In a large number of applications, engineers have to estimate values of an unknown function given some observed samples. This task is referred to as function approximation or as generalization. One way to solve the problem is to regress a family of parameterized functions so as to make it fit at best the observed samples. Yet, usually batch methods are used and parameterization is habitually linear. Moreover, very few approaches try to quantify uncertainty reduction occurring when acquiring more samples (thus more information), which can be quite useful depending on the application. In this paper we propose a sparse nonlinear bayesian online kernel regression. Sparsity is achieved in a preprocessing step by using a dictionary method. The nonlinear bayesian kernel regression can therefore be considered as achieved online by a Sigma Point Kalman Filter. First experiments on a cardinal sine regression show that our approach is promising.
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