Statistical modeling of covariate-varying networks
Description
- High-dimensional networks play a key role in understanding complex relationships. These relationships are often dynamic in nature and can change with multiple external factors such as time or disease status. Existing methods for estimating high-dimensional graphical models are often limited to static graphs or those that can change with a single covariate. This project developed a novel model class called covariate-varying networks (CVNs) that can change depending on multiple external covariates. We introducsparsity by applying L_1 penalty on the precision matrices of m >= 2 graphs we aim to estimate. These graphs often exhibit a level of similarity, termed smoothness, which is represented by a meta-graph with m nodes, each corresponding to a graph one wants to estimate. The (weighted) adjacency matrix of the meta-graph represents the strength of similarity enforced among the m graphs. The resulting optimization problem is solved by using an alternating direction method of multipliers (ADMM). A crucial step within the ADMM involves solving a weighted fused signal approximator (wFLSA), which, to the best of our knowledge, has not been previously addressed. We do this by reformulating it as a Generalized LASSO problem and solving it with an ADMM tailored explicitly for this task. The wFLSA method also has valuable other applications, such as in image smoothing and change-point detection in time series. Both methods, CVN and wFLSA, were implemented in R and were released as R packages to facilitate broader use and application. Since the CVN model estimation requires the selection of regularization parameters, we compared appropriate methods for this task in simulation studies. Results show that current methods, including StARS (Stability Approach to Regularization Selection), often perform poorly, underscoring the need for further research. Further insights were gained in the performance of LASSO-type variable selection procedures that we compared with 'best subset' selection. It was shown that penalized variable selection performs better, especially in cases with correlated variables or low signal-to-noise ratio.
Funding period
- Begin: September 2020
End: July 2024
Sponsor
- German Research Foundation