In the current era of vast data and transparent machine learning, it is essential for techniques to operate at a large scale while providing a clear mathematical comprehension of the internal workings of the method. Although there already exist interpretable semi-parametric regression methods for large-scale applications that take into account non-linearity in the data, the complexity of the models is still often limited. One of the main challenges is the absence of interactions in these models, which are left out for the sake of better interpretability but also due to impractical computational costs. To overcome this limitation, we propose a new approach using a factorization method to derive a highly scalable higher-order tensor product spline model. Our method allows for the incorporation of all (higher-order) interactions of non-linear feature effects while having computational costs proportional to a model without interactions. We further develop a meaningful penalization scheme and examine the induced optimization problem. We conclude by evaluating the predictive and estimation performance of our method.

翻译：在大数据与可解释机器学习并行的当前时代，技术方法需具备大规模运算能力，同时提供对其内部工作机制的清晰数学理解。尽管针对大规模应用已存在考虑数据非线性的可解释半参数回归方法，但这些模型的复杂度仍常常受限。主要挑战之一在于模型缺乏交互项——为提升可解释性而忽略交互作用，但更深层原因在于其不可实际承受的计算成本。为突破这一限制，我们提出采用分解方法构建高度可扩展的高阶张量积样条模型。该模型在保持与无交互项模型相当计算成本的前提下，能够纳入所有（高阶）非线性特征效应的交互作用。我们进一步开发了具有实际意义的惩罚方案，并研究了由此引发的优化问题。最后通过评估方法的预测与估计性能完成验证。