tfp.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] and [Betancourt (2018)][2].

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)).)

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.

[2]: Michael Betancourt. A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv preprint arXiv:1701.02434, 2018. https://arxiv.org/abs/1701.02434

__init__

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__init__(
    target_log_prob_fn,
    step_size,
    max_tree_depth=10,
    max_energy_diff=1000.0,
    unrolled_leapfrog_steps=1,
    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.
  • 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 i.e. the number of nodes in a binary tree max_tree_depth nodes deep. The default setting of 10 takes up to 1024 leapfrog steps.
  • max_energy_diff: Scaler threshold of energy differences at each leapfrog, divergence samples are defined as leapfrog steps that exceed this threshold. Default to 1000.
  • 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.
  • 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.

max_energy_diff

max_tree_depth

name

parameters

read_instruction

step_size

target_log_prob_fn

unrolled_leapfrog_steps

write_instruction

Methods

bootstrap_results

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bootstrap_results(init_state)

Creates initial previous_kernel_results using a supplied state.

loop_tree_doubling

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loop_tree_doubling(
    step_size,
    momentum_state_memory,
    current_step_meta_info,
    iter_,
    initial_step_state,
    initial_step_metastate
)

Main loop for tree doubling.

one_step

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one_step(
    current_state,
    previous_kernel_results
)

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).

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.