Cluster-Based Generalized Additive Models Informed by Random Fourier Features

In the development of learning systems, there is an ongoing need to reconcile the strong predictive performance offered by opaque black-box models with the level of transparency required for critical applications. This work introduces a methodological framework that combines spectral representation learning with transparent statistical modeling to construct a mixture of generalized additive models (GAMs). The approach utilizes random Fourier feature embeddings to uncover locally adaptive structures within the data. High-dimensional random feature representations are compressed via principal component analysis to derive a latent space that informs a Gaussian mixture model, which performs soft clustering to partition the input space into distinct regimes. Within each cluster, a local GAM captures nonlinear univariate effects through interpretable spline-based smoothers. Numerical experiments across diverse regression benchmarks demonstrate that the proposed method consistently improves upon classical global interpretable models by effectively modeling data heterogeneity. Furthermore, the mixture-of-GAMs framework achieves performance comparable to explainable boosting machine, random forest, and multilayer perceptron on certain tasks. Overall, this construction provides a principled approach for integrating representation learning with transparent statistical modeling.