In the age of big data and interpretable machine learning, approaches need to work at scale and at the same time allow for a clear mathematical understanding of the method's inner workings. While there exist inherently interpretable semi-parametric regression techniques for large-scale applications to account for non-linearity in the data, their model complexity is still often restricted. One of the main limitations are missing interactions in these models, which are not included for the sake of better interpretability, but also due to untenable computational costs. To address this shortcoming, we derive a scalable high-order tensor product spline model using a factorization approach. Our method allows to include all (higher-order) interactions of non-linear feature effects while having computational costs proportional to a model without interactions. We prove both theoretically and empirically that our methods scales notably better than existing approaches, derive meaningful penalization schemes and also discuss further theoretical aspects. We finally investigate predictive and estimation performance both with synthetic and real data.

翻译：在大数据和可解释的机器学习的时代,方法需要以规模化的方式工作,同时能够对方法的内部作用有明确的数学理解。虽然在大规模应用中存在着可解释的半参数回归技术,以说明数据的非线性,但其模型复杂性仍然常常受到限制。主要局限之一是这些模型中缺少互动,这些模型的相互作用不是为了更好的解释,而是由于计算成本不合理。为了解决这一缺陷,我们利用一种因子化方法,得出了一个可缩放的高阶高压高压产品样板模型。我们的方法允许将非线性地物效应的所有(高度)相互作用纳入其中,同时使计算成本与模型成比例,而没有相互作用。我们从理论上和从经验上证明,我们的方法尺度明显优于现有方法,得出有意义的惩罚计划,并讨论进一步的理论问题。我们最后用合成数据和真实数据来调查预测和估计绩效。