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Runs one step of the No U-Turn Sampler.
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)].
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, ...] 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
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.
 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__( 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.
target_log_prob_fn: Python callable which takes an argument like
*current_stateif 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).
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-1i.e. the number of nodes in a binary tree
max_tree_depthnodes 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.
intgiving 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.
strname prefixed to Ops created by this function. Default value:
True if Markov chain converges to specified distribution.
TransitionKernels which are "uncalibrated" are often calibrated by
composing them with the
previous_kernel_results using a supplied
one_step( current_state, previous_kernel_results )
Runs one iteration of the No U-Turn Sampler.
Tensors representing the current state(s) of the Markov chain(s). The first
rdimensions index independent chains,
r = tf.rank(target_log_prob_fn(*current_state)).
Tensors representing values from previous calls to this function (or from the
Tensoror Python list of
Tensors representing the state(s) of the Markov chain(s) after taking
self.num_trajectories_per_stepsteps. Has same type and shape as
collections.namedtupleof internal calculations used to advance the chain.