mcmc_simple_step_size_adaptation: Adapts the inner kernel's 'step_size' based on...
In tfprobability: Interface to 'TensorFlow Probability'

mcmc_simple_step_size_adaptation

R Documentation

Adapts the inner kernel's `step_size` based on `log_accept_prob`.

Description

The simple policy multiplicatively increases or decreases the step_size of the inner kernel based on the value of log_accept_prob. It is based on equation 19 of Andrieu and Thoms (2008). Given enough steps and small enough adaptation_rate the median of the distribution of the acceptance probability will converge to the target_accept_prob. A good target acceptance probability depends on the inner kernel. If this kernel is HamiltonianMonteCarlo, then 0.6-0.9 is a good range to aim for. For RandomWalkMetropolis this should be closer to 0.25. See the individual kernels' docstrings for guidance.

Usage

mcmc_simple_step_size_adaptation(
  inner_kernel,
  num_adaptation_steps,
  target_accept_prob = 0.75,
  adaptation_rate = 0.01,
  step_size_setter_fn = NULL,
  step_size_getter_fn = NULL,
  log_accept_prob_getter_fn = NULL,
  validate_args = FALSE,
  name = NULL
)

Arguments

`inner_kernel`	`TransitionKernel`-like object.
`num_adaptation_steps`	Scalar `integer` `Tensor` number of initial steps to during which to adjust the step size. This may be greater, less than, or equal to the number of burnin steps.
`target_accept_prob`	A floating point `Tensor` representing desired acceptance probability. Must be a positive number less than 1. This can either be a scalar, or have shape `list(num_chains)`. Default value: `0.75` (the center of asymptotically optimal rate for HMC).
`adaptation_rate`	`Tensor` representing amount to scale the current `step_size`.
`step_size_setter_fn`	A function with the signature `(kernel_results, new_step_size) -> new_kernel_results` where `kernel_results` are the results of the `inner_kernel`, `new_step_size` is a `Tensor` or a nested collection of `Tensor`s with the same structure as returned by the `step_size_getter_fn`, and `new_kernel_results` are a copy of `kernel_results` with the step size(s) set.
`step_size_getter_fn`	A function with the signature `(kernel_results) -> step_size` where `kernel_results` are the results of the `inner_kernel`, and `step_size` is a floating point `Tensor` or a nested collection of such `Tensor`s.
`log_accept_prob_getter_fn`	A function with the signature `(kernel_results) -> log_accept_prob` where `kernel_results` are the results of the `inner_kernel`, and `log_accept_prob` is a floating point `Tensor`. `log_accept_prob` can either be a scalar, or have shape `list(num_chains)`. If it's the latter, `step_size` should also have the same leading dimension.
`validate_args`	`Logical`. When `True` kernel parameters are checked for validity. When `False` invalid inputs may silently render incorrect outputs.
`name`	string prefixed to Ops created by this class. Default: "simple_step_size_adaptation".

Details

In general, adaptation prevents the chain from reaching a stationary distribution, so obtaining consistent samples requires num_adaptation_steps be set to a value somewhat smaller than the number of burnin steps. However, it may sometimes be helpful to set num_adaptation_steps to a larger value during development in order to inspect the behavior of the chain during adaptation.

The step size is assumed to broadcast with the chain state, potentially having leading dimensions corresponding to multiple chains. When there are fewer of those leading dimensions than there are chain dimensions, the corresponding dimensions in the log_accept_prob are averaged (in the direct space, rather than the log space) before being used to adjust the step size. This means that this kernel can do both cross-chain adaptation, or per-chain step size adaptation, depending on the shape of the step size.

For example, if your problem has a state with shape [S], your chain state has shape [C0, C1, Y] (meaning that there are C0 * C1 total chains) and log_accept_prob has shape [C0, C1] (one acceptance probability per chain), then depending on the shape of the step size, the following will happen:

Step size has shape [], [S] or [1], the log_accept_prob will be averaged across its C0 and C1 dimensions. This means that you will learn a shared step size based on the mean acceptance probability across all chains. This can be useful if you don't have a lot of steps to adapt and want to average away the noise.
Step size has shape [C1, 1] or [C1, S], the log_accept_prob will be averaged across its C0 dimension. This means that you will learn a shared step size based on the mean acceptance probability across chains that share the coordinate across the C1 dimension. This can be useful when the C1 dimension indexes different distributions, while C0 indexes replicas of a single distribution, all sampled in parallel.
Step size has shape [C0, C1, 1] or [C0, C1, S], then no averaging will happen. This means that each chain will learn its own step size. This can be useful when all chains are sampling from different distributions. Even when all chains are for the same distribution, this can help during the initial warmup period.
Step size has shape [C0, 1, 1] or [C0, 1, S], the log_accept_prob will be averaged across its C1 dimension. This means that you will learn a shared step size based on the mean acceptance probability across chains that share the coordinate across the C0 dimension. This can be useful when the C0 dimension indexes different distributions, while C1 indexes replicas of a single distribution, all sampled in parallel.

Value

a Monte Carlo sampling kernel

References

Examples


  target_log_prob_fn <- tfd_normal(loc = 0, scale = 1)$log_prob
  num_burnin_steps <- 500
  num_results <- 500
  num_chains <- 64L
  step_size <- tf$fill(list(num_chains), 0.1)

  kernel <- mcmc_hamiltonian_monte_carlo(
    target_log_prob_fn = target_log_prob_fn,
    num_leapfrog_steps = 2,
    step_size = step_size
  ) %>%
    mcmc_simple_step_size_adaptation(num_adaptation_steps = round(num_burnin_steps * 0.8))

  res <- kernel %>% mcmc_sample_chain(
    num_results = num_results,
    num_burnin_steps = num_burnin_steps,
    current_state = rep(0, num_chains),
    trace_fn = function(x, pkr) {
      list (
        pkr$inner_results$accepted_results$step_size,
        pkr$inner_results$log_accept_ratio
      )
    }
  )

  samples <- res$all_states
  step_size <- res$trace[[1]]
  log_accept_ratio <- res$trace[[2]]

tfprobability documentation built on Sept. 1, 2022, 5:07 p.m.