Prediction with high dimensional regression via hierarchically structured Gaussian mixtures and latent variables

Chun‐Chen Tu, Florence Forbes, Benjamin Lemasson and Naisyin Wang

Journal of the Royal Statistical Society Series C, 2019, vol. 68, issue 5, 1485-1507

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.

Date: 2019
References: Add references at CitEc
Citations:

Downloads: (external link)
https://doi.org/10.1111/rssc.12370

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:bla:jorssc:v:68:y:2019:i:5:p:1485-1507

Ordering information: This journal article can be ordered from
http://ordering.onli ... 1111/(ISSN)1467-9876

Access Statistics for this article

Journal of the Royal Statistical Society Series C is currently edited by R. Chandler and P. W. F. Smith

More articles in Journal of the Royal Statistical Society Series C from Royal Statistical Society Contact information at EDIRC.
Bibliographic data for series maintained by Wiley Content Delivery ().