# sghmc: Stochastic Gradient Hamiltonian Monte Carlo In sgmcmc: Stochastic Gradient Markov Chain Monte Carlo

## Description

Simulates from the posterior defined by the functions logLik and logPrior using stochastic gradient Hamiltonian Monte Carlo. The function uses TensorFlow, so needs TensorFlow for python installed. Currently we use the approximation \hat β = 0, as used in the simulations by the original reference. This will be changed in future implementations.

## Usage

 1 2 3 sghmc(logLik, dataset, params, stepsize, logPrior = NULL, minibatchSize = 0.01, alpha = 0.01, L = 5L, nIters = 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. 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 (α 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. nIters optional. Default 10^4L. Integer specifying number of iterations 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,...)

## Examples

  1 2 3 4 5 6 7 8 9 10 11 12 13 ## Not run: # Simulate from a Normal Distribution with uninformative, improper 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-5) output = sghmc(logLik, dataset, params, stepsize) # For more examples see vignettes ## End(Not run) 

sgmcmc documentation built on Oct. 30, 2019, 11:39 a.m.