Create an sghmc object

Creates an sghmc (stochastic gradient Hamiltonian Monte Carlo) object which can be passed to sgmcmcStep to simulate from 1 step of SGLD 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.

sghmcSetup(logLik, dataset, params, stepsize, logPrior = NULL,
  minibatchSize = 0.01, alpha = 0.01, L = 5L, 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.
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.
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 'sghmc' 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. The sghmc object has the following attributes:

params

list of tf$Variables with the same names as the params list passed to sghmcSetup. This is the object passed to the logLik and logPrior functions you declared to calculate the log posterior gradient estimate.

estLogPost

a tensor that estimates the log posterior given the current placeholders and params.

N

dataset size.

data

dataset as passed to sghmcSetup.

n

minibatchSize as passed to sghmcSetup.

placeholders

list of tf$placeholder objects with the same names as dataset used to feed minibatches of data to sgmcmcStep. These objects get fed to the dataset argument of the logLik and logPrior functions you declared.

stepsize

list of stepsizes as passed to sghmcSetup.

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.

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)
sghmc = sghmcSetup(logLik, dataset, params, stepsize)
nIters = 10^4L
# Initialize location estimate
locEstimate = 0
# Initialise TensorFlow session
sess = initSess(sghmc)
for ( i in 1:nIters ) {
    sgmcmcStep(sghmc, sess)
    locEstimate = locEstimate + 1 / nIters * getParams(sghmc, sess)$theta
}
# For more examples see vignettes
# }