Author
Listed:
- Chun‐Chen Tu
- Florence Forbes
- Benjamin Lemasson
- Naisyin Wang
Abstract
We propose a hierarchical Gaussian locally linear mapping structured mixture model, named HGLLiM, to predict low dimensional responses based on high dimensional covariates when the associations between the responses and the covariates are non‐linear. For tractability, HGLLiM adopts inverse regression to handle the high dimension and locally linear mappings to capture potentially non‐linear relations. Data with similar associations are grouped together to form a cluster. A mixture is composed of several clusters following a hierarchical structure. This structure enables shared covariance matrices and latent factors across smaller clusters to limit the number of parameters to estimate. Moreover, HGLLiM adopts a robust estimation procedure for model stability. We use three real data sets to demonstrate different features of HGLLiM. With the face data set, HGLLiM shows ability to model non‐linear relationships through mixtures. With the orange juice data set, we show that the prediction performance of HGLLiM is robust to the presence of outliers. Moreover, we demonstrate that HGLLiM is capable of handling large‐scale complex data by using the data acquired from a magnetic resonance vascular fingerprinting study. These examples illustrate the wide applicability of HGLLiM to handle different aspects of a complex data structure in prediction.
Suggested Citation
Chun‐Chen Tu & Florence Forbes & Benjamin Lemasson & Naisyin Wang, 2019.
"Prediction with high dimensional regression via hierarchically structured Gaussian mixtures and latent variables,"
Journal of the Royal Statistical Society Series C, Royal Statistical Society, vol. 68(5), pages 1485-1507, November.
Handle:
RePEc:bla:jorssc:v:68:y:2019:i:5:p:1485-1507
DOI: 10.1111/rssc.12370
Download full text from publisher
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:bla:jorssc:v:68:y:2019:i:5:p:1485-1507. 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: Wiley Content Delivery (email available below). General contact details of provider: https://edirc.repec.org/data/rssssea.html .
Please note that corrections may take a couple of weeks to filter through
the various RePEc services.