Meta Additive Model: Interpretable Sparse Learning With Auto Weighting

TL;DR

The paper introduces Meta Additive Model (MAM), a bilevel optimization-based approach that learns data-driven loss weighting for interpretable sparse learning, improving robustness and performance in noisy, imbalanced, or complex data scenarios.

Contribution

It proposes a novel meta additive model that automatically learns loss weights via an MLP, enhancing robustness and interpretability across various high-dimensional tasks.

Findings

MAM outperforms state-of-the-art models on synthetic and real data.

MAM provides theoretical guarantees on convergence and variable selection.

MAM effectively handles complex noise, outliers, and imbalanced data.

Abstract

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.