arXiv subjects

Eric F. Lock

Publications and source records attributed to Eric F. Lock.

27 records · Page 2Linked to original sources

arXiv2018

Supervised multiway factorization

We describe a probabilistic PARAFAC/CANDECOMP (CP) factorization for multiway (i.e., tensor) data that incorporates auxiliary covariates, SupCP. SupCP generalizes the supervised singular value decomposition (SupSVD) for vector-valued observations, to allow for observations that have the form of a matrix or higher-order array. Such data are increasingly encountered in biomedical research and other fields. We describe a likelihood-based latent variable representation of the CP factorization, in which the latent variables are informed by additional covariates. We give conditions for identifiability, and develop an EM algorithm for simultaneous estimation of all model parameters. SupCP can be used for dimension reduction, capturing latent structures that are more accurate and interpretable due to covariate supervision. Moreover, SupCP specifies a full probability distribution for a multiway data observation with given covariate values, which can be used for predictive modeling. We conduct comprehensive simulations to evaluate the SupCP algorithm. We apply it to a facial image database with facial descriptors (e.g., smiling / not smiling) as covariates, and to a study of amino acid fluorescence. Software is available at https://github.com/lockEF/SupCP .

stat.ME↗

arXiv2017

Linked Matrix Factorization

In recent years, a number of methods have been developed for the dimension reduction and decomposition of multiple linked high-content data matrices. Typically these methods assume that just one dimension, rows or columns, is shared among the data sources. This shared dimension may represent common features that are measured for different sample sets (i.e., horizontal integration) or a common set of samples with measurements for different feature sets (i.e., vertical integration). In this article we introduce an approach for simultaneous horizontal and vertical integration, termed Linked Matrix Factorization (LMF), for the more general situation where some matrices share rows (e.g., features) and some share columns (e.g., samples). Our motivating application is a cytotoxicity study with accompanying genomic and molecular chemical attribute data. In this data set, the toxicity matrix (cell lines $\times$ chemicals) shares its sample set with a genotype matrix (cell lines $\times$ SNPs), and shares its feature set with a chemical molecular attribute matrix (chemicals $\times$ attributes). LMF gives a unified low-rank factorization of these three matrices, which allows for the decomposition of systematic variation that is shared among the three matrices and systematic variation that is specific to each matrix. This may be used for efficient dimension reduction, exploratory visualization, and the imputation of missing data even when entire rows or columns are missing from a constituent data matrix. We present theoretical results concerning the uniqueness, identifiability, and minimal parametrization of LMF, and evaluate it with extensive simulation studies.

stat.ME↗

arXiv2017

Prediction with Dimension Reduction of Multiple Molecular Data Sources for Patient Survival

Predictive modeling from high-dimensional genomic data is often preceded by a dimension reduction step, such as principal components analysis (PCA). However, the application of PCA is not straightforward for multi-source data, wherein multiple sources of 'omics data measure different but related biological components. In this article we utilize recent advances in the dimension reduction of multi-source data for predictive modeling. In particular, we apply exploratory results from Joint and Individual Variation Explained (JIVE), an extension of PCA for multi-source data, for prediction of differing response types. We conduct illustrative simulations to illustrate the practical advantages and interpretability of our approach. As an application example we consider predicting survival for Glioblastoma Multiforme (GBM) patients from three data sources measuring mRNA expression, miRNA expression, and DNA methylation. We also introduce a method to estimate JIVE scores for new samples that were not used in the initial dimension reduction, and study its theoretical properties; this method is implemented in the R package R.JIVE on CRAN, in the function 'jive.predict'.

q-bio.QM↗

arXiv2017

Tensor-on-tensor regression

We propose a framework for the linear prediction of a multi-way array (i.e., a tensor) from another multi-way array of arbitrary dimension, using the contracted tensor product. This framework generalizes several existing approaches, including methods to predict a scalar outcome from a tensor, a matrix from a matrix, or a tensor from a scalar. We describe an approach that exploits the multiway structure of both the predictors and the outcomes by restricting the coefficients to have reduced CP-rank. We propose a general and efficient algorithm for penalized least-squares estimation, which allows for a ridge (L_2) penalty on the coefficients. The objective is shown to give the mode of a Bayesian posterior, which motivates a Gibbs sampling algorithm for inference. We illustrate the approach with an application to facial image data. An R package is available at https://github.com/lockEF/MultiwayRegression .

