tfp.substrates.numpy.mcmc.TransitionKernel

Base class for all MCMC TransitionKernels.

This class defines the minimal requirements to efficiently implement a Markov chain Monte Carlo (MCMC) transition kernel. A transition kernel returns a new state given some old state. It also takes (and returns) "side information" which may be used for debugging or optimization purposes (i.e, to "recycle" previously computed results).

Example (random walk transition kernel):

In this example we make isotropic Gaussian proposals of a given step size.

from tensorflow_probability.substrates.numpy.mcmc import kernel as kernel_base
from tensorflow_probability.python.internal.backend.numpy.compat import v2 as tf
import tensorflow_probability as tfp; tfp = tfp.substrates.numpy

tfd = tfp.distributions

RWResult = collections.namedtuple("RWResult", 'target_log_prob')

class RandomWalkProposalKernel(kernel_base.TransitionKernel):
  def __init__(self, target_log_prob_fn, step_size):
    self._parameters = dict(
      target_log_prob_fn = target_log_prob_fn,
      step_size = step_size)

  @property
  def target_log_prob_fn(self):
    return self._parameters['target_log_prob_fn']

  @property
  def step_size(self):
    return self._parameters['step_size']

  @property
  def is_calibrated(self):
    return False

  def one_step(self, current_state, previous_kernel_results, seed=None):
    scale = tf.broadcast_to(self.step_size, tf.shape(current_state))
    isotropic_normal = tfd.Normal(loc=current_state, scale=scale)

    next_state = isotropic_normal.sample(seed=seed)
    next_target_log_prob = self.target_log_prob_fn(next_state)
    new_kernel_results = previous_kernel_results._replace(
      target_log_prob = next_target_log_prob)

    return next_state, new_kernel_results

  def bootstrap_results(self, init_state):
    kernel_results = RWResult(
      target_log_prob = self.target_log_prob_fn(init_state))
    return kernel_results

experimental_shard_axis_names The shard axis names for members of the state.
is_calibrated Returns True if Markov chain converges to specified distribution.

TransitionKernels which are "uncalibrated" are often calibrated by composing them with the tfp.mcmc.MetropolisHastings TransitionKernel.

Methods

bootstrap_results

View source

bootstrap_results(
    init_state
)

Returns an object with the same type as returned by one_step(...)[1].

Args
init_state Tensor or Python list of Tensors representing the initial state(s) of the Markov chain(s).

Returns
kernel_results A (possibly nested) tuple, namedtuple or list of Tensors representing internal calculations made within this function.

copy

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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

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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

@abc.abstractmethod
one_step(
    current_state, previous_kernel_results, seed=None
)

Takes one step of the TransitionKernel.

Must be overridden by subclasses.

Args
current_state Tensor or Python list of Tensors representing the current state(s) of the Markov chain(s).
previous_kernel_results A (possibly nested) tuple, namedtuple or list of Tensors representing internal calculations made within the previous call to this function (or as returned by bootstrap_results).
seed PRNG seed; see tfp.random.sanitize_seed for details.

Returns
next_state Tensor or Python list of Tensors representing the next state(s) of the Markov chain(s).
kernel_results A (possibly nested) tuple, namedtuple or list of Tensors representing internal calculations made within this function.