# Fit the hub graphical lasso, hub covariance graph, and hub binary network

### Description

This package is called hglasso, for "hub graphical lasso". It implements three methods:hub graphical lasso, hub covariance graph, and hub binary network. All are described in the paper "Learning graphical models with hubs", by Tan et al. (2014).

The main functions are as follows: (1) hglasso (2) hcov (3) hbn

The first function, hglasso, performs hub graphical lasso. The second function, hcov, performs hub covariance graph estimation. The third function, hbn, performs hub binary network estimation.

### Details

Package: | hglasso |

Type: | Package |

Version: | 1.2 |

Date: | 2014-08-09 |

License: | GPL (>=2.0) |

LazyLoad: | yes |

The package includes the following functinos:

`hglasso` : | Performs hub graphical lasso |

`hcov` : | Performs hub covariance graph estimation |

`hbn` : | Performs hub binary network estimation |

`HubNetwork` : | Generates inverse covariance matrix or covariance matrix with hubs |

`binaryMCMC` : | Generates samples for binary Ising model via Gibbs sampling |

`image.hglasso` : | Creates image plot of the matrix V and Z |

`plot.hglasso` : | Creates a graphical representation of the estimated matrix Theta |

`summary.hglasso` : | Provides summary for the matrix Theta, Z, and V |

`hglassoBIC` : | Calculate BIC-type criterion for `hglasso` |

### Author(s)

Kean Ming Tan and Karthik Mohan

Karthik Mohan implemented the Barzilai-Borwein method for `hbn`

Maintainer: Kean Ming Tan <keanming@uw.edu>

### References

Tan, KM., London, P., Mohan, K., Lee, S-I., Fazel, M., and Witten, D. (2014). Learning graphical models with hubs. To appear in Journal of Machine Learning Research. arXiv.org/pdf/1402.7349.pdf.

### See Also

`hglasso`

`hcov`

`hbn`

### Examples

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 | ```
##############################################
# Example from Figure 1 in the manuscript
# A toy example to illustrate the results from
# Hub Graphical Lasso
##############################################
#library(mvtnorm)
#set.seed(1)
#n=100
#p=100
# A network with 4 hubs
#network<-HubNetwork(p,0.99,4,0.1)
#Theta <- network$Theta
#truehub <- network$hubcol
# The four hub nodes have indices 14, 42, 45, 78
#print(truehub)
# Generate data matrix x
#x <- rmvnorm(n,rep(0,p),solve(Theta))
#x <- scale(x)
# Run Hub Graphical Lasso to estimate the inverse covariance matrix
# res1<-hglasso(cov(x),0.3,0.3,1.5)
# print out a summary of the object hglasso
#summary(res1)
# we see that the estimated hub nodes have indices 14, 42, 45, 78
# We successfully recover the 4 hub nodes
# Plot the matrices V and Z
#image(res1)
#dev.off()
# Plot a graphical representation of the estimated inverse
# covariance matrix --- conditional independence graph
#plot(res1,main="Conditional Independence Graph")
``` |