Hamiltonian Monte Carlo (HMC) is a Markov chain Monte Carlo (MCMC) algorithm
that takes a series of gradient-informed steps to produce a Metropolis
proposal. This class implements one random HMC step from a given
current_state. Mathematical details and derivations can be found in
Neal (2011).
mcmc_hamiltonian_monte_carlo(
target_log_prob_fn,
step_size,
num_leapfrog_steps,
state_gradients_are_stopped = FALSE,
step_size_update_fn = NULL,
seed = NULL,
store_parameters_in_results = FALSE,
name = NULL
)a Monte Carlo sampling kernel
Function which takes an argument like
current_state (if it's a list current_state will be unpacked) and returns its
(possibly unnormalized) log-density under the target distribution.
Tensor or list of Tensors representing the step
size for the leapfrog integrator. Must broadcast with the shape of
current_state. Larger step sizes lead to faster progress, but
too-large step sizes make rejection exponentially more likely. When
possible, it's often helpful to match per-variable step sizes to the
standard deviations of the target distribution in each variable.
Integer number of steps to run the leapfrog integrator
for. Total progress per HMC step is roughly proportional to
step_size * num_leapfrog_steps.
logical indicating that the proposed
new state be run through tf$stop_gradient. This is particularly useful
when combining optimization over samples from the HMC chain.
Default value: FALSE (i.e., do not apply stop_gradient).
Function taking current step_size
(typically a tf$Variable) and kernel_results (typically
collections$namedtuple) and returns updated step_size (Tensors).
Default value: NULL (i.e., do not update step_size automatically).
integer to seed the random number generator.
If TRUE, then step_size and
num_leapfrog_steps are written to and read from eponymous fields in
the kernel results objects returned from one_step and
bootstrap_results. This allows wrapper kernels to adjust those
parameters on the fly. This is incompatible with step_size_update_fn,
which must be set to NULL.
string prefixed to Ops created by this function.
Default value: NULL (i.e., 'hmc_kernel').
The one_step function can update multiple chains in parallel. It assumes
that all leftmost dimensions of current_state index independent chain states
(and are therefore updated independently). The output of
target_log_prob_fn(current_state) should sum log-probabilities across all
event dimensions. Slices along the rightmost dimensions may have different
target distributions; for example, current_state[0, :] could have a
different target distribution from current_state[1, :]. These semantics are
governed by target_log_prob_fn(current_state). (The number of independent
chains is tf$size(target_log_prob_fn(current_state)).)
Other mcmc_kernels:
mcmc_dual_averaging_step_size_adaptation(),
mcmc_metropolis_adjusted_langevin_algorithm(),
mcmc_metropolis_hastings(),
mcmc_no_u_turn_sampler(),
mcmc_random_walk_metropolis(),
mcmc_replica_exchange_mc(),
mcmc_simple_step_size_adaptation(),
mcmc_slice_sampler(),
mcmc_transformed_transition_kernel(),
mcmc_uncalibrated_hamiltonian_monte_carlo(),
mcmc_uncalibrated_langevin(),
mcmc_uncalibrated_random_walk()