| Neural network is an important model in the field of machine learning,which has attracted attention due to its high-precision prediction performance.However,due to the lack of interpretability of the prediction process,it is often referred to as a“black box model”.With the advent of the era of big data,the scale of data continues to expand,but the quality of the dataset shows a downward trend.A large number of complex data,such as redundant features and corrupted samples,that are not related to the real distribution,are included in the training dataset of neural networks.This not only increases the complexity of building the model but also leads to the curse of dimensionality and overfitting problems,which can severely undermine prediction performance.In order to address the above challenges,this paper combines neural networks with the partially linear additive model in the field of machine learning and the modal regression in the field of statistics,and proposes the neural partially linear additive model,the modal neural network,and the modal neural partially linear additive model.The contributions of this paper are as follows:（1）Aiming at the lack of interpretability of neural networks,we propose a novel neural partially linear additive model（NPLAM）.Our proposed model integrates the neural network into the partially linear additive model framework,and tackles the two interpretability problems of feature selection and structure discovery by introducing learnable double gates and the 1L regular terms.Moreover,due to the powerful function approximation ability of the neural network in terms of nonlinear functions,this model has excellent fitting performance.In theory,the generalization error bound of the model is established with Rademacher complexity.Experiments on both simulations and real-world datasets verify the effectiveness of the proposed model in feature selection and structure discovery,and exhibiting competitive prediction performance.（2）In order to solve the problem of poor prediction performance of neural networks under corrupted samples such as noise or outliers,we propose a novel modal neural network（MNN）.Our proposed model can learn the most likely function trend of training samples and reduce the adverse effects of corrupted samples on neural network learning.Furthermore,our method has asymptotic guarantees and demonstrates better performance than baseline models in robustness experiments.Further,we propose a modal neural partially linear additive model（MNPLAM）to improve the robustness of NPLAM.Theoretically,we establish the generalization error bound of our method with the Rademacher complex.Experimentally,experiments based on simulation and real-world datasets validate the advantages of the proposed model in terms of interpretability,robustness,and competitiveness. |
