nimble (version 0.8.0)

runCrossValidate: Perform k-fold cross-validation on a NIMBLE model fit by MCMC

Description

Takes a NIMBLE model MCMC configuration and conducts k-fold cross-validation of the MCMC fit, returning a measure of the model's predictive performance.

Usage

runCrossValidate(MCMCconfiguration, k, foldFunction = "random",
  lossFunction = "MSE", MCMCcontrol = list(), returnSamples = FALSE,
  nCores = 1, nBootReps = 200, silent = FALSE)

Value

an R list with four elements:

• CVvalue The CV value, measuring the model's ability to predict new data. Smaller relative values indicate better model performance.

• CVstandardError The standard error of the CV value, giving an indication of the total Monte Carlo error in the CV estimate.

• foldCVInfo An list of fold CV values and standard errors for each fold.

• samples An R list, only returned when returnSamples = TRUE. The i'th element of this list will be a matrix of posterior samples from the model with the i'th fold of data left out. There will be k sets of samples.

The <code>foldFunction</code> Argument

If the default 'random' method is not used, the foldFunction argument must be an R function that takes a single integer-valued argument i. i is guaranteed to be within the range \([1, k]\). For each integer value i, the function should return a character vector of node names corresponding to the data nodes that will be left out of the model for that fold. The returned node names can be expanded, but don't need to be. For example, if fold i is inteded to leave out the model nodes x[1], x[2] and x[3] then the function could return either c('x[1]', 'x[2]', 'x[3]') or 'x[1:3]'.

The <code>lossFunction</code> Argument

If you don't wish to use NIMBLE's built-in "MSE" or "predictive" loss functions, you may provide your own R function as the lossFunction argument to runCrossValidate. A user-supplied lossFunction must be an R function that takes two arguments: the first, named simulatedDataValues, will be a vector of simulated data values. The second, named actualDataValues, will be a vector of observed data values corresponding to the simulated data values in simulatedDataValues. The loss function should return a single scalar number. See ‘Examples’ for an example of a user-defined loss function.

The <code>MCMCcontrol</code> Argument

The MCMCcontrol argument is a list with the following elements:

• niter an integer argument determining how many MCMC iterations should be run for each loss value calculation. Defaults to 10000, but should probably be manually set.

• nburnin the number of samples from the start of the MCMC chain to discard as burn-in for each loss value calculation. Must be between 0 and niter. Defaults to 10

Details

k-fold CV in NIMBLE proceeds by separating the data in a nimbleModel into k folds, as determined by the foldFunction argument. For each fold, the corresponding data are held out of the model, and MCMC is run to estimate the posterior distribution and simultaneously impute posterior predictive values for the held-out data. Then, the posterior predictive values are compared to the known, held-out data values via the specified lossFunction. The loss values are averaged over the posterior samples for each fold, and these averaged values for each fold are then averaged over all folds to produce a single out-of-sample loss estimate. Additionally, estimates of the Monte Carlo error for each fold are returned.

Examples

# NOT RUN {
## We conduct CV on the classic "dyes" BUGS model.

dyesCode <- nimbleCode({
  for (i in 1:BATCHES) {
    for (j in 1:SAMPLES) {
      y[i,j] ~ dnorm(mu[i], tau.within);
    }
    mu[i] ~ dnorm(theta, tau.between);
  }

  theta ~ dnorm(0.0, 1.0E-10);
  tau.within ~ dgamma(0.001, 0.001);  sigma2.within <- 1/tau.within;
  tau.between ~ dgamma(0.001, 0.001);  sigma2.between <- 1/tau.between;
})

dyesData <- list(y = matrix(c(1545, 1540, 1595, 1445, 1595,
                              1520, 1440, 1555, 1550, 1440,
                              1630, 1455, 1440, 1490, 1605,
                              1595, 1515, 1450, 1520, 1560, 
                              1510, 1465, 1635, 1480, 1580,
                              1495, 1560, 1545, 1625, 1445), 
                              nrow = 6, ncol = 5))
                              
dyesConsts <- list(BATCHES = 6,
                   SAMPLES = 5)
                   
dyesInits <- list(theta = 1500, tau.within = 1, tau.between =  1)

dyesModel <- nimbleModel(code = dyesCode,
                         constants = dyesConsts,
                         data = dyesData,
                         inits = dyesInits)

# Define the fold function.
# This function defines the data to leave out for the i'th fold
# as the i'th row of the data matrix y.  This implies we will have
# 6 folds.

dyesFoldFunction <- function(i){
  foldNodes_i <- paste0('y[', i, ', ]')  # will return 'y[1,]' for i = 1 e.g.
  return(foldNodes_i)
}

# We define our own loss function as well.
# The function below will compute the root mean squared error.

RMSElossFunction <- function(simulatedDataValues, actualDataValues){
  dataLength <- length(simulatedDataValues) # simulatedDataValues is a vector
  SSE <- 0
  for(i in 1:dataLength){
    SSE <- SSE + (simulatedDataValues[i] - actualDataValues[i])^2
  }
  MSE <- SSE / dataLength
  RMSE <- sqrt(MSE)
  return(RMSE)
}

dyesMCMCconfiguration <- configureMCMC(dyesModel)
  
crossValOutput <- runCrossValidate(MCMCconfiguration = dyesMCMCconfiguration,
                                   k = 6,
                                   foldFunction = dyesFoldFunction,
                                   lossFunction = RMSElossFunction,
                                   MCMCcontrol = list(niter = 5000,
                                                      nburnin = 500))
# }
# NOT RUN {
# }