Generalized Additive Models

Andrew Polar and Mike Poluektov

Quick introduction

Generalized additive models

$$y_i = \sum_{j=1}^m f_j (x_{ij}), \quad _{i=1,2,...} $$

are usually compared to linear regression

$$y_i = \sum_{j=1}^m h_j \cdot x_{ij} = \mathbf{h^T x_i}, \quad _{i=1,2,...} $$

for emphasizing obvious advantage.

Usual approach to identification of the model functions $f_j$ is function-by-function descent, where approximation to each function is improved one-by-one, having all others known

$$f_k(x_{ik}) = y_i - \sum_{j=1, j \neq k}^m f_j(x_{ij}), \quad _{i=1,2,...} $$

Suggested solution

We suggest drastically different approach, which is record-by-record. The explanation is provided in a math video similar to 3 blue 1 brown format.