Caroline Uhler

A Complete Neandertal Mitochondrial Genome Sequence Determined by High-Throughput Sequencing

A complete mitochondrial (mt) genome sequence was reconstructed from a 38,000 year-old Neandertal individual with 8341 mtDNA sequences identified among 4.8 Gb of DNA generated from approximately 0.3 g of bone. Analysis of the assembled sequence unequivocally establishes that the Neandertal mtDNA falls outside the variation of extant human mtDNAs, and allows an estimate of the divergence date between the two mtDNA lineages of 660,000 +/- 140,000 years. Of the 13 proteins encoded in the mtDNA, subunit 2 of cytochrome c oxidase of the mitochondrial electron transport chain has experienced the largest number of amino acid substitutions in human ancestors since the separation from Neandertals. There is evidence that purifying selection in the Neandertal mtDNA was reduced compared with other primate lineages, suggesting that the effective population size of Neandertals was small.

Hypersurfaces and Their Singularities in Partial Correlation Testing

An asymptotic theory is developed for computing volumes of regions in the parameter space of a directed Gaussian graphical model that are obtained by bounding partial correlations. We study these volumes using the method of real log canonical thresholds from algebraic geometry. Our analysis involves the computation of the singular loci of correlation hypersurfaces. Statistical applications include the strong-faithfulness assumption for the PC algorithm and the quantification of confounder bias in causal inference. A detailed analysis is presented for trees, bow ties, tripartite graphs, and complete graphs.

Commuting birth-and-death processes

We use methods from combinatorics and algebraic statistics to study analogues of birth-and-death processes that have as their state space a finite subset of the

Differentially-Private Logistic Regression for Detecting Multiple-SNP Association in GWAS Databases

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Faithfulness and learning hypergraphs from discrete distributions

-dimensional lattice and for which the

Scalable privacy-preserving data sharing methodology for genome-wide association studies

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Multivariate Gaussians, semidefinite matrix completion, and convex algebraic geometry

matrices that record the transition probabilities in each of the lattice directions commute pairwise. One reason such processes are of interest is that the transition matrix is straightforward to diagonalize, and hence it is easy to compute

Detecting epistasis via Markov bases

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Sequencing and analysis of a complete Neandertal mitochondrial genome.

step transition probabilities. The set of commuting birth-and-death processes decomposes as a union of toric varieties, with the main component being the closure of all processes whose nearest neighbor transition probabilities are positive. We exhibit an explicit monomial parametrization for this main component, and we explore the boundary components using primary decomposition.

A Strategy for Detecting Multiple Trait Loci in Disease Association Studies

Following the publication of an attack on genome-wide association studies (GWAS) data proposed by Homer et al., considerable attention has been given to developing methods for releasing GWAS data in a privacy-preserving way. Here, we develop an end-to-end differentially private method for solving regression problems with convex penalty functions and selecting the penalty parameters by cross-validation. In particular, we focus on penalized logistic regression with elastic-net regularization, a method widely used to in GWAS analyses to identify disease-causing genes. We show how a differentially private procedure for penalized logistic regression with elastic-net regularization can be applied to the analysis of GWAS data and evaluate our method’s performance.