selectPenalty {BSL}

Selecting the Penalty Parameter

Description

This is the main function for selecting the shrinkage (graphical lasso or Warton's estimator) penalty parameter for method BSL or semiBSL based on a point estimate of the parameters. Parallel computing is supported with the R package foreach. The penalty selection method is outlined in An et al. (2019).

Usage

selectPenalty(
  ssy,
  n,
  lambda,
  M,
  sigma = 1.5,
  model,
  theta = NULL,
  method = c("BSL", "semiBSL"),
  shrinkage = c("glasso", "Warton"),
  parallelSim = FALSE,
  parallelSimArgs = NULL,
  parallelMain = FALSE,
  verbose = 1L,
  ...
)

Arguments

ssy

A summary statistic vector for the observed data.

n

A vector of possible values of n, the number of simulations from the model per MCMC iteration for estimating the synthetic likelihood.

lambda

A list, with each entry containing the vector of penalty values to test for the corresponding choice of n.

M

The number of repeats to use in estimating the standard deviation of the estimated log synthetic likelihood.

sigma

The standard deviation of the log synthetic likelihood estimator to aim for, usually a value between 1 and 2. This parameter helps to control the mixing of a Markov chain.

model

A “MODEL” object generated with function newModel. See newModel.

theta

A point estimate of the parameter value which all of the simulations will be based on. By default, if theta is NULL, it will be replaced by theta0 from the given model.

method

A string argument indicating the method to be used. If the method is “BSL”, the shrinkage is applied to the Gaussian covariance matrix. Otherwise if the method is “semiBSL”, the shrinkage is applied to the correlation matrix of the Gaussian copula.

shrinkage

A string argument indicating which shrinkage method to be used. Current options are “glasso” for the graphical lasso method of Friedman et al. (2008) and “Warton” for the ridge regularisation method of Warton (2008).

parallelSim

A logical value indicating whether parallel computing should be used for simulation and summary statistic evaluation. Default is FALSE.

parallelSimArgs

A list of additional arguments to pass into the foreach function. Only used when parallelSim is TRUE, default is NULL.

parallelMain

A logical value indicating whether parallel computing should be used to computing the graphical lasso function. Notice that this should only be turned on when there are a lot of candidate values in lambda. Default is FALSE.

verbose

An integer indicating the verbose style. 0L means no verbose messages will be printed. 1L uses a custom progress bar to track the progress. 2L prints the iteration numbers (1:M) to track the progress. The default is 1L.

...

Other arguments to pass to gaussianSynLike (“BSL” method) or semiparaKernelEstimate (“semiBSL” method).

Value

An S4 object PENALTY of the penalty selection results. The show and plot methods are provided with the S4 class.

Author(s)

Ziwen An, Leah F. South and Christopher Drovandi

References

An Z, South LF, Nott DJ, Drovandi CC (2019). “Accelerating Bayesian Synthetic Likelihood With the Graphical Lasso.” Journal of Computational and Graphical Statistics, 28(2), 471–475. doi: 10.1080/10618600.2018.1537928.

Friedman J, Hastie T, Tibshirani R (2008). “Sparse Inverse Covariance Estimation with the Graphical Lasso.” Biostatistics, 9(3), 432–441.

Warton DI (2008). “Penalized Normal Likelihood and Ridge Regularization of Correlation and Covariance Matrices.” Journal of the American Statistical Association, 103(481), 340–349. doi: 10.1198/016214508000000021.

See Also

PENALTY for the usage of the S4 class. ma2, cell and mgnk for examples. bsl for the main function to run BSL.

Examples

## Not run: 
data(ma2)
model <- newModel(fnSimVec = ma2_sim_vec, fnSum = ma2_sum, simArgs = ma2$sim_args,
                  theta0 = ma2$start, fnLogPrior = ma2_prior)
theta <- c(0.6,0.2)

# Performing tuning for BSLasso (BSL with glasso shrinkage estimation)
ssy <- ma2_sum(ma2$data)
lambda_all <- list(exp(seq(-3,0.5,length.out=20)), exp(seq(-4,-0.5,length.out=20)),
                   exp(seq(-5.5,-1.5,length.out=20)), exp(seq(-7,-2,length.out=20)))
set.seed(100)
sp_ma2 <- selectPenalty(ssy = ssy, n = c(50, 150, 300, 500), lambda_all, theta = theta,
    M = 100, sigma = 1.5, model = model, method = 'BSL', shrinkage = 'glasso')
sp_ma2
plot(sp_ma2)

## End(Not run)