Generalized reduced rank latent factor regression for high dimensional tensor fields, and neuroimaging-genetic applications.
We propose a generalized reduced rank latent factor regression model (GRRLF) for the analysis of tensor field responses and high dimensional covariates. The model is motivated by the need from imaging-genetic studies to identify genetic variants that are associated with brain imaging phenotypes, often in the form of high dimensional tensor fields. GRRLF identifies from the structure in the data the effective dimensionality of the data, and then jointly performs dimension reduction of the covariates, dynamic identification of latent factors, and nonparametric estimation of both covariate and latent response fields. After accounting for the latent and covariate effects, GRLLF performs a nonparametric test on the remaining factor of interest. GRRLF provides a better factorization of the signals compared with common solutions, and is less susceptible to overfitting because it exploits the effective dimensionality. The generality and the flexibility of GRRLF also allow various statistical models to be handled in a unified framework and solutions can be efficiently computed. Within the field of neuroimaging, it improves the sensitivity for weak signals and is a promising alternative to existing approaches. The operation of the framework is demonstrated with both synthetic datasets and a real-world neuroimaging example in which the effects of a set of genes on the structure of the brain at the voxel level were measured, and the results compared favorably with those from existing approaches.
Centre for Computational Systems Biology and School of Mathematical Sciences, Fudan University, Shanghai, PR China; Department of Computer Science, Warwick University, Coventry, UK.
Chenyang
C
Tao
Department of Statistics, University of Warwick, Coventry, UK.
Thomas E
TE
Nichols
Imaging Genetics Center, Institute for Neuroimaging & Informatics, University of Southern California, Los Angeles, CA, USA.
Xue
X
Hua
Imaging Genetics Center, Institute for Neuroimaging & Informatics, University of Southern California, Los Angeles, CA, USA; Interdepartmental Neuroscience Graduate Program, UCLA School of Medicine, Los Angeles, CA, USA.
Christopher R K
CRK
Ching
Department of Computer Science, Warwick University, Coventry, UK; Oxford Centre for Computational Neuroscience, Oxford, UK.
Edmund T
ET
Rolls
Imaging Genetics Center, Institute for Neuroimaging & Informatics, University of Southern California, Los Angeles, CA, USA; Departments of Neurology, Psychiatry, Radiology, Engineering, Pediatrics, and Ophthalmology, USC, Los Angeles, CA, USA.
Paul M
PM
Thompson
Centre for Computational Systems Biology and School of Mathematical Sciences, Fudan University, Shanghai, PR China; Department of Computer Science, Warwick University, Coventry, UK; School of Life Science and the Collaborative Innovation Center for Brain Science, Fudan University, Shanghai 200433, PR China. Electronic address: jianfeng64@gmail.com.
Jianfeng
J
Feng
D055106:Genome-Wide Association Study / Q000379:methods*; D006801:Humans; D001523:Mental Disorders / Q000000981:diagnostic imaging* / Q000235:genetics*; D008962:Models, Theoretical; D059906:Neuroimaging / Q000379:methods*
Dimension reduction; Generalized linear model; High dimensional tensor field; Latent factor; Least squares kernel machines; Nuclear norm regularization; Reduced rank regression; Riemannian manifold
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