UC Irvine

This dissertation presents novel neural network-based methods for estimating conditional distribution functions across diverse settings. We introduce a robust approach for survival analysis with right-censored and time-varying covariates, estimating the conditional hazard function and deriving the conditional survival function. This method outperforms traditional Cox proportional hazards models and recent neural network models in both simulated and real-world data scenarios. Expanding the methodology to uncensored data, we propose a unified approach for estimating conditional distribution functions for continuous responses with multiple covariates. Our method shows improved robustness, accuracy, and computational efficiency compared to kernel-based and mean regression neural network methods. Further, we address limitations of traditional models by using DeepONet to capture complex, long-term effects of covariates on hazard functions, demonstrating enhanced flexibility and adaptability. We also develop a deep operator neural network framework for functional data analysis, where covariates are functions, paving the way for advanced analysis of complex data structures.