The computation of a similarity measure for genomic data is a standard tool in computational genetics. The principal components of such matrices are routinely used to correct for biases due to confounding by population stratification, for instance in linear regressions. However, the calculation of both a similarity matrix and its singular value decomposition (SVD) are computationally intensive. The contribution of this article is threefold. First, we demonstrate that the calculation of three matrices (called the covariance matrix, the weighted Jaccard matrix, and the genomic relationship matrix) can be reformulated in a unified way which allows for the application of a randomized SVD algorithm, which is faster than the traditional computation. The fast SVD algorithm we present is adapted from an existing randomized SVD algorithm and ensures that all computations are carried out in sparse matrix algebra. The algorithm only assumes that row-wise and column-wise subtraction and multiplication of a vector with a sparse matrix is available, an operation that is efficiently implemented in common sparse matrix packages. An exception is the so-called Jaccard matrix, which does not have a structure applicable for the fast SVD algorithm. Second, an approximate Jaccard matrix is introduced to which the fast SVD computation is applicable. Third, we establish guaranteed theoretical bounds on the accuracy (in [Formula: see text] norm and angle) between the principal components of the Jaccard matrix and the ones of our proposed approximation, thus putting the proposed Jaccard approximation on a solid mathematical foundation, and derive the theoretical runtime of our algorithm. We illustrate that the approximation error is low in practice and empirically verify the theoretical runtime scalings on both simulated data and data of the 1000 Genome Project.

Chronic obstructive pulmonary disease (COPD) is a complex disease influenced by well-established environmental exposures (most notably, cigarette smoking) and incompletely defined genetic factors. The chromosome 4q region harbors multiple genetic risk loci for COPD, including signals near HHIP, FAM13A, GSTCD, TET2, and BTC. Leveraging RNA-Seq data from lung tissue in COPD cases and controls, we estimated the co-expression network for genes in the 4q region bounded by HHIP and BTC (~70MB), through partial correlations informed by protein-protein interactions. We identified several co-expressed gene pairs based on partial correlations, including NPNT-HHIP, BTC-NPNT and FAM13A-TET2, which were replicated in independent lung tissue cohorts. Upon clustering the co-expression network, we observed that four genes previously associated to COPD: BTC, HHIP, NPNT and PPM1K appeared in the same network community. Finally, we discovered a sub-network of genes differentially co-expressed between COPD vs controls (including FAM13A, PPA2, PPM1K and TET2). Many of these genes were previously implicated in cell-based knock-out experiments, including the knocking out of SPP1 which belongs to the same genomic region and could be a potential local key regulatory gene. These analyses identify chromosome 4q as a region enriched for COPD genetic susceptibility and differential co-expression.

Most predictive models based on gene expression data do not leverage information related to gene splicing, despite the fact that splicing is a fundamental feature of eukaryotic gene expression. Cigarette smoking is an important environmental risk factor for many diseases, and it has profound effects on gene expression. Using smoking status as a prediction target, we developed deep neural network predictive models using gene, exon, and isoform level quantifications from RNA sequencing data in 2,557 subjects in the COPDGene Study. We observed that models using exon and isoform quantifications clearly outperformed gene-level models when using data from 5 genes from a previously published prediction model. Whereas the test set performance of the previously published model was 0.82 in the original publication, our exon-based models including an exon-to-isoform mapping layer achieved a test set AUC (area under the receiver operating characteristic) of 0.88, which improved to an AUC of 0.94 using exon quantifications from a larger set of genes. Isoform variability is an important source of latent information in RNA-seq data that can be used to improve clinical prediction models.

Utilizing expert input often improves clustering performance. However in a knowledge discovery problem, ground truth is unknown even to an expert. Thus, instead of one expert, we solicit the opinion from multiple experts. The key question motivating this work is: which experts should be assigned higher weights when there is disagreement on whether to put a pair of samples in the same group? To model the uncertainty in constraints from different experts, we build a probabilistic model for pairwise constraints through jointly modeling each expert’s accuracy and the mapping from features to latent cluster assignments. After learning our probabilistic discriminative clustering model and accuracies of different experts, 1) samples that were not annotated by any expert can be clustered using the discriminative clustering model; and 2) experts with higher accuracies are automatically assigned higher weights in determining the latent cluster assignments. Experimental results on UCI benchmark datasets and a real-world disease subtyping dataset demonstrate that our proposed approach outperforms competing alternatives, including semi-crowdsourced clustering, semi-supervised clustering with constraints from majority voting, and consensus clustering.

