# Generalized Conditional Gradient for Sparse Estimation

arXiv: https://arxiv.org/abs/1410.4828 · HTML: https://mlsanity.com/paper/1410.4828/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 17 Oct 2014.

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

- [Sparse Visual Counterfactual Explanations in Image Space](https://mlsanity.com/paper/2205.07972/) (2022)
- [Regularized Frank-Wolfe for Dense CRFs: Generalizing Mean Field and Beyond](https://mlsanity.com/paper/2110.14759/) (2021)
- [PARQ: Piecewise-Affine Regularized Quantization](https://mlsanity.com/paper/2503.15748/) (2025)
- [Approximate Frank-Wolfe Algorithms over Graph-structured Support Sets](https://mlsanity.com/paper/2107.00472/) (2021)
- [Screening for a Reweighted Penalized Conditional Gradient Method](https://mlsanity.com/paper/2107.01106/) (2021)
- [Reliable Pseudo-labeling via Optimal Transport with Attention for Short Text Clustering](https://mlsanity.com/paper/2501.15194/) (2025)

## Abstract (arXiv)

Structured sparsity is an important modeling tool that expands the applicability of convex formulations for data analysis, however it also creates significant challenges for efficient algorithm design. In this paper we investigate the generalized conditional gradient (GCG) algorithm for solving structured sparse optimization problems---demonstrating that, with some enhancements, it can provide a more efficient alternative to current state of the art approaches. After providing a comprehensive overview of the convergence properties of GCG, we develop efficient methods for evaluating polar operators, a subroutine that is required in each GCG iteration. In particular, we show how the polar operator can be efficiently evaluated in two important scenarios: dictionary learning and structured sparse estimation. A further improvement is achieved by interleaving GCG with fixed-rank local subspace optimization. A series of experiments on matrix completion, multi-class classification, multi-view dictionary learning and overlapping group lasso shows that the proposed method can significantly reduce the training cost of current alternatives.