Fast large scale Gaussian process regression using approximate matrix-vector products
Fast large scale Gaussian process regression using approximate matrix-vector products
复制标题
DOI：
--
复制
发表时间：
2006
期刊：
影响因子：
--
通讯作者：
V. Raykar;R. Duraiswami
中科院分区：
文献类型：
--
作者：
V. Raykar;R. Duraiswami
高斯过程允许在贝叶斯框架中处理非线性非参数回归问题。然而，使用 N 个示例训练此类模型的计算成本为 O(N3)。线性系统求解的迭代方法可以将成本降低到 O(N2)，这对于大型数据集来说仍然是令人望而却步的。我们考虑使用 2-精确矩阵向量积算法将计算复杂度降低到 O(N)。利用不精确Krylov子空间方法的理论，我们展示了如何选择2来保证迭代方法的收敛。我们使用改进的快速高斯变换来测试我们的想法。我们展示了在大型数据集上实现的加速。对于平均值的预测，计算复杂度从 O(N) 降低到 O(1)。我们的实验表明，对于低维数据 (d ≤ 8)，所提出的方法可提供显着的加速。
Gaussian processes allow the treatment of non-linear non-parametric regression problems in a Bayesian framework. However the computational cost of training such a model with N examples scales as O(N3). Iterative methods for the solution of linear systems can bring this cost down to O(N2), which is still prohibitive for large data sets. We consider the use of 2-exact matrix-vector product algorithms to reduce the computational complexity to O(N). Using the theory of inexact Krylov subspace methods we show how to choose 2 to guarantee the convergence of the iterative methods. We test our ideas using the improved fast Gauss transform. We demonstrate the speedup achieved on large data sets. For prediction of the mean the computational complexity is reduced from O(N) to O(1). Our experiments indicated that for low dimensional data (d ≤ 8) the proposed method gives substantial speedups.