# Minimax Additive Regression under Unknown Dependent Designs

arXiv: https://arxiv.org/abs/2609.39212 · HTML: https://mlsanity.com/paper/2609.39212/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 30 references that are in the map.
- First posted on arXiv 30 Sep 2026.

## Builds on (most cited first, 11 of 11)

- [An Introduction to Matrix Concentration Inequalities](https://mlsanity.com/paper/1501.01571/) (2015)
- [Neural Additive Models: Interpretable Machine Learning with Neural Nets](https://mlsanity.com/paper/2004.13912/) (2020)
- [InterpretML: A Unified Framework for Machine Learning Interpretability](https://mlsanity.com/paper/1909.09223/) (2019)
- [NODE-GAM: Neural Generalized Additive Model for Interpretable Deep Learning](https://mlsanity.com/paper/2106.01613/) (2021)
- [Neural Basis Models for Interpretability](https://mlsanity.com/paper/2205.14120/) (2022)
- [Purifying Interaction Effects with the Functional ANOVA: An Efficient Algorithm for Recovering Identifiable Additive Models](https://mlsanity.com/paper/1911.04974/) (2019)
- [Deep Neural Networks for Nonparametric Interaction Models with Diverging Dimension](https://mlsanity.com/paper/2302.05851/) (2023)
- [Minimax Optimal Rates of Estimation in High Dimensional Additive Models: Universal Phase Transition](https://mlsanity.com/paper/1503.02817/) (2015)
- [Generalized Sparse Additive Models](https://mlsanity.com/paper/1903.04641/) (2019)
- [Tree Ensemble Explainability through the Hoeffding Functional Decomposition and TreeHFD Algorithm](https://mlsanity.com/paper/2510.24815/) (2025)
- [Generalized Functional ANOVA: A Complete Theoretical Framework](https://mlsanity.com/paper/2605.18422/) (2026)

## Abstract (arXiv)

We study additive regression under an unknown and potentially non product design distribution, allowing the number of covariates to grow with the sample size. We consider a coupled class that separately controls the smoothness of the marginal densities and of each additive component multiplied by the corresponding marginal density. Under joint-density bounds that hold uniformly in the dimension and suitable dimension-growth conditions, we establish matching minimax bounds for prediction. With known marginal densities, the classical additive rate is attainable. When the marginals are unknown, this rate is preserved if the densities are at least as smooth as the weighted components. Otherwise, marginal-density smoothness determines the minimax rate over the coupled class. Finally, we recover all additive components with total squared error of the same order as the prediction error.