Functional Regression

Functional regression focuses on predicting a response variable that is a function, rather than a scalar, aiming to model the complex relationships between functional predictors and functional or scalar responses. Current research emphasizes developing robust and efficient algorithms, including those based on neural networks (like Neural Operator Flows), kernel methods (especially in Reproducing Kernel Hilbert Spaces), and distributed learning approaches to handle large datasets and high dimensionality. These advancements are improving the accuracy and scalability of functional regression, with significant implications for diverse fields like medical imaging analysis, time series forecasting, and the solution of partial differential equations.