# Meta Additive Model: Interpretable Sparse Learning With Auto Weighting

arXiv: https://arxiv.org/abs/2604.20111 · HTML: https://mlsanity.com/paper/2604.20111/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 48 references that are in the map.
- First posted on arXiv 22 Apr 2026.

## Builds on (most cited first, 21 of 21)

- [MaskGAN: Towards Diverse and Interactive Facial Image Manipulation](https://mlsanity.com/paper/1907.11922/) (2019)
- [Neural Additive Models: Interpretable Machine Learning with Neural Nets](https://mlsanity.com/paper/2004.13912/) (2020)
- [Train longer, generalize better: closing the generalization gap in large batch training of neural networks](https://mlsanity.com/paper/1705.08741/) (2017)
- [Forward and Reverse Gradient-Based Hyperparameter Optimization](https://mlsanity.com/paper/1703.01785/) (2017)
- [Bilevel Optimization: Convergence Analysis and Enhanced Design](https://mlsanity.com/paper/2010.07962/) (2020)
- [Tilted Empirical Risk Minimization](https://mlsanity.com/paper/2007.01162/) (2020)
- [Neural Basis Models for Interpretability](https://mlsanity.com/paper/2205.14120/) (2022)
- [Lower Bounds and Accelerated Algorithms for Bilevel Optimization](https://mlsanity.com/paper/2102.03926/) (2021)
- [Stability and Generalization of Bilevel Programming in Hyperparameter Optimization](https://mlsanity.com/paper/2106.04188/) (2021)
- [Probabilistic Bilevel Coreset Selection](https://mlsanity.com/paper/2301.09880/) (2023)
- [Generalization Analysis for Contrastive Representation Learning](https://mlsanity.com/paper/2302.12383/) (2023)
- [CMW-Net: Learning a Class-Aware Sample Weighting Mapping for Robust Deep Learning](https://mlsanity.com/paper/2202.05613/) (2022)
- [Additive Gaussian Processes Revisited](https://mlsanity.com/paper/2206.09861/) (2022)
- [Learning an Explicit Hyperparameter Prediction Function Conditioned on Tasks](https://mlsanity.com/paper/2107.02378/) (2021)
- [Generalizing Importance Weighting to A Universal Solver for Distribution Shift Problems](https://mlsanity.com/paper/2305.14690/) (2023)
- [Additive Approximations in High Dimensional Nonparametric Regression via the SALSA](https://mlsanity.com/paper/1602.00287/) (2016)
- [Consistency Analysis of an Empirical Minimum Error Entropy Algorithm](https://mlsanity.com/paper/1412.5272/) (2014)
- [CAT: Interpretable Concept-based Taylor Additive Models](https://mlsanity.com/paper/2406.17931/) (2024)
- [Learning rates for the risk of kernel based quantile regression estimators in additive models](https://mlsanity.com/paper/1405.3379/) (2014)
- [Fine-grained Analysis of Stability and Generalization for Stochastic Bilevel Optimization](https://mlsanity.com/paper/2604.04090/) (2026)
- [Forward Stagewise Additive Model for Collaborative Multiview Boosting](https://mlsanity.com/paper/1608.01874/) (2016)

## Abstract (arXiv)

Sparse additive models have attracted much attention in high-dimensional data analysis due to their flexible representation and strong interpretability. However, most existing models are limited to single-level learning under the mean-squared error criterion, whose empirical performance can degrade significantly in the presence of complex noise, such as non-Gaussian perturbations, outliers, noisy labels, and imbalanced categories. The sample reweighting strategy is widely used to reduce the model's sensitivity to atypical data; however, it typically requires prespecifying the weighting functions and manually selecting additional hyperparameters. To address this issue, we propose a new meta additive model (MAM) based on the bilevel optimization framework, which learns data-driven weighting of individual losses by parameterizing the weighting function via an MLP trained on meta data. MAM is capable of a variety of learning tasks, including variable selection, robust regression estimation, and imbalanced classification. Theoretically, MAM provides guarantees on convergence in computation, algorithmic generalization, and variable selection consistency under mild conditions. Empirically, MAM outperforms several state-of-the-art additive models on both synthetic and real-world data under various data corruptions.