MCPeSe

Monte Carlo Penalty Selection (MCPeSe) for graphical lasso.

Example

library(huge)

source("mcpese.R")

##########################################################

# Initialize seed number:

#seed = Sys.time()

#seed = as.integer(seed)

#seed = seed %% 100000

seed = 59040

set.seed(seed)

##########################################################

# Graphical model simulation:

p = 200

n = 210

Model = "hub"

HugeData = huge.generator(n=n, d=p, graph=Model) 

nlambda = 100

##########################################################

# Compute Glasso solution path:

L = huge(HugeData$data, nlambda=nlambda, method="glasso")

##########################################################

# Run the A-R selection (uniform prior),

ARSelect = mcpese(L, n=n, M=1000)

names(ARSelect)

rhos = ARSelect$rhos

ARSelect$accept.rate

##########################################################

# Run the M-H selection (uniform prior),

MHSelect = mcpese(L, n=n, nSteps=1000, method="M-H")

names(MHSelect)

rhos = MHSelect$rhos

MHSelect$accept.rate

plot(rhos, type="l")

##########################################################

# Either use the mean of rho values...

mean(rhos)

#ThetaARSelect = huge(Y, lambda=mean(rhos), method="glasso")
#ThetaAR = as.matrix(ThetaARSelect$icov[[1]])

# ... or pick the smallest tuning parameter value from the solution path
# which is larger or equal to the mean value:

optARrhoIndx = ARSelect$opt.index # This is sup{i : rho[i] >= mean(rhos)}

optMHrhoIndx = MHSelect$opt.index

huge.plot(HugeData$theta)

title("Ground truth")

##########################################################

huge.plot(L$path[[optARrhoIndx]])

title("Accept-Reject sampling")

##########################################################

huge.plot(L$path[[optMHrhoIndx]])

title("Metropolis-Hastings sampling")

Reference

The MCPeSe method is described in:

Kuismin and Sillanpaa (2020). MCPeSe: Monte Carlo penalty selection for graphical lasso, Bioinformatics, https://doi.org/10.1093/bioinformatics/btaa734.

File "CodeCollection.zip" is a collection of scripts used to prepare the material in this paper.