Generalised Additive Models: Tackling Dimensionality Issue

This lecture by the instructor covers the concept of estimating smooth functions in the context of Generalised Additive Models (GAMs). Starting from the estimation of a univariate function, the lecture progresses to the extension of GAMs for multivariate covariates. The curse of dimensionality is discussed, highlighting the challenges faced in high-dimensional spaces. The Backfitting Algorithm is introduced as a method to fit additive models efficiently. Additionally, the lecture explores the Projection Pursuit Regression approach, which decomposes the response variable into smooth functions dependent on a global linear feature. Pros and cons of this approach are discussed, emphasizing the trade-off between interpretability and predictive performance.