View source on GitHub |
Runs one step of the No U-Turn Sampler.
Inherits From: TransitionKernel
tfp.substrates.jax.mcmc.NoUTurnSampler(
target_log_prob_fn,
step_size,
max_tree_depth=10,
max_energy_diff=1000.0,
unrolled_leapfrog_steps=1,
parallel_iterations=10,
experimental_shard_axis_names=None,
name=None
)
Used in the notebooks
Used in the tutorials |
---|
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
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.
|
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. |
parallel_iterations
|
The number of iterations allowed to run in parallel.
It must be a positive integer. See tf.while_loop for more details.
|
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., 'NoUTurnSampler').
|
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.
|
max_energy_diff
|
|
max_tree_depth
|
|
name
|
|
parallel_iterations
|
|
parameters
|
|
read_instruction
|
|
step_size
|
|
target_log_prob_fn
|
|
unrolled_leapfrog_steps
|
|
write_instruction
|
Methods
bootstrap_results
bootstrap_results(
init_state
)
Creates initial previous_kernel_results
using a supplied state
.
copy
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
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. |
init_momentum_state_memory
init_momentum_state_memory(
input_tensors
)
Allocate TensorArray for storing state and momentum.
one_step
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 Tensor s representing the
current state(s) of the Markov chain(s).
|
previous_kernel_results
|
A (possibly nested) tuple , namedtuple or
list of Tensor s 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 Tensor s representing the
next state(s) of the Markov chain(s).
|
kernel_results
|
A (possibly nested) tuple , namedtuple or list of
Tensor s representing internal calculations made within this function.
|