An Efficient Approach to Regression Problems with Tensor Neural Networks
This work addresses the challenge of precise high-dimensional data analysis and predictive modeling, offering a domain-specific tool for applications requiring efficient computation and insights into data structure.
The paper tackles nonparametric regression problems by introducing a tensor neural network (TNN) that improves approximation accuracy and generalization for high-dimensional functions, outperforming conventional networks like FFN and RBN with similar parameter counts.
This paper introduces a tensor neural network (TNN) to address nonparametric regression problems, leveraging its distinct sub-network structure to effectively facilitate variable separation and enhance the approximation of complex, high-dimensional functions. The TNN demonstrates superior performance compared to conventional Feed-Forward Networks (FFN) and Radial Basis Function Networks (RBN) in terms of both approximation accuracy and generalization capacity, even with a comparable number of parameters. A significant innovation in our approach is the integration of statistical regression and numerical integration within the TNN framework. This allows for efficient computation of high-dimensional integrals associated with the regression function and provides detailed insights into the underlying data structure. Furthermore, we employ gradient and Laplacian analysis on the regression outputs to identify key dimensions influencing the predictions, thereby guiding the design of subsequent experiments. These advancements make TNN a powerful tool for applications requiring precise high-dimensional data analysis and predictive modeling.