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This paper introduces a Meta Additive Model (MAM) that learns data-driven weighting of individual losses within a bilevel optimization framework, using an MLP to parameterize the weighting function based on meta-data. This approach addresses the limitations of existing sparse additive models that struggle with complex noise by adaptively reweighting samples. MAM demonstrates improved performance in variable selection, robust regression, and imbalanced classification tasks, with theoretical guarantees on convergence, generalization, and variable selection consistency.
Forget hand-tuning loss functions: this meta-learning approach automatically learns optimal sample reweighting for sparse additive models, boosting robustness and accuracy.
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.
