Max Affine

Max-affine regression focuses on modeling data generated by the maximum of several affine functions, a structure arising in diverse applications like multiclass classification and auction problems. Current research emphasizes efficient algorithms, including gradient descent, stochastic gradient descent, and approximate message passing, to estimate the parameters of these models, often within high-dimensional settings and under noisy conditions. These advancements improve the accuracy and scalability of solving max-affine regression problems, impacting fields requiring the modeling of piecewise linear relationships and latent variable selection. The development of novel algorithms and a deeper theoretical understanding of their performance are key areas of ongoing investigation.