5,590 research outputs found
Learning non-Gaussian graphical models via Hessian scores and triangular transport
Undirected probabilistic graphical models represent the conditional
dependencies, or Markov properties, of a collection of random variables.
Knowing the sparsity of such a graphical model is valuable for modeling
multivariate distributions and for efficiently performing inference. While the
problem of learning graph structure from data has been studied extensively for
certain parametric families of distributions, most existing methods fail to
consistently recover the graph structure for non-Gaussian data. Here we propose
an algorithm for learning the Markov structure of continuous and non-Gaussian
distributions. To characterize conditional independence, we introduce a score
based on integrated Hessian information from the joint log-density, and we
prove that this score upper bounds the conditional mutual information for a
general class of distributions. To compute the score, our algorithm SING
estimates the density using a deterministic coupling, induced by a triangular
transport map, and iteratively exploits sparse structure in the map to reveal
sparsity in the graph. For certain non-Gaussian datasets, we show that our
algorithm recovers the graph structure even with a biased approximation to the
density. Among other examples, we apply sing to learn the dependencies between
the states of a chaotic dynamical system with local interactions.Comment: 40 pages, 12 figure
Application of new probabilistic graphical models in the genetic regulatory networks studies
This paper introduces two new probabilistic graphical models for
reconstruction of genetic regulatory networks using DNA microarray data. One is
an Independence Graph (IG) model with either a forward or a backward search
algorithm and the other one is a Gaussian Network (GN) model with a novel
greedy search method. The performances of both models were evaluated on four
MAPK pathways in yeast and three simulated data sets. Generally, an IG model
provides a sparse graph but a GN model produces a dense graph where more
information about gene-gene interactions is preserved. Additionally, we found
two key limitations in the prediction of genetic regulatory networks using DNA
microarray data, the first is the sufficiency of sample size and the second is
the complexity of network structures may not be captured without additional
data at the protein level. Those limitations are present in all prediction
methods which used only DNA microarray data.Comment: 38 pages, 3 figure
Learning Bayesian Networks with the bnlearn R Package
bnlearn is an R package which includes several algorithms for learning the
structure of Bayesian networks with either discrete or continuous variables.
Both constraint-based and score-based algorithms are implemented, and can use
the functionality provided by the snow package to improve their performance via
parallel computing. Several network scores and conditional independence
algorithms are available for both the learning algorithms and independent use.
Advanced plotting options are provided by the Rgraphviz package.Comment: 22 pages, 4 picture
Structure learning of undirected graphical models for count data
Biological processes underlying the basic functions of a cell involve complex
interactions between genes. From a technical point of view, these interactions
can be represented through a graph where genes and their connections are,
respectively, nodes and edges. The main objective of this paper is to develop a
statistical framework for modelling the interactions between genes when the
activity of genes is measured on a discrete scale. In detail, we define a new
algorithm for learning the structure of undirected graphs, PC-LPGM, proving its
theoretical consistence in the limit of infinite observations. The proposed
algorithm shows promising results when applied to simulated data as well as to
real data
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