Expert input can improve clustering performance. In today’s collaborative environment, the availability of crowdsourced multiple expert input is becoming common. Given multiple experts’ inputs, most existing approaches can only discover one clustering structure. However, data is multi-faced by nature and can be clustered in different ways (also known as views). In an exploratory analysis problem where ground truth is not known, different experts may have diverse views on how to cluster data. In this paper, we address the problem on how to automatically discover multiple ways to cluster data given potentially diverse inputs from multiple uncertain experts. We propose a novel Bayesian probabilistic model that automatically learns the multiple expert views and the clustering structure associated with each view. The benefits of learning the experts’ views include 1) enabling the discovery of multiple diverse clustering structures, and 2) improving the quality of clustering solution in each view by assigning higher weights to experts with higher confidence. In our approach, the expert views, multiple clustering structures and expert confidences are jointly learned via variational inference. Experimental results on synthetic datasets, benchmark datasets and a real-world disease subtyping problem show that our proposed approach outperforms competing baselines, including meta clustering, semi-supervised clustering, semi-crowdsourced clustering and consensus clustering.

Clustering is a challenging problem because given the same data set, it can be grouped in multiple different ways. Which of these clustering solutions is interesting depends on its domain application. Thus, incorporating domain expert input often improves clustering performance. However, most existing semi-supervised clustering techniques can only incorporate instance-level constraints (a few labels or must-link/cannot-link constraints), which domain experts may not be comfortable providing in knowledge discovery problems because categories are not known. Fortunately, domain experts often have an idea regarding properties that clustering solutions should have in order to be useful in domain application based on domain relevant scores. In this paper, we provide a framework for jointly optimizing the usefulness and quality of a clustering solution. Experiments on a synthetic data, a benchmark data, and a real-world disease subtyping problem demonstrate the usefulness of our proposed approach.

We introduce a novel Bayesian nonparametric model that uses the concept of disease trajectories for disease subtype identification. Although our model is general, we demonstrate that by treating fractions of tissue patterns derived from medical images as compositional data, our model can be applied to study distinct progression trends between population subgroups. Specifically, we apply our algorithm to quantitative emphysema measurements obtained from chest CT scans in the COPDGene Study and show several distinct progression patterns. As emphysema is one of the major components of chronic obstructive pulmonary disease (COPD), the third leading cause of death in the United States [1], an improved definition of emphysema and COPD subtypes is of great interest. We investigate several models with our algorithm, and show that one with age , pack years (a measure of cigarette exposure), and smoking status as predictors gives the best compromise between estimated predictive performance and model complexity. This model identified nine subtypes which showed significant associations to seven single nucleotide polymorphisms (SNPs) known to associate with COPD. Additionally, this model gives better predictive accuracy than multiple, multivariate ordinary least squares regression as demonstrated in a five-fold cross validation analysis. We view our subtyping algorithm as a contribution that can be applied to bridge the gap between CT-level assessment of tissue composition to population-level analysis of compositional trends that vary between disease subtypes.

Clustering is a technique that is usually applied as a tool for exploratory data analysis. Because of the exploratory nature of this task, it would be beneficial if a clustering method generates interpretable results, and allows incorporating domain knowledge. This motivates us to develop a probabilistic discriminative model that learns a rectangular decision rule for each cluster, we call Discriminative Rectangle Mixture (DReaM) model. DReaM gives interpretable clustering results, because the rectangular decision rules discovered explicitly illustrate how one cluster is defined and differs from other clusters. It also facilitates us to take advantage of existing rules because we can choose informative prior distributions for the rectangular rules. Moreover, DReaM allows that the features for generating rules do not have to be the same as the features for discovering cluster structure. We approximate the distribution for the rules discovered via variational inference. Experimental results demonstrate that DReaM gives more interpretable clustering results, and yet its performance is comparable to existing clustering methods when solving traditional clustering. Furthermore, in real applications, DReaM is able to effectively take advantage of domain knowledge, and to generate reasonable clustering results.

