41,642 research outputs found
Efficient Distributed Estimation of Inverse Covariance Matrices
In distributed systems, communication is a major concern due to issues such
as its vulnerability or efficiency. In this paper, we are interested in
estimating sparse inverse covariance matrices when samples are distributed into
different machines. We address communication efficiency by proposing a method
where, in a single round of communication, each machine transfers a small
subset of the entries of the inverse covariance matrix. We show that, with this
efficient distributed method, the error rates can be comparable with estimation
in a non-distributed setting, and correct model selection is still possible.
Practical performance is shown through simulations
Decomposable Principal Component Analysis
We consider principal component analysis (PCA) in decomposable Gaussian
graphical models. We exploit the prior information in these models in order to
distribute its computation. For this purpose, we reformulate the problem in the
sparse inverse covariance (concentration) domain and solve the global
eigenvalue problem using a sequence of local eigenvalue problems in each of the
cliques of the decomposable graph. We demonstrate the application of our
methodology in the context of decentralized anomaly detection in the Abilene
backbone network. Based on the topology of the network, we propose an
approximate statistical graphical model and distribute the computation of PCA
Learning and comparing functional connectomes across subjects
Functional connectomes capture brain interactions via synchronized
fluctuations in the functional magnetic resonance imaging signal. If measured
during rest, they map the intrinsic functional architecture of the brain. With
task-driven experiments they represent integration mechanisms between
specialized brain areas. Analyzing their variability across subjects and
conditions can reveal markers of brain pathologies and mechanisms underlying
cognition. Methods of estimating functional connectomes from the imaging signal
have undergone rapid developments and the literature is full of diverse
strategies for comparing them. This review aims to clarify links across
functional-connectivity methods as well as to expose different steps to perform
a group study of functional connectomes
Nonparametric Stein-type Shrinkage Covariance Matrix Estimators in High-Dimensional Settings
Estimating a covariance matrix is an important task in applications where the
number of variables is larger than the number of observations. Shrinkage
approaches for estimating a high-dimensional covariance matrix are often
employed to circumvent the limitations of the sample covariance matrix. A new
family of nonparametric Stein-type shrinkage covariance estimators is proposed
whose members are written as a convex linear combination of the sample
covariance matrix and of a predefined invertible target matrix. Under the
Frobenius norm criterion, the optimal shrinkage intensity that defines the best
convex linear combination depends on the unobserved covariance matrix and it
must be estimated from the data. A simple but effective estimation process that
produces nonparametric and consistent estimators of the optimal shrinkage
intensity for three popular target matrices is introduced. In simulations, the
proposed Stein-type shrinkage covariance matrix estimator based on a scaled
identity matrix appeared to be up to 80% more efficient than existing ones in
extreme high-dimensional settings. A colon cancer dataset was analyzed to
demonstrate the utility of the proposed estimators. A rule of thumb for adhoc
selection among the three commonly used target matrices is recommended.Comment: To appear in Computational Statistics and Data Analysi
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