Didong Li, Andrew Jones, Sudipto Banerjee, Barbara Engelhardt
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引用次数: 0
Abstract
Gaussian processes are pervasive in functional data analysis, machine learning, and spatial statistics for modeling complex dependencies. Scientific data are often heterogeneous in their inputs and contain multiple known discrete groups of samples; thus, it is desirable to leverage the similarity among groups while accounting for heterogeneity across groups. We propose multi-group Gaussian processes (MGGPs) defined over , where is a finite set representing the group label, by developing general classes of valid (positive definite) covariance functions on such domains. MGGPs are able to accurately recover relationships between the groups and efficiently share strength across samples from all groups during inference, while capturing distinct group-specific behaviors in the conditional posterior distributions. We demonstrate inference in MGGPs through simulation experiments, and we apply our proposed MGGP regression framework to gene expression data to illustrate the behavior and enhanced inferential capabilities of multi-group Gaussian processes by jointly modeling continuous and categorical variables.
高斯过程在功能数据分析、机器学习和复杂依赖关系建模的空间统计中无处不在。科学数据的输入通常是异构的,并且包含多个已知的离散样本组;因此,在考虑组间异质性的同时,利用组间的相似性是可取的。我们通过在这些域上建立有效(正定)协方差函数的一般类,提出了定义在R p x上的多群高斯过程(MGGPs),其中的是表示群标记的有限集合。mggp能够准确地恢复组之间的关系,并在推理过程中有效地在所有组的样本之间共享强度,同时在条件后验分布中捕获不同的组特定行为。我们通过模拟实验证明了MGGP中的推理,并将我们提出的MGGP回归框架应用于基因表达数据,通过联合建模连续变量和分类变量来说明多组高斯过程的行为和增强的推理能力。
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