asggm {AdaptiveSparsity}

Adaptively Sparse Gaussian Graphical Model

Description

implements a parameter-free adaptively sparse Gaussian graphical model.

Usage

## S3 method for class 'formula'
asggm(formula, data=list(), ...)
## Default S3 method:
asggm(x, iterations = 100000000, init = NULL, epsilon = 0.001, ...)

Arguments

formula

an object of class “formula” (or one that can be coerced to that class): a symbolic description of the model to be fitted. See lm Details for further information.

data

an optional data frame, list or environment containing the variables in the model.

x

design matrix

iterations

number of iterations of the algorithm to run.

init

optional initialization, for instance, the cholesky of x. If NULL, it defaults to the cholesky of x.

epsilon

amount to add for numerical stability.

...

further arguments

Details

An effective approach to structure learning and parameter estimation for Gaussian graphical models is to impose a sparsity prior, such as a Laplace prior, on the entries of the precision matrix. We introduce a parameter-free method for estimating a precision matrix with sparsity that adapts to the data automatically, achieved by formulating a hierarchical Bayesian model of the precision matrix with a non-informative Jeffreys' hyperprior. We also naturally enforce the symmetry and positive-definiteness constraints on the precision matrix by parameterizing it with the Cholesky decomposition.

Value

asggm returns an object of class "asggm".

An object of class “asggm” is a list containing at least the following components:

Author(s)

Kristen Zygmunt, Eleanor Wong, Tom Fletcher

References

Wong, Eleanor, Suyash Awate, and P. Thomas Fletcher. “Adaptive Sparsity in Gaussian Graphical Models.”In Proceedings of the 30th International Conference on Machine Learning (ICML-13), pp. 311-319. 2013.

Examples

A = diag(3)
asggm(A)