# Generalization Error Bounds for Multiclass Sparse Linear Classifiers

arXiv: https://arxiv.org/abs/2204.06264 · HTML: https://mlsanity.com/paper/2204.06264/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 43 references that are in the map.
- First posted on arXiv 13 Apr 2022.

## Builds on (most cited first, 7 of 7)

- [SLOPE - Adaptive variable selection via convex optimization](https://mlsanity.com/paper/1407.3824/) (2014)
- [High-dimensional classification by sparse logistic regression](https://mlsanity.com/paper/1706.08344/) (2017)
- [Multiclass Classification Calibration Functions](https://mlsanity.com/paper/1609.06385/) (2016)
- [Group SLOPE - adaptive selection of groups of predictors](https://mlsanity.com/paper/1610.04960/) (2016)
- [Tight Risk Bounds for Multi-Class Margin Classifiers](https://mlsanity.com/paper/1507.03040/) (2015)
- [Multiclass classification by sparse multinomial logistic regression](https://mlsanity.com/paper/2003.01951/) (2020)
- [Nuclear penalized multinomial regression with an application to predicting at bat outcomes in baseball](https://mlsanity.com/paper/1706.10272/) (2017)

## Built on by (most cited first, 6 of 6)

- [Forgetting, Ignorance or Myopia: Revisiting Key Challenges in Online Continual Learning](https://mlsanity.com/paper/2409.19245/) (2024)
- [Dimension-free uniform concentration bound for logistic regression](https://mlsanity.com/paper/2405.18055/) (2024)
- [Classification by sparse generalized additive models](https://mlsanity.com/paper/2212.01792/) (2022)
- [Solving Sparse & High-Dimensional-Output Regression via Compression](https://mlsanity.com/paper/2410.15762/) (2024)
- [How Many Samples Are Enough for Learning Across Domains?](https://mlsanity.com/paper/2609.39336/) (2026)
- [Can Domain Generalization be Guaranteed in Small-Sample Learning?](https://mlsanity.com/paper/2609.39512/) (2026)

## Abstract (arXiv)

We consider high-dimensional multiclass classification by sparse multinomial logistic regression. Unlike binary classification, in the multiclass setup one can think about an entire spectrum of possible notions of sparsity associated with different structural assumptions on the regression coefficients matrix. We propose a computationally feasible feature selection procedure based on penalized maximum likelihood with convex penalties capturing a specific type of sparsity at hand. In particular, we consider global sparsity, double row-wise sparsity, and low-rank sparsity, and show that with the properly chosen tuning parameters the derived plug-in classifiers attain the minimax generalization error bounds (in terms of misclassification excess risk) within the corresponding classes of multiclass sparse linear classifiers. The developed approach is general and can be adapted to other types of sparsity as well.