Meta Additive Model: Interpretable Sparse Learning With Auto Weighting
This addresses robust and interpretable high-dimensional data analysis for applications like variable selection and imbalanced classification, representing an incremental improvement with automated weighting.
The paper tackles the problem of sparse additive models degrading under complex noise like outliers and imbalanced data by proposing a meta additive model (MAM) that learns data-driven weighting via bilevel optimization, achieving superior performance on synthetic and real-world data compared to state-of-the-art methods.
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.