiveness, or lack thereof, and may thus provide a more personalized and userattractive experience of the presentation. In order to infer users' attention and visual interest regarding interface objects, our system analyzes eye movements in real-time. Interest detection algorithms used in previous research determine an object of interest based on the time that eye gaze dwells on that object. However, this kind of algorithm is not well suited for dynamic presentations where the goal is to assess the user's focus of attention regarding a dynamically changing presentation. Here, the current context of the object of attention has to be considered, i. e., whether the visual object is part of (or contributes to) the current presentation content or not. Therefore, we propose a new approach that estimates the interest (or non-interest) of a user by means of dynamic Bayesian networks. Each of a predefined set of visual objects has a dynamic Bayesian network assigned to it, which calculates the current interest of the user in this object. The estimation takes into account (1) each new gaze point, (2) the current context of the object, and (3) preceding estimations of the object itself. Based on these estimations the presentation agents can provide timely and appropriate response.