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Kernel Adaptive Filtering (KAF) are mathematically principled methods whichsearch for a function in a Reproducing Kernel Hilbert Space. While they workwell for tasks such as time series prediction and system identification theyare plagued by a linear relationship between number of training samples andmodel size, hampering their use on the very large data sets common in today'sdata saturated world. Previous methods try to solve this issue bysparsification. We describe a novel view of optimal filtering which may providea route towards solutions in a RKHS which do not necessarily have this lineargrowth in model size. We do this by defining a RKHS in which the time structureof a stochastic process is still present. Using correntropy [11], an extensionof the idea of a covariance function, we create a time based functional whichdescribes some potentially nonlinear desired mapping function. This form of asolution may provide a fruitful line of research for creating more efficientrepresentations of functionals in a RKHS, while theoretically providingcomputational complexity in the test set similar to Wiener solution.

An Alternate View on Optimal Filtering in an RKHS