This paper introduces sparse-group boosting and a simulation-based group balancing algorithm within the ‘sgboost’ R package to mitigate variable selection bias in high-dimensional grouped data, demonstrating improved fairness and interpretability through simulations and ecological data analysis.
Supervised Learning, Regression, Feature Engineering, Efficiency, Robustness
Fabian Obster, Christian Heumann
University of the Bundeswehr Munich, LMU Munich
Generated by grok-3
Background Problem
The paper addresses the challenge of variable selection bias in boosting methods, particularly in high-dimensional datasets with natural groupings of covariates (e.g., gene data, survey data, or climate economics data). Traditional boosting methods often over-select larger or more complex groups due to inherent biases, leading to reduced model interpretability and fairness. The motivation stems from the increasing availability of such datasets in fields like economics, climate research, and bioinformatics, where capturing both group-level and individual variable effects is crucial for accurate modeling and actionable insights. The key problem solved is the mitigation of selection bias by balancing selection frequencies across groups, while also providing a practical tool for sparse-group boosting via the ‘sgboost’ R package.
Method
The paper proposes sparse-group boosting, an extension of traditional boosting that incorporates structured sparsity for both group and individual variable selection, combined with a novel group balancing algorithm. The core idea is to balance selection probabilities across groups of varying sizes by dynamically adjusting the degrees of freedom (df) using a simulation-based approach. The implementation involves two main components:
- Sparse-Group Boosting Framework: This extends boosting by defining candidate sets for individual variables and groups, using Ridge regression with regularization controlled via degrees of freedom. At each boosting iteration, the algorithm selects the base-learner (individual or group) that minimizes the residual sum of squares (RSS), as detailed in Algorithm 1.
- Group Balancing Algorithm: This simulation-based method iteratively adjusts the degrees of freedom for each group to equalize selection frequencies under a null hypothesis of no association. It simulates multiple outcome variables, fits models, computes selection frequencies, and updates degrees of freedom proportionally to the imbalance, as outlined in Algorithm 2. Key parameters like learning rate and number of simulations impact convergence and stability. The method integrates into the ‘sgboost’ R package, offering tools for model fitting, tuning, visualization, and interpretation, with a focus on enhancing interpretability in high-dimensional grouped data settings.
Experiment
The experiments are conducted on both simulated and real-world datasets to evaluate the sparse-group boosting framework and the group balancing algorithm. Simulated data includes a linear regression setup with 100 observations, 200 predictors in 40 equal-sized groups, designed to reflect real-world sparsity structures. Real-world data involves ecological data from 801 farmers in Chile and Tunisia, with 84 variables in 14 groups, modeling binary decisions on climate adaptation using logistic regression. The experimental setup tests model performance via cross-validation to determine optimal boosting iterations (e.g., 204 for simulated, 466 for real data) and visualizes results through variable importance, coefficient paths, and effect sizes. For group balancing, four scenarios with varying group sizes, sample sizes, and outcome distributions are simulated to compare selection frequencies under equal penalties, equal degrees of freedom, and the proposed balancing method. Results show that the balancing algorithm significantly reduces selection bias compared to baselines, achieving near-equal selection frequencies across groups, even in challenging settings like p > n. However, the improvement in predictive performance over existing methods like sparse-group lasso is not extensively quantified, and the computational cost of the balancing algorithm is acknowledged as a limitation. The setup is reasonable for demonstrating bias reduction but lacks broader comparisons and scalability tests on larger datasets.
Further Thoughts
The group balancing algorithm’s simulation-based approach to adjust degrees of freedom is a novel contribution, but its computational intensity raises concerns about scalability to very large datasets, especially in fields like genomics where thousands of groups might be involved. An interesting direction could be exploring hybrid methods that combine this balancing technique with faster regularization approaches like sparse-group lasso to balance accuracy and efficiency. Additionally, the non-uniqueness of solutions in the balancing algorithm suggests a need for standardized initialization or constraints to ensure reproducibility, which could be critical for adoption in applied research. I also see potential connections to federated learning contexts, where grouped data structures across distributed datasets might benefit from such bias mitigation strategies, though privacy constraints would need to be addressed. Finally, comparing this method’s impact on downstream tasks (e.g., policy recommendations in climate economics) against other interpretable machine learning frameworks could further validate its practical utility.