REGULARIZED LEAST SQUARE KERNEL REGRESSION FOR STREAMING DATA

We study the use of kernel ridge regression (KRR) in the block-wise streaming data. The algorithm works in an online manner: when a new data block comes in, the algorithm computes a local estimator based on the incoming data block and updates the predictive model by weighted average of all local estimators. Assuming the block data sizes increase at a mild rate and the regularization parameters are selected adaptively according to the sample size of all available data at the time of updating the model, we prove the convergence of the average KRR estimator. The rate is optimal when the regression function can be well approximated by the reproducing kernel Hilbert space in the L-2 sense.