Operator-valued kernel recursive least squares algorithm

The paper develops recursive least square algorithms for nonlinear filtering of multivariate or functional data streams. The framework relies on kernel Hilbert spaces of operators. The results generalize to this framework the kernel recursive least squares developed in the scalar case. We particularly propose two possible extensions of the notion of approximate linear dependence of the regressors, which in the context of the paper, are operators. The development of the algorithms are done in infinite-dimensional spaces using matrices of operators. The algorithms are easily written in finite-dimensional settings using block matrices, and are illustrated in this context for the prediction of a bivariate time series.