sgmcmc (version 0.2.5)

sgnhtcv: Stochastic Gradient Nose Hoover Thermostat with Control Variates

Description

Simulates from the posterior defined by the functions logLik and logPrior using stochastic gradient Nose Hoover Thermostat with an improved gradient estimate that is calculated using control variates. The thermostat step needs a dot product to be calculated between two vectors. So when the algorithm uses parameters that are higher order than vectors (e.g. matrices and tensors), the thermostat step uses a tensor contraction. Tensor contraction is otherwise known as the inner product between two tensors.

Usage

sgnhtcv(logLik, dataset, params, stepsize, optStepsize, logPrior = NULL,
  minibatchSize = 0.01, a = 0.01, nIters = 10^4L, 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).

a

optional. Default 0.01. List of numeric values corresponding to SGNHT diffusion factors (see Algorithm 2 of 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.

nIters

optional. Default 10^4L. Integer specifying number of iterations to perform.

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

Returns list of arrays for each parameter containing the MCMC chain. Dimension of the form (nIters,paramDim1,paramDim2,...). Names are the same as the params list.

References

• Baker, J., Fearnhead, P., Fox, E. B., and Nemeth, C. (2017). Control variates for stochastic gradient MCMC. ArXiv preprint arXiv:1706.05439.

• Ding, N., Fang, Y., Babbush, R., Chen, C., Skeel, R. D., and Neven, H. (2014). Bayesian sampling using stochastic gradient thermostats. NIPS (pp. 3203-3211).

Examples

# NOT RUN {
# Simulate from a Normal Distribution with uninformative prior
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
output = sgnhtcv(logLik, dataset, params, stepsize, optStepsize)
# }