  We propose two new methods to address the weak scaling problems of KRR: the
Balanced KRR (BKRR) and K-means KRR (KKRR). These methods consider alternative
ways to partition the input dataset into p different parts, generating p
different models, and then selecting the best model among them. Compared to a
conventional implementation, KKRR2 (optimized version of KKRR) improves the
weak scaling efficiency from 0.32% to 38% and achieves a 591times speedup for
getting the same accuracy by using the same data and the same hardware (1536
processors). BKRR2 (optimized version of BKRR) achieves a higher accuracy than
the current fastest method using less training time for a variety of datasets.
For the applications requiring only approximate solutions, BKRR2 improves the
weak scaling efficiency to 92% and achieves 3505 times speedup (theoretical
speedup: 4096 times).