MOTIVATION: Population stratification is one of the major sources of confounding in genetic association studies, potentially causing false-positive and false-negative results. Here, we present a novel approach for the identification of population substructure in high-density genotyping data/next generation sequencing data. The approach exploits the co-appearances of rare genetic variants in individuals. The method can be applied to all available genetic loci and is computationally fast. Using sequencing data from the 1000 Genomes Project, the features of the approach are illustrated and compared to existing methodology (i.e. EIGENSTRAT). We examine the effects of different cutoffs for the minor allele frequency on the performance of the approach. We find that our approach works particularly well for genetic loci with very small minor allele frequencies. The results suggest that the inclusion of rare-variant data/sequencing data in our approach provides a much higher resolution picture of population substructure than it can be obtained with existing methodology. Furthermore, in simulation studies, we find scenarios where our method was able to control the type 1 error more precisely and showed higher power. CONTACT: [email protected] SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

MOTIVATION: For samples of unrelated individuals, we propose a general analysis framework in which hundred thousands of genetic loci can be tested simultaneously for association with complex phenotypes. The approach is built on spatial-clustering methodology, assuming that genetic loci that are associated with the target phenotype cluster in certain genomic regions. In contrast to standard methodology for multilocus analysis, which has focused on the dimension reduction of the data, our multilocus association-clustering test profits from the availability of large numbers of genetic loci by detecting clusters of loci that are associated with the phenotype. RESULTS: The approach is computationally fast and powerful, enabling the simultaneous association testing of large genomic regions. Even the entire genome or certain chromosomes can be tested simultaneously. Using simulation studies, the properties of the approach are evaluated. In an application to a genome-wide association study for chronic obstructive pulmonary disease, we illustrate the practical relevance of the proposed method by simultaneously testing all genotyped loci of the genome-wide association study and by testing each chromosome individually. Our findings suggest that statistical methodology that incorporates spatial-clustering information will be especially useful in whole-genome sequencing studies in which millions or billions of base pairs are recorded and grouped by genomic regions or genes, and are tested jointly for association. AVAILABILITY AND IMPLEMENTATION: Implementation of the approach is available upon request.

MOTIVATION: For the analysis of rare variants in sequence data, numerous approaches have been suggested. Fixed and flexible threshold approaches collapse the rare variant information of a genomic region into a test statistic with reduced dimensionality. Alternatively, the rare variant information can be combined in statistical frameworks that are based on suitable regression models, machine learning, etc. Although the existing approaches provide powerful tests that can incorporate information on allele frequencies and prior biological knowledge, differences in the spatial clustering of rare variants between cases and controls cannot be incorporated. Based on the assumption that deleterious variants and protective variants cluster or occur in different parts of the genomic region of interest, we propose a testing strategy for rare variants that builds on spatial cluster methodology and that guides the identification of the biological relevant segments of the region. Our approach does not require any assumption about the directions of the genetic effects. RESULTS: In simulation studies, we assess the power of the clustering approach and compare it with existing methodology. Our simulation results suggest that the clustering approach for rare variants is well powered, even in situations that are ideal for standard methods. The efficiency of our spatial clustering approach is not affected by the presence of rare variants that have opposite effect size directions. An application to a sequencing study for non-syndromic cleft lip with or without cleft palate (NSCL/P) demonstrates its practical relevance. The proposed testing strategy is applied to a genomic region on chromosome 15q13.3 that was implicated in NSCL/P etiology in a previous genome-wide association study, and its results are compared with standard approaches. AVAILABILITY: Source code and documentation for the implementation in R will be provided online. Currently, the R-implementation only supports genotype data. We currently are working on an extension for VCF files. CONTACT: [email protected].