Bayesian Multi-Group Gaussian Process Models for Heterogeneous Group-Structured Data.

IF 5.2 3区 计算机科学 Q1 AUTOMATION & CONTROL SYSTEMS
Journal of Machine Learning Research Pub Date : 2025-01-01
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 R p × 𝒞 , where 𝒞 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.

异构组结构数据的贝叶斯多组高斯过程模型。
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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来源期刊
Journal of Machine Learning Research
Journal of Machine Learning Research 工程技术-计算机:人工智能
CiteScore
18.80
自引率
0.00%
发文量
2
审稿时长
3 months
期刊介绍: The Journal of Machine Learning Research (JMLR) provides an international forum for the electronic and paper publication of high-quality scholarly articles in all areas of machine learning. All published papers are freely available online. JMLR has a commitment to rigorous yet rapid reviewing. JMLR seeks previously unpublished papers on machine learning that contain: new principled algorithms with sound empirical validation, and with justification of theoretical, psychological, or biological nature; experimental and/or theoretical studies yielding new insight into the design and behavior of learning in intelligent systems; accounts of applications of existing techniques that shed light on the strengths and weaknesses of the methods; formalization of new learning tasks (e.g., in the context of new applications) and of methods for assessing performance on those tasks; development of new analytical frameworks that advance theoretical studies of practical learning methods; computational models of data from natural learning systems at the behavioral or neural level; or extremely well-written surveys of existing work.
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