Naiman Joseph, Song Peter Xuekun
Department of Biostatistics, University of Michigan, Ann Arbor, MI 48109, USA.
Entropy (Basel). 2022 Jan 28;24(2):203. doi: 10.3390/e24020203.
Motivated by mobile devices that record data at a high frequency, we propose a new methodological framework for analyzing a semi-parametric regression model that allow us to study a nonlinear relationship between a scalar response and multiple functional predictors in the presence of scalar covariates. Utilizing functional principal component analysis (FPCA) and the least-squares kernel machine method (LSKM), we are able to substantially extend the framework of semi-parametric regression models of scalar responses on scalar predictors by allowing multiple functional predictors to enter the nonlinear model. Regularization is established for feature selection in the setting of reproducing kernel Hilbert spaces. Our method performs simultaneously model fitting and variable selection on functional features. For the implementation, we propose an effective algorithm to solve related optimization problems in that iterations take place between both linear mixed-effects models and a variable selection method (e.g., sparse group lasso). We show algorithmic convergence results and theoretical guarantees for the proposed methodology. We illustrate its performance through simulation experiments and an analysis of accelerometer data.
受高频记录数据的移动设备的启发，我们提出了一种新的方法框架，用于分析半参数回归模型，该模型使我们能够在存在标量协变量的情况下研究标量响应与多个函数预测变量之间的非线性关系。利用函数主成分分析（FPCA）和最小二乘核机器方法（LSKM），我们能够通过允许多个函数预测变量进入非线性模型，大幅扩展标量响应对标量预测变量的半参数回归模型框架。在再生核希尔伯特空间的设置中建立了正则化用于特征选择。我们的方法同时对函数特征进行模型拟合和变量选择。为了实现这一点，我们提出了一种有效的算法来解决相关的优化问题，即在线性混合效应模型和变量选择方法（例如，稀疏组套索）之间进行迭代。我们展示了所提出方法的算法收敛结果和理论保证。我们通过模拟实验和加速度计数据分析来说明其性能。
