# An Inequality with Applications to Structured Sparsity and Multitask Dictionary Learning

arXiv: https://arxiv.org/abs/1402.1864 · HTML: https://mlsanity.com/paper/1402.1864/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Feb 2014.

## Built on by (most cited first, 5 of 5)

- [Distributionally Robust Learning](https://mlsanity.com/paper/2108.08993/) (2021)
- [Gap Minimization for Knowledge Sharing and Transfer](https://mlsanity.com/paper/2201.11231/) (2022)
- [Loss Gradient Gaussian Width based Generalization and Optimization Guarantees](https://mlsanity.com/paper/2406.07712/) (2024)
- [Towards Initialization-dependent and Non-vacuous Generalization Bounds for Overparameterized Shallow Neural Networks](https://mlsanity.com/paper/2604.00505/) (2026)
- [Sample-Weighted End-to-End Trace-Norm Geometry for Multitask Learning](https://mlsanity.com/paper/2609.29520/) (2026)

## Abstract (arXiv)

From concentration inequalities for the suprema of Gaussian or Rademacher processes an inequality is derived. It is applied to sharpen existing and to derive novel bounds on the empirical Rademacher complexities of unit balls in various norms appearing in the context of structured sparsity and multitask dictionary learning or matrix factorization. A key role is played by the largest eigenvalue of the data covariance matrix.