onlineFDR: an R package to control the false discovery rate for growing data repositories.

SUMMARY: In many areas of biological research, hypotheses are tested in a sequential manner, without having access to future P-values or even the number of hypotheses to be tested. A key setting where this online hypothesis testing occurs is in the context of publicly available data repositories, where the family of hypotheses to be tested is continually growing as new data is accumulated over time. Recently, Javanmard and Montanari proposed the first procedures that control the FDR for online hypothesis testing. We present an R package, onlineFDR, which implements these procedures and provides wrapper functions to apply them to a historic dataset or a growing data repository. AVAILABILITY AND IMPLEMENTATION: The R package is freely available through Bioconductor (http://www.bioconductor.org/packages/onlineFDR). SUPPLEMENTARY INFORMATION: Supplementary data are available at Bioinformatics online.

Phase transitions in semidefinite relaxations.

Statistical inference problems arising within signal processing, data mining, and machine learning naturally give rise to hard combinatorial optimization problems. These problems become intractable when the dimensionality of the data is large, as is often the case for modern datasets. A popular idea is to construct convex relaxations of these combinatorial problems, which can be solved efficiently for large-scale datasets. Semidefinite programming (SDP) relaxations are among the most powerful methods in this family and are surprisingly well suited for a broad range of problems where data take the form of matrices or graphs. It has been observed several times that when the statistical noise is small enough, SDP relaxations correctly detect the underlying combinatorial structures. In this paper we develop asymptotic predictions for several detection thresholds, as well as for the estimation error above these thresholds. We study some classical SDP relaxations for statistical problems motivated by graph synchronization and community detection in networks. We map these optimization problems to statistical mechanics models with vector spins and use nonrigorous techniques from statistical mechanics to characterize the corresponding phase transitions. Our results clarify the effectiveness of SDP relaxations in solving high-dimensional statistical problems.

Novel probabilistic models of spatial genetic ancestry with applications to stratification correction in genome-wide association studies.

Motivation: Genetic variation in human populations is influenced by geographic ancestry due to spatial locality in historical mating and migration patterns. Spatial population structure in genetic datasets has been traditionally analyzed using either model-free algorithms, such as principal components analysis (PCA) and multidimensional scaling, or using explicit spatial probabilistic models of allele frequency evolution. We develop a general probabilistic model and an associated inference algorithm that unify the model-based and data-driven approaches to visualizing and inferring population structure. Our spatial inference algorithm can also be effectively applied to the problem of population stratification in genome-wide association studies (GWAS), where hidden population structure can create fictitious associations when population ancestry is correlated with both the genotype and the trait. Results: Our algorithm Geographic Ancestry Positioning (GAP) relates local genetic distances between samples to their spatial distances, and can be used for visually discerning population structure as well as accurately inferring the spatial origin of individuals on a two-dimensional continuum. On both simulated and several real datasets from diverse human populations, GAP exhibits substantially lower error in reconstructing spatial ancestry coordinates compared to PCA. We also develop an association test that uses the ancestry coordinates inferred by GAP to accurately account for ancestry-induced correlations in GWAS. Based on simulations and analysis of a dataset of 10 metabolic traits measured in a Northern Finland cohort, which is known to exhibit significant population structure, we find that our method has superior power to current approaches. Availability and Implementation: Our software is available at https://github.com/anand-bhaskar/gap . Contacts: abhaskar@stanford.edu or ajavanma@usc.edu. Supplementary information: Supplementary data are available at Bioinformatics online.