tfp.experimental.mcmc.NoUTurnSampler

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Class NoUTurnSampler

Runs one step of the No U-Turn Sampler.

Inherits From: TransitionKernel

The No U-Turn Sampler (NUTS) is an adaptive variant of the Hamiltonian Monte Carlo (HMC) method for MCMC. NUTS adapts the distance traveled in response to the curvature of the target density. Conceptually, one proposal consists of reversibly evolving a trajectory through the sample space, continuing until that trajectory turns back on itself (hence the name, "No U-Turn"). This class implements one random NUTS step from a given current_state. Mathematical details and derivations can be found in [Hoffman, Gelman (2011)][1].

The one_step function can update multiple chains in parallel. It assumes that a prefix of 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][0, ...] could have a different target distribution from current_state[0][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)).)

TODO(axch): Examples (e.g., a la HMC). For them to be sensible, need to pick sensible step sizes, or implement step size adaptation, or both.

References

[1] Matthew D. Hoffman, Andrew Gelman. The No-U-Turn Sampler: Adaptively Setting Path Lengths in Hamiltonian Monte Carlo. 2011. https://arxiv.org/pdf/1111.4246.pdf.

__init__

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__init__(
    target_log_prob_fn,
    step_size,
    max_tree_depth=10,
    unrolled_leapfrog_steps=1,
    num_trajectories_per_step=1,
    use_auto_batching=True,
    stackless=False,
    backend=None,
    seed=None,
    name=None
)

Initializes this transition kernel.

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. Due to limitations of the underlying auto-batching system, target_log_prob_fn may be invoked with junk data at some batch indexes, which it must process without crashing. (The results at those indexes are ignored).
  • step_size: Tensor or Python 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.
  • max_tree_depth: Maximum depth of the tree implicitly built by NUTS. The maximum number of leapfrog steps is bounded by 2**max_tree_depth-1 i.e. the number of nodes in a binary tree max_tree_depth nodes deep. The default setting of 10 takes up to 1023 leapfrog steps.
  • unrolled_leapfrog_steps: The number of leapfrogs to unroll per tree expansion step. Applies a direct linear multipler to the maximum trajectory length implied by max_tree_depth. Defaults to 1. This parameter can be useful for amortizing the auto-batching control flow overhead.
  • num_trajectories_per_step: Python int giving the number of NUTS trajectories to run as "one" step. Setting this higher than 1 may be favorable for performance by giving the autobatching system the opportunity to batch gradients across consecutive trajectories. The intermediate samples are thinned: only the last sample from the run (in each batch member) is returned.
  • use_auto_batching: Boolean. If False, do not invoke the auto-batching system; operate on batch size 1 only.
  • stackless: Boolean. If True, invoke the stackless version of the auto-batching system. Only works in Eager mode.
  • backend: Auto-batching backend object. Falls back to a default TensorFlowBackend().
  • seed: Python integer to seed the random number generator.
  • name: Python str name prefixed to Ops created by this function. Default value: None (i.e., 'nuts_kernel').

Properties

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.

parameters

Methods

bootstrap_results

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bootstrap_results(init_state)

Creates initial previous_kernel_results using a supplied state.

one_step

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one_step(
    current_state,
    previous_kernel_results
)

Runs one iteration of the No U-Turn Sampler.

Args:

  • current_state: Tensor or Python list of Tensors 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 Tensors representing values from previous calls to this function (or from the bootstrap_results function.)

Returns:

  • next_state: Tensor or Python list of Tensors representing the state(s) of the Markov chain(s) after taking self.num_trajectories_per_step steps. Has same type and shape as current_state.
  • kernel_results: collections.namedtuple of internal calculations used to advance the chain.