In this fascinating web content written by John Mount, the author explores the application of homotopy to statistics and machine learning. He discusses how a single model fit can represent various modeling situations, using examples such as the Lasso and fitting classification models with different data prevalences. The author introduces a unique example titled “Surely That Can’t Change Sign Back and Forth,” where he demonstrates that even in linear regression, fit coefficients can change signs multiple times. This challenges the intuition that fit coefficients interpolate continuously. Mount emphasizes the nonlinear nature of regression fitting in explanatory variables but linear in outcomes, urging readers to explore this concept further.
https://win-vector.com/2024/09/17/machine-learning-model-homotopy/