Author
Listed:
- Yabo Niu
- Yang Ni
- Debdeep Pati
- Bani K. Mallick
Abstract
In a traditional Gaussian graphical model, data homogeneity is routinely assumed with no extra variables affecting the conditional independence. In modern genomic datasets, there is an abundance of auxiliary information, which often gets under-utilized in determining the joint dependency structure. In this article, we consider a Bayesian approach to model undirected graphs underlying heterogeneous multivariate observations with additional assistance from covariates. Building on product partition models, we propose a novel covariate-dependent Gaussian graphical model that allows graphs to vary with covariates so that observations whose covariates are similar share a similar undirected graph. To efficiently embed Gaussian graphical models into our proposed framework, we explore both Gaussian likelihood and pseudo-likelihood functions. For Gaussian likelihood, a G-Wishart distribution is used as a natural conjugate prior, and for the pseudo-likelihood, a product of Gaussian-conditionals is used. Moreover, the proposed model has large prior support and is flexible to approximate any ν-Hölder conditional variance-covariance matrices with ν∈(0,1] . We further show that based on the theory of fractional likelihood, the rate of posterior contraction is minimax optimal assuming the true density to be a Gaussian mixture with a known number of components. The efficacy of the approach is demonstrated via simulation studies and an analysis of a protein network for a breast cancer dataset assisted by mRNA gene expression as covariates. Supplementary materials for this article are available online.
Suggested Citation
Yabo Niu & Yang Ni & Debdeep Pati & Bani K. Mallick, 2024.
"Covariate-Assisted Bayesian Graph Learning for Heterogeneous Data,"
Journal of the American Statistical Association, Taylor & Francis Journals, vol. 119(547), pages 1985-1999, July.
Handle:
RePEc:taf:jnlasa:v:119:y:2024:i:547:p:1985-1999
DOI: 10.1080/01621459.2023.2233744
Download full text from publisher
As the access to this document is restricted, you may want to search for a different version of it.
Corrections
All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:taf:jnlasa:v:119:y:2024:i:547:p:1985-1999. See general information about how to correct material in RePEc.
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
We have no bibliographic references for this item. You can help adding them by using this form .
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/UASA20 .
Please note that corrections may take a couple of weeks to filter through
the various RePEc services.