Simulates from the posterior defined by the functions logLik and logPrior using stochastic gradient Nose Hoover Thermostat. 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.
sgnht(logLik, dataset, params, stepsize, logPrior = NULL, minibatchSize = 0.01, a = 0.01, nIters = 10^4L, verbose = TRUE, seed = NULL)
| 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. |
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| 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). |
| 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. |
| 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. |
Returns list of arrays for each parameter containing the MCMC chain. Dimension of the form (nIters,paramDim1,paramDim2,...)
# 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" = 5e-6) output = sgnht(logLik, dataset, params, stepsize) # For more examples see vignettes # }