A1665
Title: Nonlinear function-on-scalar regression using continuous neural networks
Authors: Sidi Wu - Fuzhou University (China) [presenting]
Abstract: Function-on-scalar regression models the relationship between scalar predictors and a functional response, such as a growth curve or a brain signal. Classical approaches typically assume linearity or additive effects, limiting their ability to capture complex nonlinear dynamics. A novel framework for nonlinear function-on-scalar regression using continuous neural networks is introduced. In contrast to existing discrete neural network methods, which employ fixed hidden layers to map effects between predictors and static features of the functional response, this design directly incorporates continuous neurons and functional weights, enabling dynamic mapping from scalar predictors to a functional response across the entire observation interval, beginning from the first hidden layer. Specifically, scalar predictors are encoded into the initial continuous layer via functional weights, producing functional outcomes. Subsequent layers then propagate these functional outcomes and functional weights through integral transformations, maintaining the functional representation continuously from input to output. Network training is achieved through a functional gradient-based optimization algorithm combined with basis expansion applied to the functional weight parameters. Numerical experiments validate the approach, demonstrating superior prediction accuracy and smoother estimates compared to existing methods across multiple scenarios.
