Create an sghmccv object

Creates an sghmccv (stochastic gradient Hamiltonian Monte Carlo with Control Variates) object which can be passed to sgmcmcStep to simulate from 1 step of sghmc, using a gradient estimate with control variates for the posterior defined by logLik and logPrior. This allows the user to code the loop themselves, as in many standard TensorFlow procedures (such as optimization). Which means they do not need to store the chain at each iteration. This is useful when the full chain needs a lot of memory.

sghmccvSetup(logLik, dataset, params, stepsize, optStepsize, logPrior = NULL,
  minibatchSize = 0.01, alpha = 0.01, L = 5L, nItersOpt = 10^4L,
  verbose = TRUE, seed = NULL)

Arguments

logLik	function which takes parameters and dataset (list of TensorFlow variables and placeholders respectively) as input. It should return a TensorFlow expression which defines the log likelihood of the model.
dataset	list of numeric R arrays which defines the datasets for the problem. The names in the list should correspond to those referred to in the logLik and logPrior functions
params	list of numeric R arrays which define the starting point of each parameter. The names in the list should correspond to those referred to in the logLik and logPrior functions
stepsize	list of numeric values corresponding to the SGLD stepsizes for each parameter The names in the list should correspond to those in params. Alternatively specify a single numeric value to use that stepsize for all parameters.
optStepsize	numeric value specifying the stepsize for the optimization to find MAP estimates of parameters. The TensorFlow GradientDescentOptimizer is used.
logPrior	optional. Default uninformative improper prior. Function which takes parameters (list of TensorFlow variables) as input. The function should return a TensorFlow tensor which defines the log prior of the model.
minibatchSize	optional. Default 0.01. Numeric or integer value that specifies amount of dataset to use at each iteration either as proportion of dataset size (if between 0 and 1) or actual magnitude (if an integer).
alpha	optional. Default 0.01. List of numeric values corresponding to the SGHMC momentum tuning constants ($\alpha$ in the original paper). One value should be given for each parameter in params, the names should correspond to those in params. Alternatively specify a single float to specify that value for all parameters.
L	optional. Default 5L. Integer specifying the trajectory parameter of the simulation, as defined in the main reference.
nItersOpt	optional. Default 10^4L. Integer specifying number of iterations of initial optimization to perform.
verbose	optional. Default TRUE. Boolean specifying whether to print algorithm progress
seed	optional. Default NULL. Numeric seed for random number generation. The default does not declare a seed for the TensorFlow session.

Value

The function returns an 'sghmccv' object, a type of sgmcmc object. Which is used to pass the required information about the current model to the sgmcmcStep function. The function sgmcmcStep runs one step of sghmc with a gradient estimate that uses control variates. Attributes of the sghmccv object you'll probably find most useful are:

params: list of tf$Variables with the same names as the params list passed to sghmccvSetup. This is the object passed to the logLik and logPrior functions you declared to calculate the log posterior gradient estimate.
paramsOpt: list of tf$Variables with the same names as the params list passed to sghmccvSetup. These variables are used to initially find MAP estimates and then store these optimal parameter estimates.
estLogPost: a tensor that estimates the log posterior given the current placeholders and params.
logPostOptGrad: list of tf$Variables with same names as params, this stores the full log posterior gradient at each MAP estimate after the initial optimization step.

Other attributes of the object are as follows:

N: dataset size.
data: dataset as passed to sghmccvSetup.
n: minibatchSize as passed to sghmccvSetup.
placeholders: list of tf$placeholder objects with the same names as dataset used to feed minibatches of data to sgmcmcStep. These are also the objects that gets fed to the dataset argument of the logLik and logPrior functions you declared.
stepsize: list of stepsizes as passed to sghmccvSetup
alpha: list of alpha tuning parameters as passed to sghmcSetup.
L: integer trajectory parameter as passed to sghmcSetup.
dynamics: a list of TensorFlow steps that are evaluated by sgmcmcStep.
estLogPostOpt: a TensorFlow tensor relying on paramsOpt and placeholders which estimates the log posterior at the optimal parameters. Used in the initial optimization step.
fullLogPostOpt: a TensorFlow tensor used in the calculation of the full log posterior gradient at the MAP estimates.
optimizer: a TensorFlow optimizer object used to find the initial MAP estimates.

Examples

# NOT RUN {
# Simulate from a Normal Distribution, unknown location and known scale with uninformative prior
# Run sgmcmc step by step and calculate estimate of location on the fly to reduce storage
dataset = list("x" = rnorm(1000))
params = list("theta" = 0)
logLik = function(params, dataset) {
    distn = tf$distributions$Normal(params$theta, 1)
    return(tf$reduce_sum(distn$log_prob(dataset$x)))
}
stepsize = list("theta" = 1e-4)
optStepsize = 1e-1
sghmccv = sghmccvSetup(logLik, dataset, params, stepsize, optStepsize)
nIters = 10^4L
# Initialize location estimate
locEstimate = 0
# Initialise TensorFlow session
sess = initSess(sghmccv)
for ( i in 1:nIters ) {
    sgmcmcStep(sghmccv, sess)
    locEstimate = locEstimate + 1 / nIters * getParams(sghmccv, sess)$theta
}
# For more examples see vignettes
# }

Arguments

Value

Examples

Contents