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ENFORCING CO-EXPRESSION IN MULTIMODAL REGRESSION FRAMEWORK.

ABSTRACT: We consider the problem of multimodal data integration for the study of complex neurological diseases (e.g. schizophrenia). Among the challenges arising in such situation, estimating the link between genetic and neurological variability within a population sample has been a promising direction. A wide variety of statistical models arose from such applications. For example, Lasso regression and its multitask extension are often used to fit a multivariate linear relationship between given phenotype(s) and associated observations. Other approaches, such as canonical correlation analysis (CCA), are widely used to extract relationships between sets of variables from different modalities. In this paper, we propose an exploratory multivariate method combining these two methods. More Specifically, we rely on a 'CCA-type' formulation in order to regularize the classical multimodal Lasso regression problem. The underlying motivation is to extract discriminative variables that display are also co-expressed across modalities. We first evaluate the method on a simulated dataset, and further validate it using Single Nucleotide Polymorphisms (SNP) and functional Magnetic Resonance Imaging (fMRI) data for the study of schizophrenia.

SUBMITTER: Zille P

PROVIDER: S-EPMC5415360 | biostudies-literature | 2017

REPOSITORIES: biostudies-literature

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ENFORCING CO-EXPRESSION IN MULTIMODAL REGRESSION FRAMEWORK.

Zille Pascal P Calhoun Vince D VD Wang Yu-Ping YP

Pacific Symposium on Biocomputing. Pacific Symposium on Biocomputing 20170101

We consider the problem of multimodal data integration for the study of complex neurological diseases (e.g. schizophrenia). Among the challenges arising in such situation, estimating the link between genetic and neurological variability within a population sample has been a promising direction. A wide variety of statistical models arose from such applications. For example, Lasso regression and its multitask extension are often used to fit a multivariate linear relationship between given phenotyp ...[more]

PMID: 27896966

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Project description:Among the challenges arising in brain imaging genetic studies, estimating the potential links between neurological and genetic variability within a population is key. In this paper, we propose a multivariate, multimodal formulation for variable selection that leverages co-expression patterns across various data modalities. Our approach is based on an intuitive combination of two widely used statistical models: sparse regression and canonical correlation analysis (CCA). While the former seeks multivariate linear relationships between a given phenotype and associated observations, the latter searches to extract co-expression patterns between sets of variables belonging to different modalities. In the following, we propose to rely on a "CCA-type" formulation in order to regularize the classical multimodal sparse regression problem (essentially incorporating both CCA and regression models within a unified formulation). The underlying motivation is to extract discriminative variables that are also co-expressed across modalities. We first show that the simplest formulation of such model can be expressed as a special case of collaborative learning methods. After discussing its limitation, we propose an extended, more flexible formulation, and introduce a simple and efficient alternating minimization algorithm to solve the associated optimization problem. We explore the parameter space and provide some guidelines regarding parameter selection. Both the original and extended versions are then compared on a simple toy data set and a more advanced simulated imaging genomics data set in order to illustrate the benefits of the latter. Finally, we validate the proposed formulation using single nucleotide polymorphisms data and functional magnetic resonance imaging data from a population of adolescents ( subjects, age 16.9 ± 1.9 years from the Philadelphia Neurodevelopmental Cohort) for the study of learning ability. Furthermore, we carry out a significance analysis of the resulting features that allow us to carefully extract brain regions and genes linked to learning and cognitive ability.

Project description:Functional data are increasingly encountered in scientific studies, and their high dimensionality and complexity lead to many analytical challenges. Various methods for functional data analysis have been developed, including functional response regression methods that involve regression of a functional response on univariate/multivariate predictors with nonparametrically represented functional coefficients. In existing methods, however, the functional regression can be sensitive to outlying curves and outlying regions of curves, so is not robust. In this paper, we introduce a new Bayesian method, robust functional mixed models (R-FMM), for performing robust functional regression within the general functional mixed model framework, which includes multiple continuous or categorical predictors and random effect functions accommodating potential between-function correlation induced by the experimental design. The underlying model involves a hierarchical scale mixture model for the fixed effects, random effect and residual error functions. These modeling assumptions across curves result in robust nonparametric estimators of the fixed and random effect functions which down-weight outlying curves and regions of curves, and produce statistics that can be used to flag global and local outliers. These assumptions also lead to distributions across wavelet coefficients that have outstanding sparsity and adaptive shrinkage properties, with great flexibility for the data to determine the sparsity and the heaviness of the tails. Together with the down-weighting of outliers, these within-curve properties lead to fixed and random effect function estimates that appear in our simulations to be remarkably adaptive in their ability to remove spurious features yet retain true features of the functions. We have developed general code to implement this fully Bayesian method that is automatic, requiring the user to only provide the functional data and design matrices. It is efficient enough to handle large data sets, and yields posterior samples of all model parameters that can be used to perform desired Bayesian estimation and inference. Although we present details for a specific implementation of the R-FMM using specific distributional choices in the hierarchical model, 1D functions, and wavelet transforms, the method can be applied more generally using other heavy-tailed distributions, higher dimensional functions (e.g. images), and using other invertible transformations as alternatives to wavelets.

Dataset Information

ENFORCING CO-EXPRESSION IN MULTIMODAL REGRESSION FRAMEWORK.

Publications

ENFORCING CO-EXPRESSION IN MULTIMODAL REGRESSION FRAMEWORK.

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