26 research outputs found
Low Complexity Regularization of Linear Inverse Problems
Inverse problems and regularization theory is a central theme in contemporary
signal processing, where the goal is to reconstruct an unknown signal from
partial indirect, and possibly noisy, measurements of it. A now standard method
for recovering the unknown signal is to solve a convex optimization problem
that enforces some prior knowledge about its structure. This has proved
efficient in many problems routinely encountered in imaging sciences,
statistics and machine learning. This chapter delivers a review of recent
advances in the field where the regularization prior promotes solutions
conforming to some notion of simplicity/low-complexity. These priors encompass
as popular examples sparsity and group sparsity (to capture the compressibility
of natural signals and images), total variation and analysis sparsity (to
promote piecewise regularity), and low-rank (as natural extension of sparsity
to matrix-valued data). Our aim is to provide a unified treatment of all these
regularizations under a single umbrella, namely the theory of partial
smoothness. This framework is very general and accommodates all low-complexity
regularizers just mentioned, as well as many others. Partial smoothness turns
out to be the canonical way to encode low-dimensional models that can be linear
spaces or more general smooth manifolds. This review is intended to serve as a
one stop shop toward the understanding of the theoretical properties of the
so-regularized solutions. It covers a large spectrum including: (i) recovery
guarantees and stability to noise, both in terms of -stability and
model (manifold) identification; (ii) sensitivity analysis to perturbations of
the parameters involved (in particular the observations), with applications to
unbiased risk estimation ; (iii) convergence properties of the forward-backward
proximal splitting scheme, that is particularly well suited to solve the
corresponding large-scale regularized optimization problem
The perception of quinine taste intensity is associated with common genetic variants in a bitter receptor cluster on chromosome 12
The perceived taste intensities of quinine HCl, caffeine, sucrose octaacetate (SOA) and propylthiouracil (PROP) solutions were examined in 1457 twins and their siblings. Previous heritability modeling of these bitter stimuli indicated a common genetic factor for quinine, caffeine and SOA (22â28%), as well as separate specific genetic factors for PROP (72%) and quinine (15%). To identify the genes involved, we performed a genome-wide association study with the same sample as the modeling analysis, genotyped for approximately 610 000 single-nucleotide polymorphisms (SNPs). For caffeine and SOA, no SNP association reached a genome-wide statistical criterion. For PROP, the peak association was within TAS2R38 (rs713598, A49P, P = 1.6 Ă 10â104), which accounted for 45.9% of the trait variance. For quinine, the peak association was centered in a region that contains bitter receptor as well as salivary protein genes and explained 5.8% of the trait variance (TAS2R19, rs10772420, R299C, P = 1.8 Ă 10â15). We confirmed this association in a replication sample of twins of similar ancestry (P = 0.00001). The specific genetic factor for the perceived intensity of PROP was identified as the gene previously implicated in this trait (TAS2R38). For quinine, one or more bitter receptor or salivary proline-rich protein genes on chromosome 12 have alleles which affect its perception but tight linkage among very similar genes precludes the identification of a single causal genetic variant
Meta-analysis of type 2 Diabetes in African Americans Consortium
Type 2 diabetes (T2D) is more prevalent in African Americans than in Europeans. However, little is known about the genetic risk in African Americans despite the recent identification of more than 70 T2D loci primarily by genome-wide association studies (GWAS) in individuals of European ancestry. In order to investigate the genetic architecture of T2D in African Americans, the MEta-analysis of type 2 DIabetes in African Americans (MEDIA) Consortium examined 17 GWAS on T2D comprising 8,284 cases and 15,543 controls in African Americans in stage 1 analysis. Single nucleotide polymorphisms (SNPs) association analysis was conducted in each study under the additive model after adjustment for age, sex, study site, and principal components. Meta-analysis of approximately 2.6 million genotyped and imputed SNPs in all studies was conducted using an inverse variance-weighted fixed effect model. Replications were performed to follow up 21 loci in up to 6,061 cases and 5,483 controls in African Americans, and 8,130 cases and 38,987 controls of European ancestry. We identified three known loci (TCF7L2, HMGA2 and KCNQ1) and two novel loci (HLA-B and INS-IGF2) at genome-wide significance (4.15 Ă 10(-94)<P<5 Ă 10(-8), odds ratio (OR)â = 1.09 to 1.36). Fine-mapping revealed that 88 of 158 previously identified T2D or glucose homeostasis loci demonstrated nominal to highly significant association (2.2 Ă 10(-23) < locus-wide P<0.05). These novel and previously identified loci yielded a sibling relative risk of 1.19, explaining 17.5% of the phenotypic variance of T2D on the liability scale in African Americans. Overall, this study identified two novel susceptibility loci for T2D in African Americans. A substantial number of previously reported loci are transferable to African Americans after accounting for linkage disequilibrium, enabling fine mapping of causal variants in trans-ethnic meta-analysis studies.Peer reviewe
A Lower Bound on Convergence of a Distributed Network Consensus Algorithm
This paper gives a lower bound on the convergence
rate of a class of network consensus algorithms.
Two different approaches using directed graphs as a main
tool are introduced: one is to compute the âscrambling
constantsâ of stochastic matrices associated with âneighbor
shared graphsâ and the other is to analyze random walks
on a sequence of graphs. Both approaches prove that
the time to reach consensus within a dynamic network
is logarithmic in the relative error and is in worst case
exponential in the size of the network.