**Lecturer: **Prof. Pascal Poupart

**Institute: **University of Waterloo, Canada

**Date and time: **30.09.2013 - 15:00

**Details:**

Consider a haptic robotic stroke rehabilitation device that helps stroke patients to follow an exercise schedule. One exercise is to move the end effector of the robotic device to a desired target position and then to move it back to the start position, while a physical resistance is applied. Several outcomes are possible for each attempt of the exercise depending on the resistance level and the distance of the target: exercise is too easy, successful exercise, target reached in an uncontrolled fashion or target not reached. In order to tailor the rehabilitation schedule to the needs of each patient, therapists are interested in profiling patients' abilities by estimating the probability of each outcome as a function of the resistance level and target distance.
In this talk, I will explain how this problem can be viewed as the estimation of a continuum of multinomial distributions. Current state-of-the-art methods for expressing a distribution over a continuum of multinomial distributions use logistic Gaussian processes. However, these methods require computationally expensive matrix operations (cubic w.r.t. the amount of data in the worst case). I'll introduce a more intuitive approach, directly correlating Dirichlet distributions by sharing evidence between them according to a kernel function, an approach which has linear time complexity. I will also show that choosing a non-static kernel function can lead to asymptotically unbiased estimates of the multinomial distributions.