24,161 research outputs found
Entropy inference and the James-Stein estimator, with application to nonlinear gene association networks
We present a procedure for effective estimation of entropy and mutual
information from small-sample data, and apply it to the problem of inferring
high-dimensional gene association networks. Specifically, we develop a
James-Stein-type shrinkage estimator, resulting in a procedure that is highly
efficient statistically as well as computationally. Despite its simplicity, we
show that it outperforms eight other entropy estimation procedures across a
diverse range of sampling scenarios and data-generating models, even in cases
of severe undersampling. We illustrate the approach by analyzing E. coli gene
expression data and computing an entropy-based gene-association network from
gene expression data. A computer program is available that implements the
proposed shrinkage estimator.Comment: 18 pages, 3 figures, 1 tabl
Feature selection for microarray gene expression data using simulated annealing guided by the multivariate joint entropy
In this work a new way to calculate the multivariate joint entropy is presented. This measure is the basis for a fast information-theoretic based evaluation of gene relevance in a Microarray Gene Expression data context. Its low complexity is based on the reuse of previous computations to calculate current feature relevance. The mu-TAFS algorithm --named as such to differentiate it from previous TAFS algorithms-- implements a simulated annealing technique specially designed for feature subset selection. The algorithm is applied to the maximization of gene subset relevance in several public-domain microarray data sets. The experimental results show a notoriously high classification performance and low size subsets formed by biologically meaningful genes.Postprint (published version
Forest Density Estimation
We study graph estimation and density estimation in high dimensions, using a
family of density estimators based on forest structured undirected graphical
models. For density estimation, we do not assume the true distribution
corresponds to a forest; rather, we form kernel density estimates of the
bivariate and univariate marginals, and apply Kruskal's algorithm to estimate
the optimal forest on held out data. We prove an oracle inequality on the
excess risk of the resulting estimator relative to the risk of the best forest.
For graph estimation, we consider the problem of estimating forests with
restricted tree sizes. We prove that finding a maximum weight spanning forest
with restricted tree size is NP-hard, and develop an approximation algorithm
for this problem. Viewing the tree size as a complexity parameter, we then
select a forest using data splitting, and prove bounds on excess risk and
structure selection consistency of the procedure. Experiments with simulated
data and microarray data indicate that the methods are a practical alternative
to Gaussian graphical models.Comment: Extended version of earlier paper titled "Tree density estimation
Ranking to Learn: Feature Ranking and Selection via Eigenvector Centrality
In an era where accumulating data is easy and storing it inexpensive, feature
selection plays a central role in helping to reduce the high-dimensionality of
huge amounts of otherwise meaningless data. In this paper, we propose a
graph-based method for feature selection that ranks features by identifying the
most important ones into arbitrary set of cues. Mapping the problem on an
affinity graph-where features are the nodes-the solution is given by assessing
the importance of nodes through some indicators of centrality, in particular,
the Eigen-vector Centrality (EC). The gist of EC is to estimate the importance
of a feature as a function of the importance of its neighbors. Ranking central
nodes individuates candidate features, which turn out to be effective from a
classification point of view, as proved by a thoroughly experimental section.
Our approach has been tested on 7 diverse datasets from recent literature
(e.g., biological data and object recognition, among others), and compared
against filter, embedded and wrappers methods. The results are remarkable in
terms of accuracy, stability and low execution time.Comment: Preprint version - Lecture Notes in Computer Science - Springer 201
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