# Implicit Differentiation for Hyperparameter Tuning the Weighted Graphical Lasso

arXiv: https://arxiv.org/abs/2307.02130 · HTML: https://mlsanity.com/paper/2307.02130/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 6 of its 19 references that are in the map.
- First posted on arXiv 5 Jul 2023.

## Builds on (most cited first, 6 of 6)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Forward and Reverse Gradient-Based Hyperparameter Optimization](https://mlsanity.com/paper/1703.01785/) (2017)
- [GLAD: Learning Sparse Graph Recovery](https://mlsanity.com/paper/1906.00271/) (2019)
- [Implicit differentiation for fast hyperparameter selection in non-smooth convex learning](https://mlsanity.com/paper/2105.01637/) (2021)
- [Local Linear Convergence of Forward-Backward under Partial Smoothness](https://mlsanity.com/paper/1407.5611/) (2014)
- [A Proximal Approach for a Class of Matrix Optimization Problems](https://mlsanity.com/paper/1801.07452/) (2018)

## Built on by (most cited first, 1 of 1)

- [Restarted contractive operators to learn at equilibrium](https://mlsanity.com/paper/2506.13239/) (2025)

## Abstract (arXiv)

We provide a framework and algorithm for tuning the hyperparameters of the Graphical Lasso via a bilevel optimization problem solved with a first-order method. In particular, we derive the Jacobian of the Graphical Lasso solution with respect to its regularization hyperparameters.