tfp.experimental.mcmc.PreconditionedHamiltonianMonteCarlo

Hamiltonian Monte Carlo, with given momentum distribution.

Inherits From: HamiltonianMonteCarlo, TransitionKernel

tfp.experimental.mcmc.PreconditionedHamiltonianMonteCarlo(
    target_log_prob_fn,
    step_size,
    num_leapfrog_steps,
    momentum_distribution=None,
    state_gradients_are_stopped=False,
    step_size_update_fn=None,
    store_parameters_in_results=False,
    experimental_shard_axis_names=None,
    name=None
)

See tfp.mcmc.HamiltonianMonteCarlo for details on HMC.

HMC produces samples much more efficiently if properly preconditioned. This can be done by choosing a momentum distribution with covariance equal to the inverse of the state's covariance.

Examples:

Simple chain with warm-up.

In this example we can use an estimate of the target covariance to sample efficiently with HMC.

import tensorflow as tf
import tensorflow_probability as tfp
tfed = tfp.experimental.distributions

# Suppose we have a target log prob fn, as well as an estimate of its
# covariance.
log_prob_fn = ...
cov_estimate = ...

# We want the mass matrix to be the *inverse* of the covariance estimate,
# so we can use the symmetric square root:
momentum_distribution = (
    tfed.MultivariateNormalPrecisionFactorLinearOperator(
        precision_factor=tf.linalg.LinearOperatorLowerTriangular(
            tf.linalg.cholesky(cov_estimate),
        ),
        precision=tf.linalg.LinearOperatorFullMatrix(cov_estimate),
)

# Run standard HMC below
num_burnin_steps = 100
num_results = 1000
adaptive_hmc = tfp.mcmc.SimpleStepSizeAdaptation(
    tfp.experimental.mcmc.PreconditionedHamiltonianMonteCarlo(
      target_log_prob_fn=log_prob_fn,
      momentum_distribution=momentum_distribution,
      step_size=0.3,
      num_leapfrog_steps=10),
    num_adaptation_steps=int(num_burnin_steps * 0.8))

@tf.function
def run_chain_and_compute_ess():
  draws = tfp.mcmc.sample_chain(
      num_results,
      num_burnin_steps=num_burnin_steps,
      current_state=tf.zeros(3),  # 3 chains.
      kernel=adaptive_hmc,
      trace_fn=None)
  return tfp.mcmc.effective_sample_size(draws, cross_chain_dims=1)

run_chain_and_compute_ess()  # Something close to 3 x 1000.

Estimate parameters of a more complicated distribution.

This demonstrates using multiple state parts, and reshaping a tfde.MultivariateNormalPrecisionFactorLinearOperator to use with a scalar or a non-square shape (in this case, [2, 3, 4]).

mvn = tfd.JointDistributionSequential([
    tfd.Normal(0., 0.1),
    tfd.Normal(0., 10.),
    tfd.Independent(tfd.Normal(tf.fill([2, 3, 4], 3.), 10.),
                    reinterpreted_batch_ndims=3)])

reshape_to_scalar = tfp.bijectors.Reshape(event_shape_out=[])
reshape_to_234 = tfp.bijectors.Reshape(event_shape_out=[2, 3, 4])
momentum_distribution = tfd.JointDistributionSequential([
    tfd.Normal(0., 10.),
    tfd.Normal(0., 0.1),
    reshape_to_234(
        tfde.MultivariateNormalPrecisionFactorLinearOperator(
            0., tf.linalg.LinearOperatorDiag(tf.fill([24], 10.))))
])
num_burnin_steps = 100
num_results = 1000
adaptive_hmc = tfp.experimental.mcmc.PreconditionedHamiltonianMonteCarlo(
  target_log_prob_fn=mvn.log_prob,
  momentum_distribution=momentum_distribution,
  step_size=0.3,
  num_leapfrog_steps=10)

@tf.function
def run_chain_and_compute_ess():
  draws = tfp.mcmc.sample_chain(
      num_results,
      num_burnin_steps=num_burnin_steps,
      current_state=mvn.sample(),
      kernel=adaptive_hmc,
      trace_fn=None)
  return tfp.mcmc.effective_sample_size(draws)

run_chain_and_compute_ess()  # [1000, 1000, 1000 * tf.ones([2, 3, 4])]

