The website jointggm.org introduces updates of a suite of graphical model tools we have developed for estimating relationships (in the form of graphs) among variables from heterogeneous data sets. Feel free to submit pull requests when you find my typos.

FASJEM R package is released!

R package: fasjem

install.packages("fasjem")
library(fasjem)
demo(fasjem)


Abstract

Estimating multiple sparse Gaussian Graphical Models (sGGMs) jointly for many related tasks (large K) under a high-dimensional (large p) situation is an important task. Most previous studies for the joint estimation of multiple sGGMs rely on penalized log-likelihood estimators that involve expensive and difficult non-smooth optimizations. We propose a novel approach, FASJEM for fast and scalable joint structure-estimation of multiple sGGMs at a large scale. As the first study of joint sGGM using the M-estimator framework, our work has three major contributions: (1) We solve FASJEM through an entry-wise manner which is parallelizable. (2) We choose a proximal algorithm to optimize FASJEM. This improves the computational efficiency from O(Kp3 ) to O(Kp2 ) and reduces the memory requirement from O(Kp2 ) to O(K). (3) We theoretically prove that FASJEM achieves a consistent estimation with a convergence rate of O(log(Kp)/ntot). On several synthetic and four real-world datasets, FASJEM shows significant improvements over baselines on accuracy, computational complexity and memory costs.

Citations

@inproceedings{wang2017fast,
title={A Fast and Scalable Joint Estimator for Learning Multiple Related Sparse Gaussian Graphical Models},
author={Wang, Beilun and Gao, Ji and Qi, Yanjun},
booktitle={Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, PMLR:, 2017.},
volume={54},
pages={1168--1177},
year={2017}
}


SIMULE R package is released!

Tool SIMULE: A constrained l1 minimization approach for estimating multiple Sparse Gaussian or Nonparanormal Graphical Models

R package: simule

install.packages("simule")
library(simule)
demo(simuleDemo)


Abstract

Identifying context-specific entity networks from aggregated data is an important task, arising often in bioinformatics and neuroimaging. Computationally, this task can be formulated as jointly estimating multiple different, but related, sparse Undirected Graphical Models (UGM) from aggregated samples across several contexts. Previous joint-UGM studies have mostly focused on sparse Gaussian Graphical Models (sGGMs) and can’t identify context-specific edge patterns directly. We, therefore, propose a novel approach, SIMULE (detecting Shared and Individual parts of MULtiple graphs Explicitly) to learn multi-UGM via a constrained L1 minimization. SIMULE automatically infers both specific edge patterns that are unique to each context and shared interactions preserved among all the contexts. Through the L1 constrained formulation, this problem is cast as multiple independent subtasks of linear programming that can be solved efficiently in parallel. In addition to Gaussian data, SIMULE can also handle multivariate Nonparanormal data that greatly relaxes the normality assumption that many real-world applications do not follow. We provide a novel theoretical proof showing that SIMULE achieves a consistent result at the rate O(log(Kp)/n_{tot}). On multiple synthetic datasets and two biomedical datasets, SIMULE shows significant improvement over state-of-the-art multi-sGGM and single-UGM baselines.

Citations

@article{wang2016constrained,
title={A constrained l1 minimization approach for estimating multiple Sparse Gaussian or Nonparanormal Graphical Models},
author={Wang, Beilun and Singh, Ritambhara and Qi, Yanjun},
journal={arXiv preprint arXiv:1605.03468},
year={2016}
}


JointGGM.org is up and running!

The website JointGGM.org introduces a suite of tools we have developed for learning the structure of multiple sparse Gaussian graphical models jointly.

Background: Sparse Gaussian Graphical Model (sGGM)

The sparse Gaussian Graphical Model(sGGM) assumes data samples are independently and identically drawn from a multivariate normal distribution with mean $\mu$ and covariance matrix $\Sigma$. The graph structure $G$ among $p$ features is encoded by the sparsity pattern of the inverse covariance matrix, also named precision matrix, $\Omega$.

In $G$ an edge does not connect $j$-th node and $k$-th node (i.e., conditional independent) if and only if $\Omega_{jk} = 0$. sGGM imposes a sparse L1 penalty on the $\Omega$.

This website: Joint learning of Multiple Sparse Gaussian Graphical Model (multi-sGGM)

Modern multi-context molecular datasets are high dimensional, heterogeneous and noisy. For such heterogeneous data samples, rather than estimating sGGM of each condition separately, a multi-task formulation that jointly estimates $K$ different but related sGGMs can lead to a better generalization.

We have designed a suite of novel and robust machine-learning algorithms to identify context-specific interaction graphs from such data.

So far, we have released the following two R packages:

No. Tool Name Short Description
1 SIMULE A Fast and Scalable Joint Estimator for Learning Multiple Related Sparse Gaussian Graphical Models
2 FASJEM A constrained l1 minimization approach for estimating multiple Sparse Gaussian or Nonparanormal Graphical Models

Possible Applications

Helping researchers effectively translate aggregated data into knowledge that take the form of graphs, this suite of toolboxes can have important biomedical applications, such as investigating molecular signatures corresponding to different drug treatments. It is expected to impact other domains as well, for instance, to identify condition-specific functional networks about human brain connectivity.

Contact

Have questions or suggestions? Feel free to ask me on Twitter or email me.