Neural networks for functional and survival data

The integration of advanced statistical methods with cutting-edge machine learning techniques has attracted substantial attention. Within this convergence, functional data analysis (FDA) and survival analysis are two pivotal areas where traditional statistical tools often encounter limitations in capturing the intricacies of dynamic processes and time-to-event outcomes. FDA is a statistical discipline that analyzes curves, surfaces and any random variables defined across infinite-dimensional spaces for various statistical tasks, including functional regression and functional data representation. We take advantage of neural networks, proposing novel models to tackle the scarce exploration of nonlinear regression analysis with scalar predictors and a functional response. In addition, a neural network-based approach is developed to address nonlinear representation learning and direct curve smoothing of discrete functional data concurrently. Time-to-event prediction, the task of predicting the time until the occurrence of a particular event of interest based on the characteristics of individuals, is a fundamental challenge in survival analysis and finds applications across diverse fields. We propose a simplified strategy to analyze right-censored survival outcomes using neural networks, enhancing estimation accuracy and computational efficiency in model discrimination in comparison to several existing survival neural networks.