We propose a variable decomposition algorithm -greedy block coordinate
descent (GBCD)- in order to make dense Gaussian process regression practical
for large scale problems. GBCD breaks a large scale optimization into a series
of small sub-problems. The challenge in variable decomposition algorithms is
the identification of a subproblem (the active set of variables) that yields
the largest improvement. We analyze the limitations of existing methods and
cast the active set selection into a zero-norm constrained optimization problem
that we solve using greedy methods. By directly estimating the decrease in the
objective function, we obtain not only efficient approximate solutions for
GBCD, but we are also able to demonstrate that the method is globally
convergent. Empirical comparisons against competing dense methods like
Conjugate Gradient or SMO show that GBCD is an order of magnitude faster.
Comparisons against sparse GP methods show that GBCD is both accurate and
capable of handling datasets of 100,000 samples or more.

通过提出变量分解算法 - greedy block coordinate descent（GBCD）-，我们将密集高斯过程回归变得实用，解决了现有方法的局限性，并将主动集选择转化为零规范约束优化问题，使用贪心方法求解，进而在实证比较中证明了 GBCD 具有全局收敛的能力并且比竞争算法更快、更准确。