4,008 research outputs found
Learning Large-Scale Bayesian Networks with the sparsebn Package
Learning graphical models from data is an important problem with wide
applications, ranging from genomics to the social sciences. Nowadays datasets
often have upwards of thousands---sometimes tens or hundreds of thousands---of
variables and far fewer samples. To meet this challenge, we have developed a
new R package called sparsebn for learning the structure of large, sparse
graphical models with a focus on Bayesian networks. While there are many
existing software packages for this task, this package focuses on the unique
setting of learning large networks from high-dimensional data, possibly with
interventions. As such, the methods provided place a premium on scalability and
consistency in a high-dimensional setting. Furthermore, in the presence of
interventions, the methods implemented here achieve the goal of learning a
causal network from data. Additionally, the sparsebn package is fully
compatible with existing software packages for network analysis.Comment: To appear in the Journal of Statistical Software, 39 pages, 7 figure
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
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 sparse conditional Gaussian graphical model for analysis of genetical genomics data
Genetical genomics experiments have now been routinely conducted to measure
both the genetic markers and gene expression data on the same subjects. The
gene expression levels are often treated as quantitative traits and are subject
to standard genetic analysis in order to identify the gene expression
quantitative loci (eQTL). However, the genetic architecture for many gene
expressions may be complex, and poorly estimated genetic architecture may
compromise the inferences of the dependency structures of the genes at the
transcriptional level. In this paper we introduce a sparse conditional Gaussian
graphical model for studying the conditional independent relationships among a
set of gene expressions adjusting for possible genetic effects where the gene
expressions are modeled with seemingly unrelated regressions. We present an
efficient coordinate descent algorithm to obtain the penalized estimation of
both the regression coefficients and the sparse concentration matrix. The
corresponding graph can be used to determine the conditional independence among
a group of genes while adjusting for shared genetic effects. Simulation
experiments and asymptotic convergence rates and sparsistency are used to
justify our proposed methods. By sparsistency, we mean the property that all
parameters that are zero are actually estimated as zero with probability
tending to one. We apply our methods to the analysis of a yeast eQTL data set
and demonstrate that the conditional Gaussian graphical model leads to a more
interpretable gene network than a standard Gaussian graphical model based on
gene expression data alone.Comment: Published in at http://dx.doi.org/10.1214/11-AOAS494 the Annals of
Applied Statistics (http://www.imstat.org/aoas/) by the Institute of
Mathematical Statistics (http://www.imstat.org
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