  In this paper, we investigate a divide and conquer approach to Kernel Ridge
Regression (KRR). Given n samples, the division step involves separating the
points based on some underlying disjoint partition of the input space (possibly
via clustering), and then computing a KRR estimate for each partition. The
conquering step is simple: for each partition, we only consider its own local
estimate for prediction. We establish conditions under which we can give
generalization bounds for this estimator, as well as achieve optimal minimax
rates. We also show that the approximation error component of the
generalization error is lesser than when a single KRR estimate is fit on the
data: thus providing both statistical and computational advantages over a
single KRR estimate over the entire data (or an averaging over random
partitions as in other recent work, [30]). Lastly, we provide experimental
validation for our proposed estimator and our assumptions.
