As the spatial features of multivariate data are increasingly central in researchers' applied problems, there is a growing demand for novel spatially-aware methods that are flexible, easily interpretable, and scalable to large data. We develop inside-out cross-covariance (IOX) models for multivariate spatial likelihood-based inference. IOX leads to valid cross-covariance matrix functions which we interpret as inducing spatial dependence on independent replicates of a correlated random vector. The resulting sample cross-covariance matrices are "inside-out" relative to the ubiquitous linear model of coregionalization (LMC). However, unlike LMCs, our methods offer direct marginal inference, easy prior elicitation of covariance parameters, the ability to model outcomes with unequal smoothness, and flexible dimension reduction. As a covariance model for a q-variate Gaussian process, IOX leads to scalable models for noisy vector data as well as flexible latent models. For large n cases, IOX complements Vecchia approximations and related process-based methods based on sparse graphical models. We demonstrate superior performance of IOX on synthetic datasets as well as on colorectal cancer proteomics data. An R package implementing the proposed methods is available at github.com/mkln/spiox.

翻译：随着多元数据的空间特征在研究者应用问题中日益重要，对兼具灵活性、易解释性且能扩展至大规模数据的新型空间感知方法的需求不断增长。本文提出用于多元空间似然推断的内外交叉协方差模型。该模型可导出有效的交叉协方差矩阵函数，我们将其解释为在相关随机向量的独立重复样本上引入空间依赖性。所得样本交叉协方差矩阵相对于普遍使用的线性协同区域化模型呈现"内外翻转"特性。然而与线性协同区域化模型不同，我们的方法具备直接边缘推断能力、协方差参数先验分布易于设定、可建模具有不同平滑度的观测结果，并能实现灵活的降维处理。作为q元高斯过程的协方差模型，该方法可扩展至含噪声向量数据的建模，并构建灵活的隐变量模型。针对大规模样本情形，本方法可与基于稀疏图模型的Vecchia近似及相关过程型方法形成互补。我们在合成数据集与结直肠癌蛋白质组学数据上验证了该模型的优越性能。相关R软件包已在github.com/mkln/spiox发布。