Error Modeling Method Of Partial Functional Regression Model

With the development of science and technology,the data collected in real life are becoming more and more complex,the dimensionality of the data is getting higher and more diverse,and the mixed data composed of functional data and numerical data have also received extensive attention from scholars.In mixed data analysis,the partial functional regression model is a common analysis model.During the modeling process,it is usually assumed that the noise term follows a Gaussian distribution,but this assumption will lead to the lack of robustness of the model.Therefore,a functional regression model based on mixed Gaussian noise assumption is constructed to improve the robustness of the traditional model,and an adaptive learning algorithm is proposed to address the low computational efficiency of the traditional scoring search method for the tuning parameters in the penalized likelihood method.The main research contents include:(1)The expansion of the functional coefficients under the reproducing kernel Hilbert space,the Taylor expansion with integral remainder term and the inner product property of the reproducing kernel space are used to obtain the expansion representation of the functional coefficients,so that the problem of estimating the functional regression coefficients is transformed into the problem of estimating the parameter vectors.(2)In order to improve the robustness of the traditional model,it is assumed that the noise in the model obeys the mixed Gaussian distribution.At the same time,in order to improve the generalization ability of the model,the statistical inference of the estimated parameters is carried out by constructing the penalty likelihood function.After that,the EM algorithm is applied to solve all parameters iteratively.(3)For the tuning parameters in the penalized likelihood function,an algorithm for adaptive learning is constructed based on the principle of minimizing the mean square error of Bayesian estimation,which automatically learns the personalized tuning parameters for each component of the parameters and updates them alternately with the estimation of the parameters in a data-driven method.The experimental analysis is conducted in simulated and real data,and the experimental results of the algorithm are compared with those of other algorithms,which prove that the algorithm proposed in this paper is robust and has better prediction ability compared with other methods.At the same time,by comparing with traditional tuning parameter scoring search methods,it is verified that the adaptive learning algorithm proposed in this paper can improve the computational speed while ensuring the effectiveness.