Description Usage Arguments Value Examples

Creates an sgnhtcv (stochastic gradient Nose Hoover thermostat with Control Variates) object
which can be passed to `sgmcmcStep`

to simulate from 1 step of sgnht, 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.

1 2 3 | ```
sgnhtcvSetup(logLik, dataset, params, stepsize, optStepsize, logPrior = NULL,
minibatchSize = 0.01, a = 0.01, nItersOpt = 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. |

`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. |

`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. |

The function returns an 'sgnhtcv' 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 sgnht with a gradient estimate that uses control variates.
Attributes of the sgnhtcv object you'll probably find most useful are:

- params
list of tf$Variables with the same names as the params list passed to

`sgnhtcvSetup`

. 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`sgnhtcvSetup`

. These variables are used to initially find MAP estimates and then store these optimal parameter estimates.- estLogPost
a tensor relying on

`params`

and`placeholders`

. This tensor 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

`sgnhtcvSetup`

.- n
minibatchSize as passed to

`sgnhtcvSetup`

.- 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

`sgnhtcvSetup`

- alpha
list of alpha tuning parameters as passed to

`sgnhtSetup`

.- L
integer trajectory parameter as passed to

`sgnhtSetup`

.- 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.

1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 | ```
## 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
sgnhtcv = sgnhtcvSetup(logLik, dataset, params, stepsize, optStepsize)
nIters = 10^4L
# Initialize location estimate
locEstimate = 0
# Initialise TensorFlow session
sess = initSess(sgnhtcv)
for ( i in 1:nIters ) {
sgmcmcStep(sgnhtcv, sess)
locEstimate = locEstimate + 1 / nIters * getParams(sgnhtcv, sess)$theta
}
# For more examples see vignettes
## End(Not run)
``` |

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

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