This work presents a new scalable automatic Bayesian Lasso methodology with variational inference for non-parametric splines regression that can capture the non-linear relationship between a response variable and predictor variables. Note that under non-parametric point of view the regression curve is assumed to lie in a infinite dimension space. Regression splines use a finite approximation of this infinite space, representing the regression function by a linear combination of basis functions. The crucial point of the approach is determining the appropriate number of bases or equivalently number of knots, avoiding over-fitting/under-fitting. A decision-theoretic approach was devised for knot selection. Comprehensive simulation studies were conducted in challenging scenarios to compare alternative criteria for knot selection, thereby ensuring the efficacy of the proposed algorithms. Additionally, the performance of the proposed method was assessed using real-world datasets. The novel procedure demonstrated good performance in capturing the underlying data structure by selecting the appropriate number of knots/basis.

这项工作提出了一种新的可扩展的自动贝叶斯套索方法，具有用于非参数样条回归的变分推理，可以捕获响应变量和预测变量之间的非线性关系。请注意，在非参数观点下，假设回归曲线位于无限维空间中。回归样条使用该无限空间的有限近似，通过基函数的线性组合来表示回归函数。该方法的关键点是确定适当的碱基数量或等效的结数，避免过度拟合/欠拟合。设计了一种决策理论方法来选择结。在具有挑战性的场景中进行了全面的模拟研究，以比较结选择的替代标准，从而确保所提出算法的有效性。此外，使用真实世界的数据集评估了所提出方法的性能。通过选择适当数量的结/基，新颖的过程在捕获底层数据结构方面表现出了良好的性能。