# Sparse Inverse Covariance Matrix Estimation Using Quadratic Approximation

arXiv: https://arxiv.org/abs/1306.3212 · HTML: https://mlsanity.com/paper/1306.3212/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 13 Jun 2013.

## Built on by (most cited first, 11 of 11)

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- [Distributed Estimation of Sparse Inverse Covariances](https://mlsanity.com/paper/2109.12020/) (2021)
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- [Learning Massive-scale Partial Correlation Networks in Clinical Multi-omics Studies with HP-ACCORD](https://mlsanity.com/paper/2412.11554/) (2024)
- [GraphFLEx: Structure Learning Framework for Large Expanding Graphs](https://mlsanity.com/paper/2505.12323/) (2025)
- [The Regularization Parameter: Sparse Precision Matrix Estimation](https://mlsanity.com/paper/2607.07735/) (2026)

## Abstract (arXiv)

The L1-regularized Gaussian maximum likelihood estimator (MLE) has been shown to have strong statistical guarantees in recovering a sparse inverse covariance matrix, or alternatively the underlying graph structure of a Gaussian Markov Random Field, from very limited samples. We propose a novel algorithm for solving the resulting optimization problem which is a regularized log-determinant program. In contrast to recent state-of-the-art methods that largely use first order gradient information, our algorithm is based on Newton's method and employs a quadratic approximation, but with some modifications that leverage the structure of the sparse Gaussian MLE problem. We show that our method is superlinearly convergent, and present experimental results using synthetic and real-world application data that demonstrate the considerable improvements in performance of our method when compared to other state-of-the-art methods.