Meta Additive Model: Interpretable Sparse Learning With Auto Weighting
Authors: Xuelin Zhang, Xinyue Liu, Lingjuan Wu, Hong Chen
Organizations: College of Informatics, Huazhong Agricultural University, Wuhan, China
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.
Semi-supervised learning with manifold regularization is a classical framework for jointly learning from both labeled and unlabeled data, where the key requirement is that the support of the unknown marginal distribution has the geometric structure of a Riemannian manifold. Typically, the Laplace-Beltrami operator-based manifold regularization can be approximated empirically by the Laplacian regularization associated with the entire training data and its corresponding graph Laplacian matrix. However, the graph Laplacian matrix depends heavily on the prespecified similarity metric and may lead to inappropriate penalties when dealing with redundant or noisy input variables. To address the above issues, this paper proposes a new Semi-Supervised Meta Additive Model (S2MAM) based on a bilevel optimization scheme that automatically identifies informative variables, updates the similarity matrix, and simultaneously achieves interpretable predictions. Theoretical guarantees are provided for S2MAM, including the computing convergence and the statistical generalization bound. Experimental assessments across 4 synthetic and 12 real-world datasets, with varying levels and categories of corruption, validate the robustness and interpretability of the proposed approach.
Sparse recovery in linear systems underpins applications from signal processing to high-dimensional regression. Sparse Bayesian Learning, grounded in the principle of automatic relevance determination (ARD), offers a practical Bayesian mechanism for feature sparsity via marginal likelihood optimization. Yet, its reliance on a homoscedastic noise model renders it sensitive to data contaminations such as outliers or misspecified noise, harming model fit and predictions. Instead, we propose jointly learning individual feature and sample relevancies, enabling simultaneous model and data sparsification via a single Bayesian objective. This symmetric pruning of model and data offers a natural extension that preserves conjugacy, admits closed-form updates for standard optimization procedures, and aligns with perspectives from robust regression and influence functions. Empirical results across diverse regression tasks affirm that a joint ARD approach consistently yields both sparse and robust prediction models.
Alexander Timans, Thomas Möllenhoff, Christian A. Naesseth +2
Tabular applications often require inspectable prediction rules and stable behavior when records are incomplete. We propose FlagGAM, a rule-basis framework that separates feature-level rule construction from prediction. A Flag Core Module converts numerical and categorical variables into sparse, human-readable univariate bases: threshold flags, category-level flags, tail-deviation bases, and categorical step functions. A default additive head combines these bases as a restricted GAM-style predictor, while the retained sparse rule-basis matrix supports mixed-type classification and regression, feature-specific weighting, and optional flexible heads. On clean benchmarks, additive FlagGAM stays close to modern additive and rule-based baselines on classification and improves over global linear modeling on regression, while remaining less flexible than tree-based predictors. Its clearest advantage appears under deployment-time perturbations: across three classification datasets, FlagGAM has the smallest mean AUROC degradation under missingness and numerical noise. Flexible heads improve absolute accuracy and approach strong tree-based baselines, but should be interpreted as nonlinear predictors over learned rule bases. These results support FlagGAM as a constrained additive rule-basis model for applications that need readable rules and stable behavior with incomplete inputs.