Random Graphical Models with QUIC-Enhanced Inference: Methodological Study

Objective: Random graph models (RGMs) provide a powerful statistical framework for uncovering interaction networks among variables in high-dimensional datasets. Although this approach has been widely explored using synthetic data, recent studies have demonstrated its potential for analyzing real microbiome data, including the Human Microbiome Project (HMP). However, applying RGMs to biological datasets remains computationally demanding, especially as parameter space grows with increasing number of microbial taxa. A major source of this inefficiency stems from the Bayesian estimation procedure, which traditionally relies on a 2-stage birth-death Markov process, as implemented in the BDgraph package. This method becomes considerably slow when dealing with large covariance structures. Therefore, aim of this study is to improve computation speed in large system structures while ensuring accurate inference. Material and Methods: To overcome these limitations, we replaced the birth-death sampling algorithm with the QUIC (Quadratic Approximation for Inverse Covariance) method for sparse precision matrix estimation. We evaluated the performance of QUIC on Operational Taxonomic Unit (OTU)-level HMP data and compared its efficiency and accuracy with the BDgraph approach. Results: Our findings indicate that QUIC dramatically improves computational speed, particularly in high-dimensional settings where BDgraph becomes prohibitively time-consuming. Importantly, inferred network structures retained their biological interpretability and adequately captured microbial interaction patterns known from previous studies. Conclusion: Integrating QUIC into the RGM workflow substantially enhances computational feasibility without compromising inferential performance. This refinement enables application of RGMs to large-scale microbiome datasets and provides a promising direction for research in network-based biological modeling.