Tensor regression methods have been widely used to predict a scalar response from covariates in the form of a multiway array. In many applications, the regions of tensor covariates used for prediction are often spatially connected with unknown shapes and discontinuous jumps on the boundaries. Moreover, the relationship between the response and the tensor covariates can be nonlinear. In this article, we develop a nonlinear Bayesian tensor additive regression model to accommodate such spatial structure. A functional fused elastic net prior is proposed over the additive component functions to comprehensively model the nonlinearity and spatial smoothness, detect the discontinuous jumps, and simultaneously identify the active regions. The great flexibility and interpretability of the proposed method against the alternatives are demonstrated by a simulation study and an analysis on facial feature data.

翻译：张量回归方法广泛应用于从多路数组形式的协变量预测标量响应。在许多应用中，用于预测的张量协变量区域通常空间相连，形状未知且边界存在不连续跳跃。此外，响应与张量协变量之间的关系可能为非线性。本文构建了一种非线性贝叶斯张量加性回归模型以适应此类空间结构。提出了一种基于加性分量函数的函数融合弹性网先验，以全面建模非线性和空间平滑性，检测不连续跳跃，并同时识别活跃区域。通过模拟研究和面部特征数据分析，证明了所提方法相较于替代方案具有更强的灵活性和可解释性。