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，对新颖、灵活、易于解释且能扩展到大规模数据的空间感知方法的需求不断增长。我们开发了基于似然推断的多元空间内外交叉协方差（IOX）模型。IOX导出了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存在的线性协同区域化模型（LMC）呈现"内外翻转"特性。然而，与LMC不同，我们的方法具备直接边缘推断能力、协方差参数先验设定的简易性、处理不同平滑度结果的能力以及灵活的降维特性。作为q元高斯过程的协方差模型，IOX可扩展至含噪声向量数据的建模，并能构建灵活的隐变量模型。针对大规模n的情形，IOX可与基于稀疏图模型的Vecchia近似及相关过程方法形成互补。我们在合成数据集和结直肠癌蛋白质组学数据上验证了IOX的优越性能。实现该方法的R软件包发布于github.com/mkln/spiox。