Abstract
We consider the problem of jointly estimating multiple inverse covariance matrices from high-dimensional data consisting of distinct classes. An ℓ2-penalized maximum likelihood approach is employed. The suggested approach is flexible and generic, incorporating several other ℓ2-penalized estimators as special cases. In addition, the approach allows specification of target matrices through which prior knowledge may be incorporated and which can stabilize the estimation procedure in high-dimensional settings. The result is a targeted fused ridge estimator that is of use when the precision matrices of the constituent classes are believed to chiefly share the same structure while potentially differing in a number of locations of interest. It has many applications in (multi)factorial study designs. We focus on the graphical interpretation of precision matrices with the proposed estimator then serving as a basis for integrative or meta-analytic Gaussian graphical modeling. Situations are considered in which the classes are defined by data sets and subtypes of diseases. The performance of the proposed estimator in the graphical modeling setting is assessed through extensive simulation experiments. Its practical usability is illustrated by the differential network modeling of 12 large-scale gene expression data sets of diffuse large B-cell lymphoma subtypes. The estimator and its related procedures are incorporated into the R-package rags2ridges.
| Original language | English |
|---|---|
| Article number | 26 |
| Pages (from-to) | 1-52 |
| Number of pages | 76 |
| Journal | Journal of Machine Learning Research |
| Volume | 21 |
| Early online date | 20 Mar 2020 |
| Publication status | Published - Mar 2020 |
Funding
Anders E. Bilgrau was supported by a grant from the Karen Elise Jensen Fonden, a travel grant from the Danish Cancer Society, and a visitor grant by the Dept. of Mathematics of the VU University Amsterdam. Carel F.W. Peeters received funding from the European Community’s Seventh Framework Programme (FP7, 2007-2013), Research Infrastructures action, under grant agreement No. FP7-269553 (EpiRadBio project). The authors thank Karen Dybkær of the Dept. of Haematology at Aalborg University Hospital, for her help on the biological interpretations in the DLBCL application. The authors would also like to thank Ali Shojaie of the Dept. of Biostatistics, University of Washington, for making the LASICH code available. Lastly, the Authors thank the Associate Editor and three anonymous reviewers, whose constructive comments have led to a considerable improvement in presentation.
Keywords
- Differential network estimation
- Gaussian graphical modeling
- Generalized fused ridge
- High-dimensional data
- Structural meta-analysis
- ℓ-penalized maximum likelihood
