# A Blockwise Descent Algorithm for Group-penalized Multiresponse and Multinomial Regression

arXiv: https://arxiv.org/abs/1311.6529 · HTML: https://mlsanity.com/paper/1311.6529/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 26 Nov 2013.

## Built on by (most cited first, 8 of 8)

- [Scalable Penalized Regression for Noise Detection in Learning with Noisy Labels](https://mlsanity.com/paper/2203.07788/) (2022)
- [A Fast and Scalable Pathwise-Solver for Group Lasso and Elastic Net Penalized Regression via Block-Coordinate Descent](https://mlsanity.com/paper/2405.08631/) (2024)
- [Noise Covariance Estimation in Multi-Task High-dimensional Linear Models](https://mlsanity.com/paper/2206.07256/) (2022)
- [A hybrid machine learning framework for clad characteristics prediction in metal additive manufacturing](https://mlsanity.com/paper/2307.01872/) (2023)
- [Knockoffs-SPR: Clean Sample Selection in Learning with Noisy Labels](https://mlsanity.com/paper/2301.00545/) (2023)
- [Nonlinear Multiple Response Regression and Learning of Latent Spaces](https://mlsanity.com/paper/2503.21608/) (2025)
- [Efficient and robust high-dimensional sparse logistic regression via nonlinear primal-dual hybrid gradient algorithms](https://mlsanity.com/paper/2111.15426/) (2021)
- [Gradient boosting with vector-valued leafs](https://mlsanity.com/paper/2606.29326/) (2026)

## Abstract (arXiv)

In this paper we purpose a blockwise descent algorithm for group-penalized multiresponse regression. Using a quasi-newton framework we extend this to group-penalized multinomial regression. We give a publicly available implementation for these in R, and compare the speed of this algorithm to a competing algorithm --- we show that our implementation is an order of magnitude faster than its competitor, and can solve gene-expression-sized problems in real time.