Args
`target_log_prob_fn`	Python callable which takes an argument like `current_state` (or `*current_state` if it's a list) and returns its (possibly unnormalized) log-density under the target distribution.
`step_size`	`Tensor` or Python `list` of `Tensor`s 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.
`num_leapfrog_steps`	Integer number of steps to run the leapfrog integrator for. Total progress per HMC step is roughly proportional to `step_size * num_leapfrog_steps`.
`momentum_distribution`	A `tfp.distributions.Distribution` instance to draw momentum from. Defaults to normal distributions with identity covariance.
`state_gradients_are_stopped`	Python `bool` 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`).
`step_size_update_fn`	Python `callable` taking current `step_size` (typically a `tf.Variable`) and `kernel_results` (typically `collections.namedtuple`) and returns updated step_size (`Tensor`s). Default value: `None` (i.e., do not update `step_size` automatically).
`store_parameters_in_results`	If `True`, then `step_size`, `momentum_distribution`, 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. In case this is `True`, the `momentum_distribution` must be a `CompositeTensor`. See `tfp.experimental.auto_composite`. This is incompatible with `step_size_update_fn`, which must be set to `None`.
`experimental_shard_axis_names`	A structure of string names indicating how members of the state are sharded.
`name`	Python `str` name prefixed to Ops created by this function. Default value: `None` (i.e., 'phmc_kernel').

Attributes
`experimental_shard_axis_names`	The shard axis names for members of the state.
`is_calibrated`	Returns `True` if Markov chain converges to specified distribution. `TransitionKernel`s which are "uncalibrated" are often calibrated by composing them with the `tfp.mcmc.MetropolisHastings` `TransitionKernel`.
`name`
`num_leapfrog_steps`	Returns the num_leapfrog_steps parameter. If `store_parameters_in_results` argument to the initializer was set to `True`, this only returns the value of the `num_leapfrog_steps` placed in the kernel results by the `bootstrap_results` method. The actual `num_leapfrog_steps` in that situation is governed by the `previous_kernel_results` argument to `one_step` method.
`parameters`	Return `dict` of `__init__` arguments and their values.
`state_gradients_are_stopped`
`step_size`	Returns the step_size parameter. If `store_parameters_in_results` argument to the initializer was set to `True`, this only returns the value of the `step_size` placed in the kernel results by the `bootstrap_results` method. The actual step size in that situation is governed by the `previous_kernel_results` argument to `one_step` method.
`target_log_prob_fn`

Methods

`bootstrap_results`

View source

bootstrap_results(
    init_state
)

Creates initial previous_kernel_results using a supplied state.

`copy`

View source

copy(
    **override_parameter_kwargs
)

Non-destructively creates a deep copy of the kernel.

Args
`**override_parameter_kwargs`	Python String/value `dictionary` of initialization arguments to override with new values.

Returns
`new_kernel`	`TransitionKernel` object of same type as `self`, initialized with the union of self.parameters and override_parameter_kwargs, with any shared keys overridden by the value of override_parameter_kwargs, i.e., `dict(self.parameters, **override_parameters_kwargs)`.

`experimental_with_shard_axes`

View source

experimental_with_shard_axes(
    shard_axis_names
)

Returns a copy of the kernel with the provided shard axis names.

Args
`shard_axis_names`	a structure of strings indicating the shard axis names for each component of this kernel's state.

Returns
A copy of the current kernel with the shard axis information.

`one_step`

View source

one_step(
    current_state, previous_kernel_results, seed=None
)

Runs one iteration of Hamiltonian Monte Carlo.

Args
`current_state`	`Tensor` or Python `list` of `Tensor`s representing the current state(s) of the Markov chain(s). The first `r` dimensions index independent chains, `r = tf.rank(target_log_prob_fn(*current_state))`.
`previous_kernel_results`	`collections.namedtuple` containing `Tensor`s representing values from previous calls to this function (or from the `bootstrap_results` function.)
`seed`	PRNG seed; see `tfp.random.sanitize_seed` for details.

Returns
`next_state`	Tensor or Python list of `Tensor`s representing the state(s) of the Markov chain(s) after taking exactly one step. Has same type and shape as `current_state`.
`kernel_results`	`collections.namedtuple` of internal calculations used to advance the chain.

Raises
`ValueError`	if there isn't one `step_size` or a list with same length as `current_state`.

tfp.experimental.mcmc.PreconditionedHamiltonianMonteCarlo

Examples:

Simple chain with warm-up.

Estimate parameters of a more complicated distribution.

Args

Attributes

Methods

bootstrap_results

copy

experimental_with_shard_axes

one_step

`bootstrap_results`

`copy`

`experimental_with_shard_axes`

`one_step`