3,058 research outputs found
Sparse regulatory networks
In many organisms the expression levels of each gene are controlled by the
activation levels of known "Transcription Factors" (TF). A problem of
considerable interest is that of estimating the "Transcription Regulation
Networks" (TRN) relating the TFs and genes. While the expression levels of
genes can be observed, the activation levels of the corresponding TFs are
usually unknown, greatly increasing the difficulty of the problem. Based on
previous experimental work, it is often the case that partial information about
the TRN is available. For example, certain TFs may be known to regulate a given
gene or in other cases a connection may be predicted with a certain
probability. In general, the biology of the problem indicates there will be
very few connections between TFs and genes. Several methods have been proposed
for estimating TRNs. However, they all suffer from problems such as unrealistic
assumptions about prior knowledge of the network structure or computational
limitations. We propose a new approach that can directly utilize prior
information about the network structure in conjunction with observed gene
expression data to estimate the TRN. Our approach uses penalties on the
network to ensure a sparse structure. This has the advantage of being
computationally efficient as well as making many fewer assumptions about the
network structure. We use our methodology to construct the TRN for E. coli and
show that the estimate is biologically sensible and compares favorably with
previous estimates.Comment: Published in at http://dx.doi.org/10.1214/10-AOAS350 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
Penalized Estimation of Directed Acyclic Graphs From Discrete Data
Bayesian networks, with structure given by a directed acyclic graph (DAG),
are a popular class of graphical models. However, learning Bayesian networks
from discrete or categorical data is particularly challenging, due to the large
parameter space and the difficulty in searching for a sparse structure. In this
article, we develop a maximum penalized likelihood method to tackle this
problem. Instead of the commonly used multinomial distribution, we model the
conditional distribution of a node given its parents by multi-logit regression,
in which an edge is parameterized by a set of coefficient vectors with dummy
variables encoding the levels of a node. To obtain a sparse DAG, a group norm
penalty is employed, and a blockwise coordinate descent algorithm is developed
to maximize the penalized likelihood subject to the acyclicity constraint of a
DAG. When interventional data are available, our method constructs a causal
network, in which a directed edge represents a causal relation. We apply our
method to various simulated and real data sets. The results show that our
method is very competitive, compared to many existing methods, in DAG
estimation from both interventional and high-dimensional observational data.Comment: To appear in Statistics and Computin
Network estimation in State Space Model with L1-regularization constraint
Biological networks have arisen as an attractive paradigm of genomic science
ever since the introduction of large scale genomic technologies which carried
the promise of elucidating the relationship in functional genomics. Microarray
technologies coupled with appropriate mathematical or statistical models have
made it possible to identify dynamic regulatory networks or to measure time
course of the expression level of many genes simultaneously. However one of the
few limitations fall on the high-dimensional nature of such data coupled with
the fact that these gene expression data are known to include some hidden
process. In that regards, we are concerned with deriving a method for inferring
a sparse dynamic network in a high dimensional data setting. We assume that the
observations are noisy measurements of gene expression in the form of mRNAs,
whose dynamics can be described by some unknown or hidden process. We build an
input-dependent linear state space model from these hidden states and
demonstrate how an incorporated regularization constraint in an
Expectation-Maximization (EM) algorithm can be used to reverse engineer
transcriptional networks from gene expression profiling data. This corresponds
to estimating the model interaction parameters. The proposed method is
illustrated on time-course microarray data obtained from a well established
T-cell data. At the optimum tuning parameters we found genes TRAF5, JUND, CDK4,
CASP4, CD69, and C3X1 to have higher number of inwards directed connections and
FYB, CCNA2, AKT1 and CASP8 to be genes with higher number of outwards directed
connections. We recommend these genes to be object for further investigation.
Caspase 4 is also found to activate the expression of JunD which in turn
represses the cell cycle regulator CDC2.Comment: arXiv admin note: substantial text overlap with arXiv:1308.359
A Regularized Method for Selecting Nested Groups of Relevant Genes from Microarray Data
Gene expression analysis aims at identifying the genes able to accurately
predict biological parameters like, for example, disease subtyping or
progression. While accurate prediction can be achieved by means of many
different techniques, gene identification, due to gene correlation and the
limited number of available samples, is a much more elusive problem. Small
changes in the expression values often produce different gene lists, and
solutions which are both sparse and stable are difficult to obtain. We propose
a two-stage regularization method able to learn linear models characterized by
a high prediction performance. By varying a suitable parameter these linear
models allow to trade sparsity for the inclusion of correlated genes and to
produce gene lists which are almost perfectly nested. Experimental results on
synthetic and microarray data confirm the interesting properties of the
proposed method and its potential as a starting point for further biological
investigationsComment: 17 pages, 8 Post-script figure
Marginal integration for nonparametric causal inference
We consider the problem of inferring the total causal effect of a single
variable intervention on a (response) variable of interest. We propose a
certain marginal integration regression technique for a very general class of
potentially nonlinear structural equation models (SEMs) with known structure,
or at least known superset of adjustment variables: we call the procedure
S-mint regression. We easily derive that it achieves the convergence rate as
for nonparametric regression: for example, single variable intervention effects
can be estimated with convergence rate assuming smoothness with
twice differentiable functions. Our result can also be seen as a major
robustness property with respect to model misspecification which goes much
beyond the notion of double robustness. Furthermore, when the structure of the
SEM is not known, we can estimate (the equivalence class of) the directed
acyclic graph corresponding to the SEM, and then proceed by using S-mint based
on these estimates. We empirically compare the S-mint regression method with
more classical approaches and argue that the former is indeed more robust, more
reliable and substantially simpler.Comment: 40 pages, 14 figure
A fast algorithm for detecting gene-gene interactions in genome-wide association studies
With the recent advent of high-throughput genotyping techniques, genetic data
for genome-wide association studies (GWAS) have become increasingly available,
which entails the development of efficient and effective statistical
approaches. Although many such approaches have been developed and used to
identify single-nucleotide polymorphisms (SNPs) that are associated with
complex traits or diseases, few are able to detect gene-gene interactions among
different SNPs. Genetic interactions, also known as epistasis, have been
recognized to play a pivotal role in contributing to the genetic variation of
phenotypic traits. However, because of an extremely large number of SNP-SNP
combinations in GWAS, the model dimensionality can quickly become so
overwhelming that no prevailing variable selection methods are capable of
handling this problem. In this paper, we present a statistical framework for
characterizing main genetic effects and epistatic interactions in a GWAS study.
Specifically, we first propose a two-stage sure independence screening (TS-SIS)
procedure and generate a pool of candidate SNPs and interactions, which serve
as predictors to explain and predict the phenotypes of a complex trait. We also
propose a rates adjusted thresholding estimation (RATE) approach to determine
the size of the reduced model selected by an independence screening.
Regularization regression methods, such as LASSO or SCAD, are then applied to
further identify important genetic effects. Simulation studies show that the
TS-SIS procedure is computationally efficient and has an outstanding finite
sample performance in selecting potential SNPs as well as gene-gene
interactions. We apply the proposed framework to analyze an
ultrahigh-dimensional GWAS data set from the Framingham Heart Study, and select
23 active SNPs and 24 active epistatic interactions for the body mass index
variation. It shows the capability of our procedure to resolve the complexity
of genetic control.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS771 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
- …