Convex Regression

Convex regression focuses on estimating functions that are constrained to be convex, a property crucial for many applications where monotonicity or other shape restrictions are inherent. Current research emphasizes developing efficient algorithms, such as gradient descent and majorization-minimization, for solving the often high-dimensional optimization problems involved, particularly within the context of graph-based data and multivariate settings. These advancements are improving the scalability and accuracy of convex regression models, impacting fields ranging from image analysis and machine learning to control systems and statistical modeling.