Online Bayesian kernel regression from nonlinear mapping of observations

In a large number of applications, engineers have to estimate a function linked to the state of a dynamic system. To do so, a sequence of samples drawn from this unknown function is observed while the system is transiting from state to state and the problem is to generalize these observations to unvisited states. Several solutions can be envisioned among which regressing a family of parameterized functions so as to make it fit at best to the observed samples. However classical methods cannot handle the case where actual samples are not directly observable but only a nonlinear mapping of them is available, which happen when a special sensor has to be used or when solving the Bellman equation in order to control the system. This paper introduces a method based on Bayesian filtering and kernel machines designed to solve the tricky problem at sight. First experimental results are promising.