Efficient Gaussian process regression for large datasets.
Efficient Gaussian process regression for large datasets.
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DOI：
10.1093/biomet/ass068
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发表时间：
2013-03
期刊：
影响因子：
2.7
通讯作者：
Tokdar ST
中科院分区：
文献类型：
--
作者：
Banerjee A;Dunson DB;Tokdar ST
高斯过程广泛应用于非参数回归、分类和时空建模，这在一定程度上得益于有关其理论特性的丰富文献。然而，它们的实际限制之一是在执行必要的矩阵求逆时计算成本高昂，通常约为 n3，其中 n 是数据点的数量。对于大型数据集，存储和处理也会导致计算瓶颈，并且估计值和预测值的数值稳定性随着 n 的增加而降低。人们提出了各种方法来解决这些问题，包括空间数据分析中的预测过程和机器学习中的回归器子集技术。这些方法的基本思想是使用数据的子集，但这引发了关于子集选择的敏感性以及估计子集未很好覆盖的区域的精细尺度结构的局限性的问题。受压缩感知文献的启发，我们提出了一种替代方法，该方法涉及将所有数据点线性投影到低维子空间上。我们从理论角度并通过模拟和真实数据示例证明了这种方法的优越性。
Gaussian processes are widely used in nonparametric regression, classification and spatiotemporal modelling, facilitated in part by a rich literature on their theoretical properties. However, one of their practical limitations is expensive computation, typically on the order of n3 where n is the number of data points, in performing the necessary matrix inversions. For large datasets, storage and processing also lead to computational bottlenecks, and numerical stability of the estimates and predicted values degrades with increasing n. Various methods have been proposed to address these problems, including predictive processes in spatial data analysis and the subset-of-regressors technique in machine learning. The idea underlying these approaches is to use a subset of the data, but this raises questions concerning sensitivity to the choice of subset and limitations in estimating fine-scale structure in regions that are not well covered by the subset. Motivated by the literature on compressive sensing, we propose an alternative approach that involves linear projection of all the data points onto a lower-dimensional subspace. We demonstrate the superiority of this approach from a theoretical perspective and through simulated and real data examples.
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影响因子：
1.6
作者：
Choi, Taeryon;Schervish, Mark J.
通讯作者：
Schervish, Mark J.
DOI：
10.1016/j.cma.2004.04.008
发表时间：
2005-01-01
影响因子：
7.2
作者：
Frauenfelder, P;Schwab, C;Todor, RA
通讯作者：
Todor, RA
DOI：
10.1111/j.1467-9868.2008.00663.x
发表时间：
2008-09-01
期刊：
Journal of the Royal Statistical Society. Series B, Statistical methodology
影响因子：
--
作者：
Banerjee S;Gelfand AE;Finley AO;Sang H
通讯作者：
Sang H
影响因子：
2.5
作者：
Candès, EJ;Romberg, J;Tao, T
通讯作者：
Tao, T
影响因子：
2.9
作者：
Csató, L;Opper, M
通讯作者：
Opper, M