stat.ME↗

arXiv2016

Discriminating sample groups with multi-way data

High-dimensional linear classifiers, such as the support vector machine (SVM) and distance weighted discrimination (DWD), are commonly used in biomedical research to distinguish groups of subjects based on a large number of features. However, their use is limited to applications where a single vector of features is measured for each subject. In practice data are often multi-way, or measured over multiple dimensions. For example, metabolite abundance may be measured over multiple regions or tissues, or gene expression may be measured over multiple time points, for the same subjects. We propose a framework for linear classification of high-dimensional multi-way data, in which coefficients can be factorized into weights that are specific to each dimension. More generally, the coefficients for each measurement in a multi-way dataset are assumed to have low-rank structure. This framework extends existing classification techniques, and we have implemented multi-way versions of SVM and DWD. We describe informative simulation results, and apply multi-way DWD to data for two very different clinical research studies. The first study uses metabolite magnetic resonance spectroscopy data over multiple brain regions to compare patients with and without spinocerebellar ataxia, the second uses publicly available gene expression time-course data to compare treatment responses for patients with multiple sclerosis. Our method improves performance and simplifies interpretation over naive applications of full rank linear classification to multi-way data. An R package is available at https://github.com/lockEF/MultiwayClassification .

stat.ME↗

arXiv2016

Bayesian Genome- and Epigenome-wide Association Studies with Gene Level Dependence

High-throughput genetic and epigenetic data are often screened for associations with an observed phenotype. For example, one may wish to test hundreds of thousands of genetic variants, or DNA methylation sites, for an association with disease status. These genomic variables can naturally be grouped by the gene they encode, among other criteria. However, standard practice in such applications is independent screening with a universal correction for multiplicity. We propose a Bayesian approach in which the prior probability of an association for a given genomic variable depends on its gene, and the gene-specific probabilities are modeled nonparametrically. This hierarchical model allows for appropriate gene and genome-wide multiplicity adjustments, and can be incorporated into a variety of Bayesian association screening methodologies with negligible increase in computational complexity. We describe an application to screening for differences in DNA methylation between lower grade glioma and glioblastoma multiforme tumor samples from The Cancer Genome Atlas. Software is available via the package BayesianScreening for R at https://github.com/lockEF/BayesianScreening .

stat.ME↗

arXiv2016

Shared kernel Bayesian screening

This article concerns testing for equality of distribution between groups. We focus on screening variables with shared distributional features such as common support, modes and patterns of skewness. We propose a Bayesian testing method using kernel mixtures, which improves performance by borrowing information across the different variables and groups through shared kernels and a common probability of group differences. The inclusion of shared kernels in a finite mixture, with Dirichlet priors on the weights, leads to a simple framework for testing that scales well for high-dimensional data. We provide closed asymptotic forms for the posterior probability of equivalence in two groups and prove consistency under model misspecification. The method is applied to DNA methylation array data from a breast cancer study, and compares favorably to competitors when type I error is estimated via permutation.

stat.ME↗

arXiv2013

Joint and individual variation explained (JIVE) for integrated analysis of multiple data types

Research in several fields now requires the analysis of data sets in which multiple high-dimensional types of data are available for a common set of objects. In particular, The Cancer Genome Atlas (TCGA) includes data from several diverse genomic technologies on the same cancerous tumor samples. In this paper we introduce Joint and Individual Variation Explained (JIVE), a general decomposition of variation for the integrated analysis of such data sets. The decomposition consists of three terms: a low-rank approximation capturing joint variation across data types, low-rank approximations for structured variation individual to each data type, and residual noise. JIVE quantifies the amount of joint variation between data types, reduces the dimensionality of the data and provides new directions for the visual exploration of joint and individual structures. The proposed method represents an extension of Principal Component Analysis and has clear advantages over popular two-block methods such as Canonical Correlation Analysis and Partial Least Squares. A JIVE analysis of gene expression and miRNA data on Glioblastoma Multiforme tumor samples reveals gene-miRNA associations and provides better characterization of tumor types. Data and software are available at https://genome.unc.edu/jive/

stat.ML↗

arXiv2013

Bayesian Consensus Clustering

The task of clustering a set of objects based on multiple sources of data arises in several modern applications. We propose an integrative statistical model that permits a separate clustering of the objects for each data source. These separate clusterings adhere loosely to an overall consensus clustering, and hence they are not independent. We describe a computationally scalable Bayesian framework for simultaneous estimation of both the consensus clustering and the source-specific clusterings. We demonstrate that this flexible approach is more robust than joint clustering of all data sources, and is more powerful than clustering each data source separately. This work is motivated by the integrated analysis of heterogeneous biomedical data, and we present an application to subtype identification of breast cancer tumor samples using publicly available data from The Cancer Genome Atlas. Software is available at http://people.duke.edu/~el113/software.html.

stat.ML↗