# Learning Massive-scale Partial Correlation Networks in Clinical Multi-omics Studies with HP-ACCORD

arXiv: https://arxiv.org/abs/2412.11554 · HTML: https://mlsanity.com/paper/2412.11554/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 56 references that are in the map.
- First posted on arXiv 16 Dec 2024.

## Builds on (most cited first, 10 of 10)

- [From error bounds to the complexity of first-order descent methods for convex functions](https://mlsanity.com/paper/1510.08234/) (2015)
- [A convex pseudo-likelihood framework for high dimensional partial correlation estimation with convergence guarantees](https://mlsanity.com/paper/1307.5381/) (2013)
- [Linearly Convergent Away-Step Conditional Gradient for Non-strongly Convex Functions](https://mlsanity.com/paper/1504.05002/) (2015)
- [Sparse Inverse Covariance Matrix Estimation Using Quadratic Approximation](https://mlsanity.com/paper/1306.3212/) (2013)
- [Optimization Methods for Sparse Pseudo-Likelihood Graphical Model Selection](https://mlsanity.com/paper/1409.3768/) (2014)
- [Nonconvex Optimization via MM Algorithms: Convergence Theory](https://mlsanity.com/paper/2106.02805/) (2021)
- [Communication-Avoiding Optimization Methods for Distributed Massive-Scale Sparse Inverse Covariance Estimation](https://mlsanity.com/paper/1710.10769/) (2017)
- [Easily parallelizable and distributable class of algorithms for structured sparsity, with optimal acceleration](https://mlsanity.com/paper/1702.06234/) (2017)
- [Sure Screening for Gaussian Graphical Models](https://mlsanity.com/paper/1407.7819/) (2014)
- [Computing Estimators of Dantzig Selector type via Column and Constraint Generation](https://mlsanity.com/paper/1908.06515/) (2019)

## Abstract (arXiv)

Graphical model estimation from multi-omics data requires a balance between statistical estimation performance and computational scalability. We introduce a novel pseudolikelihood-based graphical model framework that reparameterizes the target precision matrix while preserving the sparsity pattern and estimates it by minimizing an ℓ1-penalized empirical risk based on a new loss function. The proposed estimator maintains estimation and selection consistency in various metrics under high-dimensional assumptions. The associated optimization problem allows for a provably fast computation algorithm using a novel operator-splitting approach and communication-avoiding distributed matrix multiplication. A high-performance computing implementation of our framework was tested using simulated data with up to one million variables, demonstrating complex dependency structures similar to those found in biological networks. Leveraging this scalability, we estimated a partial correlation network from a dual-omic liver cancer data set. The co-expression network estimated from the ultrahigh-dimensional data demonstrated superior specificity in prioritizing key transcription factors and co-activators by excluding the impact of epigenetic regulation, thereby highlighting the value of computational scalability in multi-omic data analysis.