# Block-diagonal covariance selection for high-dimensional Gaussian graphical models

arXiv: https://arxiv.org/abs/1511.04033 · HTML: https://mlsanity.com/paper/1511.04033/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Nov 2015.

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

- [A non-asymptotic approach for model selection via penalization in high-dimensional mixture of experts models](https://mlsanity.com/paper/2104.02640/) (2021)
- [Non-asymptotic model selection in block-diagonal mixture of polynomial experts models](https://mlsanity.com/paper/2104.08959/) (2021)
- [Efficient Sparse PCA via Block-Diagonalization](https://mlsanity.com/paper/2410.14092/) (2024)
- [Inference of Multiscale Gaussian Graphical Model](https://mlsanity.com/paper/2202.05775/) (2022)
- [ISDE : Independence Structure Density Estimation](https://mlsanity.com/paper/2203.09783/) (2022)
- [Community Detection with Heterogeneous Block Covariance Model](https://mlsanity.com/paper/2412.03780/) (2024)

## Abstract (arXiv)

Gaussian graphical models are widely utilized to infer and visualize networks of dependencies between continuous variables. However, inferring the graph is difficult when the sample size is small compared to the number of variables. To reduce the number of parameters to estimate in the model, we propose a non-asymptotic model selection procedure supported by strong theoretical guarantees based on an oracle inequality and a minimax lower bound. The covariance matrix of the model is approximated by a block-diagonal matrix. The structure of this matrix is detected by thresholding the sample covariance matrix, where the threshold is selected using the slope heuristic. Based on the block-diagonal structure of the covariance matrix, the estimation problem is divided into several independent problems: subsequently, the network of dependencies between variables is inferred using the graphical lasso algorithm in each block. The performance of the procedure is illustrated on simulated data. An application to a real gene expression dataset with a limited sample size is also presented: the dimension reduction allows attention to be objectively focused on interactions among smaller subsets of genes, leading to a more parsimonious and interpretable modular network.