Nonlinear Regression

Nonlinear regression aims to model relationships between variables where the dependence is not a simple linear function, focusing on accurately predicting outcomes and understanding the underlying nonlinear structure. Current research emphasizes developing computationally efficient algorithms like Braced Fourier Continuation and Regression (BFCR), addressing challenges posed by overparameterization through Bayesian frameworks, and improving extrapolation capabilities with novel methods such as "engression." These advancements are crucial for various applications, including anomaly detection, material modeling, and improving the reliability and security of machine learning models by providing better uncertainty quantification and addressing vulnerabilities like membership inference attacks.