On the Relationship between Online Gaussian Process Regression and   Kernel Least Mean Squares Algorithms
  We study the relationship between online Gaussian process (GP) regression and kernel least mean squares (KLMS) algorithms. While the latter have no capacity of storing the entire posterior distribution during online learning, we discover that their operation corresponds to the assumption of a fixed posterior covariance that follows a simple parametric model. Interestingly, several well-known KLMS algorithms correspond to specific cases of this model. The probabilistic perspective allows us to understand how each of them handles uncertainty, which could explain some of their performance differences. 
Steven Van Vaerenbergh, Jesus Fernandez-Bes, V\'ictor Elvira
stat.ML cs.IT cs.LG math.IT