Recent advances of kernel regression assume that target signals lie over a feature graph such that their values can be predicted with the assistance of the graph learned from training data. In this article, we propose a novel kernel regression framework whose outputs follow a matrix-variate Gaussian distribution (MVGD) such that the kernel matrix can be viewed as the column covariance matrix of outputs, and the hyperparameters of a chosen kernel can be optimized using gradient methods. Furthermore, in contrast to the state-of-the-art kernel regression algorithms over graph (KRG), a sample graph of target outputs is introduced to work with regression coefficients and hyperparameters of a chosen kernel in our algorithms. The proposed KRG framework is decomposed into two stages, including the estimation of row and column covariance matrices of MVGD and graph learning along with the estimation of regression coefficients. Numerical approaches are developed to tackle the corresponding optimization problems. Experimental results over synthetic and real-world datasets demonstrate that the performance of the proposed algorithms is superior to that of the state-of-the-art methods.

中文翻译：

---

样本图上矩阵变量高斯分布信号的核回归


核回归的最新进展假设目标信号位于特征图上，以便可以借助从训练数据中学习到的图来预测它们的值。在本文中，我们提出了一种新颖的核回归框架，其输出遵循矩阵变量高斯分布（MVGD），使得核矩阵可以被视为输出的列协方差矩阵，并且可以使用以下方法来优化所选核的超参数梯度方法。此外，与最先进的图核回归算法（KRG）相比，我们引入了目标输出的样本图来处理算法中所选核的回归系数和超参数。所提出的 KRG 框架分为两个阶段，包括 MVGD 的行和列协方差矩阵的估计和图学习以及回归系数的估计。开发了数值方法来解决相应的优化问题。合成数据集和真实数据集的实验结果表明，所提出的算法的性能优于最先进的方法。