[Paper Review] The huge Package for High-dimensional Undirected Graph Estimation in R

Tuo Zhao, Han Liu+3 more|PubMed|Jun 26, 2020

Statistical Methods and Inference23 references485 citations

TL;DR

The paper introduces the huge R package for scalable high-dimensional undirected graph estimation, implementing multiple methods (MB and glasso) with semiparametric and screening options, and compares performance to glasso.

ABSTRACT

We describe an R package named huge which provides easy-to-use functions for estimating high dimensional undirected graphs from data. This package implements recent results in the literature, including Friedman et al. (2007), Liu et al. (2009, 2012) and Liu et al. (2010). Compared with the existing graph estimation package glasso, the huge package provides extra features: (1) instead of using Fortan, it is written in C, which makes the code more portable and easier to modify; (2) besides fitting Gaussian graphical models, it also provides functions for fitting high dimensional semiparametric Gaussian copula models; (3) more functions like data-dependent model selection, data generation and graph visualization; (4) a minor convergence problem of the graphical lasso algorithm is corrected; (5) the package allows the user to apply both lossless and lossy screening rules to scale up large-scale problems, making a tradeoff between computational and statistical efficiency.

Motivation & Objective

• Provide an R package that estimates high-dimensional undirected graphs from data.
• Integrate multiple estimation methods (MB and graphical lasso) with enhancements for scalability.
• Support semiparametric Gaussian copula modeling and data-driven model selection.
• Offer data generation, preprocessing, visualization, and screening options to improve efficiency.

Proposed method

• Core engine implemented in C for portability and efficiency.
• Supports MB covariance selection and graphical lasso estimation with coordinate descent and sparse matrices.
• Implements nonparanormal transformation for semiparametric Gaussian copula graphs.
• Incorporates lossless and lossy correlation screening to reduce dimensionality before estimation.
• Provides model selection via StARS, RIC, and extended BIC (for graphical lasso).
• Includes graph visualization via igraph-based plotting.

Experimental results

Research questions

• RQ1 How can high-dimensional undirected graphs be efficiently estimated from data using MB and graphical lasso approaches in R?
• RQ2 What are the benefits of integrating screening (lossless and lossy) before graph estimation in terms of speed and accuracy?
• RQ3 How does the nonparanormal transformation enable semiparametric Gaussian copula graph estimation in high dimensions?
• RQ4 How do different model selection criteria (StARS, RIC, EBIC) perform for choosing regularization parameters in huge?

Key findings

• Huge achieves faster performance than glasso in MB-based estimation, especially with lossy screening (speedups up to ~500%).
• Lossy screening reduces per-variable lasso problems from d to n, improving efficiency when d >> n.
• Graphical lasso estimation with huge also benefits from lossless and lossy screening, yielding significant speedups over glasso.
• The package provides additional methods (e.g., correlation thresholding) and a comprehensive framework (data generation, preprocessing, visualization).
• Experiments show varied runtimes across d and n, highlighting scalability advantages of huge under high-dimensional regimes.