Genomic association studies of common or rare protein-coding variation have established robust statistical approaches to account for multiple testing. Here, we present a comparable framework to evaluate rare and de novo noncoding single nucleotide variants, insertion/deletions, and all classes of structural variation from whole-genome sequencing (WGS). Integrating genomic annotations at the level of nucleotides, genes, and regulatory regions, we define 51,801 annotation categories. Analyses of 519 autism spectrum disorder families did not identify association with any categories after correction for 4,123 effective tests. Without appropriate correction, biologically plausible associations are observed in both cases and controls. Despite excluding previously identified gene-disrupting mutations, coding regions still exhibited the strongest associations. Thus, in autism the contribution of de novo noncoding variation is probably modest compared to de novo coding variants. Robust results from future WGS studies will require large cohorts and comprehensive analytical strategies that consider the substantial multiple testing burden.

Whole-genome sequencing (WGS) has facilitated the first genome-wide evaluations of the contribution of de novo noncoding mutations to complex disorders. Using WGS, we assess genetic variation from 7,608 samples in 1,902 autism spectrum disorder (ASD) families, identifying 255,106 de novo mutations. In contrast to coding mutations, no noncoding functional annotation category, analyzed in isolation, is significantly associated with ASD. Casting noncoding variation in the context of a de novo risk score across multiple annotation categories, however, does demonstrate association with mutations localized to promoter regions. The strongest driver of this promoter signal emanates from evolutionarily conserved transcription factor binding sites distal to the transcription start site. These data suggest that de novo mutations in promoter regions, characterized by evolutionary and functional signatures, contribute to ASD.

Reliable uncertainty estimation for time series prediction is critical in many fields, including physics, biology, and manufacturing. At Uber, probabilistic time series forecasting is used for robust prediction of number of trips during special events, driver incentive allocation, as well as real-time anomaly detection across millions of metrics. Classical time series models are often used in conjunction with a probabilistic formulation for uncertainty estimation. However, such models are hard to tune, scale, and add exogenous variables to. Motivated by the recent resurgence of Long Short Term Memory networks, we propose a novel end-to-end Bayesian deep model that provides time series prediction along with uncertainty estimation. We provide detailed experiments of the proposed solution on completed trips data, and successfully apply it to large-scale time series anomaly detection at Uber.Comment: To appear in DSBDA-2017 @ ICDM'1

In this paper, which is the second in a series of two, the preasymptotic error analysis of the continuous interior penalty finite element method (CIP-FEM) and the FEM for the Helmholtz equation in two and three dimensions is continued. While Part I contained results on the linear CIP-FEM and FEM, the present part deals with approximation spaces of order p ≥ 1. By using a modified duality argument, preasymptotic error estimates are derived for both methods under the condition of kh, where k is the wave number, h is the mesh size, and C 0 is a constant independent of k, h, p, and the penalty parameters. It is shown that the pollution errors of both methods inif the exact solution u ∈ H 2 (Ω) which coincide with existent dispersion analyses for the FEM on Cartesian grids. Here σ is a constant independent of k, h, p and the penalty parameters. Moreover, it is proved that the CIP-FEM is stable for any k, h, p > 0 and penalty parameters with positive imaginary parts. Besides the advantage of the absolute stability of the CIP-FEM compared to the FEM, the penalty parameters may be tuned to reduce the pollution effects.Key words. Helmholtz equation, large wave number, preasymptotic error estimates, continuous interior penalty finite element methods, finite element methods

Recent advances in technology have enabled the measurement of RNA levels for individual cells. Compared to traditional tissue-level bulk RNA-seq data, single cell sequencing yields valuable insights about gene expression profiles for different cell types, which is potentially critical for understanding many complex human diseases. However, developing quantitative tools for such data remains challenging because of high levels of technical noise, especially the “dropout” events. A “dropout” happens when the RNA for a gene fails to be amplified prior to sequencing, producing a “false” zero in the observed data. In this paper, we propose a Unified RNA-Sequencing Model (URSM) for both single cell and bulk RNA-seq data, formulated as a hierarchical model. URSM borrows the strength from both data sources and carefully models the dropouts in single cell data, leading to a more accurate estimation of cell type specific gene expression profile. In addition, URSM naturally provides inference on the dropout entries in single cell data that need to be imputed for downstream analyses, as well as the mixing proportions of different cell types in bulk samples. We adopt an empirical Bayes’ approach, where parameters are estimated using the EM algorithm and approximate inference is obtained by Gibbs sampling. Simulation results illustrate that URSM outperforms existing approaches both in correcting for dropouts in single cell data, as well as in deconvolving bulk samples. We also demonstrate an application to gene expression data on fetal brains, where our model successfully imputes the dropout genes and reveals cell type specific expression patterns.