generalized additive models with neural networks

**Generalized Additive Models with Neural Networks** extend the **classic GAM framework by replacing spline-based shape functions with neural network sub-models** — each $f_i(x_i)$ is a neural network that learns arbitrarily complex univariate transformations while maintaining the additive (interpretable) structure. **GAM-NN Architecture** - **Classic GAM**: $g(mu) = eta_0 + f_1(x_1) + f_2(x_2) + ldots$ where $f_i$ are smooth splines. - **Neural GAM**: Replace splines with neural networks — more flexible but still additive. - **Interaction Terms**: Can add pairwise interaction networks $f_{ij}(x_i, x_j)$ for controlled interaction modeling (GA$^2$M). - **Link Function**: Supports any link function (identity, logit, log) for different response types. **Why It Matters** - **Best of Both Worlds**: Neural network flexibility with GAM interpretability. - **Pairwise Interactions**: GA$^2$M adds interpretable pairwise interactions while remaining interpretable. - **Healthcare/Finance**: Adopted in domains requiring model interpretability by regulation (FDA, banking). **Neural GAMs** are **flexible yet transparent** — using neural networks within the additive model framework for interpretable, regulation-friendly predictions.