# Cluster-Based Generalized Additive Models Informed by Random Fourier Features

arXiv: https://arxiv.org/abs/2512.19373 · HTML: https://mlsanity.com/paper/2512.19373/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 16 of its 58 references that are in the map.
- First posted on arXiv 22 Dec 2025.

## Builds on (most cited first, 16 of 16)

- [Distilling the Knowledge in a Neural Network](https://mlsanity.com/paper/1503.02531/) (2015)
- [A Unified Approach to Interpreting Model Predictions](https://mlsanity.com/paper/1705.07874/) (2017)
- [XGBoost: A Scalable Tree Boosting System](https://mlsanity.com/paper/1603.02754/) (2016)
- [Deep Inside Convolutional Networks: Visualising Image Classification Models and Saliency Maps](https://mlsanity.com/paper/1312.6034/) (2013)
- [Towards A Rigorous Science of Interpretable Machine Learning](https://mlsanity.com/paper/1702.08608/) (2017)
- [InterpretML: A Unified Framework for Machine Learning Interpretability](https://mlsanity.com/paper/1909.09223/) (2019)
- [Generalization Properties of Learning with Random Features](https://mlsanity.com/paper/1602.04474/) (2016)
- [On the Equivalence between Kernel Quadrature Rules and Random Feature Expansions](https://mlsanity.com/paper/1502.06800/) (2015)
- [Random Fourier Features for Kernel Ridge Regression: Approximation Bounds and Statistical Guarantees](https://mlsanity.com/paper/1804.09893/) (2018)
- [Interpreting Blackbox Models via Model Extraction](https://mlsanity.com/paper/1705.08504/) (2017)
- [Interpretable Mixture of Experts](https://mlsanity.com/paper/2206.02107/) (2022)
- [End-to-end Kernel Learning via Generative Random Fourier Features](https://mlsanity.com/paper/2009.04614/) (2020)
- [Mathematical Perspective of Machine Learning](https://mlsanity.com/paper/2007.01503/) (2020)
- [Mixture of Linear Models Co-supervised by Deep Neural Networks](https://mlsanity.com/paper/2108.04035/) (2021)
- [Pursuing Sources of Heterogeneity in Modeling Clustered Population](https://mlsanity.com/paper/2003.04787/) (2020)
- [Convergence for adaptive resampling of random Fourier features](https://mlsanity.com/paper/2509.03151/) (2025)

## Abstract (arXiv)

In developing data-driven modeling methodologies, there is an ongoing need to reconcile the strong predictive performance of opaque black-box models with the transparency required for critical applications. This work introduces an interpretable and computationally tractable regression framework for heterogeneous data by combining response-informed spectral representation learning with localized additive modeling. The method first fits a random Fourier feature regression model and constructs a spectral feature map from the learned amplitudes and adaptively resampled frequencies, so that the representation reflects predictive variation in the data. This representation is then compressed by principal component analysis to obtain a low-dimensional latent embedding, in which a Gaussian mixture model performs soft regime discovery. Within each regime, a cluster-specific generalized additive model captures nonlinear covariate effects through interpretable spline-based univariate smooth functions. The final predictor is formed as a soft mixture of these local additive models, enabling flexible modeling of a nonlinear, heterogeneous structure while preserving interpretability. Numerical experiments across several benchmark regression datasets show that the proposed method consistently improves upon classical globally interpretable baselines while remaining competitive with more flexible black-box models. Overall, the framework provides a unified approach to heterogeneous regression that combines predictive adaptivity with interpretable local covariate effects.