Elastic Net Penalized Maximum Likelihood for Structural Equation Models with Network GPT Framework

Provides elastic net penalized maximum likelihood estimator for structural equation models (SEM). The package implements `lasso` and `elastic net` (l1/l2) penalized SEM and estimates the model parameters with an efficient block coordinate ascent algorithm that maximizes the penalized likelihood of the SEM. Hyperparameters are inferred from cross-validation (CV). A Stability Selection (STS) function is also available to provide accurate causal effect selection. The software achieves high accuracy performance through a `Network Generative Pre-trained Transformer` (Network GPT) Framework with two steps: 1) pre-trains the model to generate a complete (fully connected) graph; and 2) uses the complete graph as the initial state to fit the `elastic net` penalized SEM.

Elastic Net Penalized Maximum Likelihood for Structural Equation Models with Netowrk GPT Framework

• References

We provide extremely efficient procedures for fitting the lasso and elastic net regularized Structural Equation Models (SEM). The model output can be used for inferring network structure (topology) and estimating causal effects. Key features include sparse variable selection and effect estimation via l1 and l2 penalized maximum likelihood estimator (MLE) implemented with BLAS/Lapack routines. The implementation enables extremely efficient computation. Details can be found in Huang A. (2014).

To achieve high performance accuracy, the software implements a Network Generative Pre-traning Transformer (GPT) framework:

• Perform a Network GPT that generates a complete (fully connected) graph from l2 penalized SEM (i.e., ridge SEM); and
• Use the complete graph as the initial state and fit the elastic net (l1 and l2) penalized SEM.

Note that the term Transformer does not carry the same meaning as the transformer architecture commonly used in Natural Language Processing (NLP). In Network GPT, the term refers to the creation and generation of the complete graph.

Version 4.0:

• Enhanced documentation with a new vignette Network Inferrence via sparseSEM to enable quick setup and running of the package;
• Added a new yeast GRN real dataset that was used to generate the graph in the vignettes;
• Added the dataset preprocessing description in the vignette; and
• further streamline function input and output from both C/C++ and R functions

Version 3.8:

• simplified user interface with central functions and simple parameters setup;
• stability selection function with both serial and parallel bootstrapping;
• streamlined function output.

Version 3 is a major release that updates BLAS/Lapack routines according to R-API change.

References