Super-sparse principal component analyses for high-throughput genomic data

<p>Abstract</p> <p>Background</p> <p>Principal component analysis (PCA) has gained popularity as a method for the analysis of high-dimensional genomic data. However, it is often difficult to interpret the results because the principal components are linear combinations of all variables, and the coefficients (loadings) are typically nonzero. These nonzero values also reflect poor estimation of the true vector loadings; for example, for gene expression data, biologically we expect only a portion of the genes to be expressed in any tissue, and an even smaller fraction to be involved in a particular process. Sparse PCA methods have recently been introduced for reducing the number of nonzero coefficients, but these existing methods are not satisfactory for high-dimensional data applications because they still give too many nonzero coefficients.</p> <p>Results</p> <p>Here we propose a new PCA method that uses two innovations to produce an extremely sparse loading vector: (i) a random-effect model on the loadings that leads to an unbounded penalty at the origin and (ii) shrinkage of the singular values obtained from the singular value decomposition of the data matrix. We develop a stable computing algorithm by modifying nonlinear iterative partial least square (NIPALS) algorithm, and illustrate the method with an analysis of the NCI cancer dataset that contains 21,225 genes.</p> <p>Conclusions</p> <p>The new method has better performance than several existing methods, particularly in the estimation of the loading vectors.</p

Machine Learning and Integrative Analysis of Biomedical Big Data.

Recent developments in high-throughput technologies have accelerated the accumulation of massive amounts of omics data from multiple sources: genome, epigenome, transcriptome, proteome, metabolome, etc. Traditionally, data from each source (e.g., genome) is analyzed in isolation using statistical and machine learning (ML) methods. Integrative analysis of multi-omics and clinical data is key to new biomedical discoveries and advancements in precision medicine. However, data integration poses new computational challenges as well as exacerbates the ones associated with single-omics studies. Specialized computational approaches are required to effectively and efficiently perform integrative analysis of biomedical data acquired from diverse modalities. In this review, we discuss state-of-the-art ML-based approaches for tackling five specific computational challenges associated with integrative analysis: curse of dimensionality, data heterogeneity, missing data, class imbalance and scalability issues

Entropy-scaling search of massive biological data

Many datasets exhibit a well-defined structure that can be exploited to design faster search tools, but it is not always clear when such acceleration is possible. Here, we introduce a framework for similarity search based on characterizing a dataset's entropy and fractal dimension. We prove that searching scales in time with metric entropy (number of covering hyperspheres), if the fractal dimension of the dataset is low, and scales in space with the sum of metric entropy and information-theoretic entropy (randomness of the data). Using these ideas, we present accelerated versions of standard tools, with no loss in specificity and little loss in sensitivity, for use in three domains---high-throughput drug screening (Ammolite, 150x speedup), metagenomics (MICA, 3.5x speedup of DIAMOND [3,700x BLASTX]), and protein structure search (esFragBag, 10x speedup of FragBag). Our framework can be used to achieve "compressive omics," and the general theory can be readily applied to data science problems outside of biology.Comment: Including supplement: 41 pages, 6 figures, 4 tables, 1 bo

Sparse multivariate factor analysis regression models and its applications to integrative genomics analysis

The multivariate regression model is a useful tool to explore complex associations between two kinds of molecular markers, which enables the understanding of the biological pathways underlying disease etiology. For a set of correlated response variables, accounting for such dependency can increase statistical power. Motivated by integrative genomic data analyses, we propose a new methodologyâ sparse multivariate factor analysis regression model (smFARM), in which correlations of response variables are assumed to follow a factor analysis model with latent factors. This proposed method not only allows us to address the challenge that the number of association parameters is larger than the sample size, but also to adjust for unobserved genetic and/or nongenetic factors that potentially conceal the underlying responseâ predictor associations. The proposed smFARM is implemented by the EM algorithm and the blockwise coordinate descent algorithm. The proposed methodology is evaluated and compared to the existing methods through extensive simulation studies. Our results show that accounting for latent factors through the proposed smFARM can improve sensitivity of signal detection and accuracy of sparse association map estimation. We illustrate smFARM by two integrative genomics analysis examples, a breast cancer dataset, and an ovarian cancer dataset, to assess the relationship between DNA copy numbers and gene expression arrays to understand genetic regulatory patterns relevant to the disease. We identify two transâ hub regions: one in cytoband 17q12 whose amplification influences the RNA expression levels of important breast cancer genes, and the other in cytoband 9q21.32â 33, which is associated with chemoresistance in ovarian cancer.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/135396/1/gepi22018.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/135396/2/gepi22018_am.pdfhttp://deepblue.lib.umich.edu/bitstream/2027.42/135396/3/gepi22018-sup-0001-SuppMat.pd

The evolutionary history and genomics of European blackcap migration

Seasonal migration is a taxonomically widespread behaviour that integrates across many traits. The European blackcap exhibits enormous variation in migration and is renowned for research on its evolution and genetic basis. We assembled a reference genome for blackcaps and obtained whole genome resequencing data from individuals across its breeding range. Analyses of population structure and demography suggested divergence began ~30,000 ya, with evidence for one admixture event between migrant and resident continent birds ~5000 ya. The propensity to migrate, orientation and distance of migration all map to a small number of genomic regions that do not overlap with results from other species, suggesting that there are multiple ways to generate variation in migration. Strongly associated single nucleotide polymorphisms (SNPs) were located in regulatory regions of candidate genes that may serve as major regulators of the migratory syndrome. Evidence for selection on shared variation was documented, providing a mechanism by which rapid changes may evolve

Efficient analysis and storage of large-scale genomic data

The impending advent of population-scaled sequencing cohorts involving tens of millions of individuals with matched phenotypic measurements will produce unprecedented volumes of genetic data. Storing and analysing such gargantuan datasets places computational performance at a pivotal position in medical genomics. In this thesis, I explore the potential for accelerating and parallelizing standard genetics workflows, file formats, and algorithms using both hardware-accelerated vectorization, parallel and distributed algorithms, and heterogeneous computing. First, I describe a novel bit-counting operation termed the positional population-count, which can be used together with succinct representations and standard efficient operations to accelerate many genetic calculations. In order to enable the use of this new operator and the canonical population count on any target machine I developed a unified low-level library using CPU dispatching to select the optimal method contingent on the available instruction set architecture and the given input size at run-time. As a proof-of-principle application, I apply the positional population-count operator to computing quality control-related summary statistics for terabyte-scaled sequencing readsets with >3,800-fold speed improvements. As another application, I describe a framework for efficiently computing the cardinality of set intersection using these operators and applied this framework to efficiently compute genome-wide linkage-disequilibrium in datasets with up to 67 million samples resulting in up to >60-fold improvements in speed for dense genotypic vectors and up to >250,000-fold savings in memory and >100,000-fold improvement in speed for sparse genotypic vectors. I next describe a framework for handling the terabytes of compressed output data and describe graphical routines for visualizing long-range linkage-disequilibrium blocks as seen over many human centromeres. Finally, I describe efficient algorithms for storing and querying very large genetic datasets and specialized algorithms for the genotype component of such datasets with >10,000-fold savings in memory compared to the current interchange format.Wellcome Trus