Kernel Ridge Regression via Partitioning
This method addresses scalability issues in KRR for large datasets, offering computational and statistical improvements, though it appears incremental as it builds on existing partitioning techniques.
The paper tackles the computational and statistical challenges of Kernel Ridge Regression (KRR) by proposing a divide-and-conquer approach that partitions input data and fits local KRR estimates, achieving optimal minimax rates and reducing approximation error compared to a single global KRR estimate.
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.