# Copyright Contributors to the Pyro project.
# SPDX-License-Identifier: Apache-2.0
from collections import namedtuple
import math
import os
from jax import device_put, lax, partial, random, vmap
from jax.dtypes import canonicalize_dtype
from jax.flatten_util import ravel_pytree
import jax.numpy as jnp
from numpyro.infer.hmc_util import (
IntegratorState,
build_tree,
euclidean_kinetic_energy,
find_reasonable_step_size,
velocity_verlet,
warmup_adapter
)
from numpyro.infer.mcmc import MCMCKernel
from numpyro.infer.util import ParamInfo, init_to_uniform, initialize_model
from numpyro.util import cond, fori_loop, identity
HMCState = namedtuple('HMCState', ['i', 'z', 'z_grad', 'potential_energy', 'energy', 'num_steps', 'accept_prob',
'mean_accept_prob', 'diverging', 'adapt_state', 'rng_key'])
"""
A :func:`~collections.namedtuple` consisting of the following fields:
- **i** - iteration. This is reset to 0 after warmup.
- **z** - Python collection representing values (unconstrained samples from
the posterior) at latent sites.
- **z_grad** - Gradient of potential energy w.r.t. latent sample sites.
- **potential_energy** - Potential energy computed at the given value of ``z``.
- **energy** - Sum of potential energy and kinetic energy of the current state.
- **num_steps** - Number of steps in the Hamiltonian trajectory (for diagnostics).
In NUTS sampler, the tree depth of a trajectory can be computed from this field
with `tree_depth = np.log2(num_steps).astype(int) + 1`.
- **accept_prob** - Acceptance probability of the proposal. Note that ``z``
does not correspond to the proposal if it is rejected.
- **mean_accept_prob** - Mean acceptance probability until current iteration
during warmup adaptation or sampling (for diagnostics).
- **diverging** - A boolean value to indicate whether the current trajectory is diverging.
- **adapt_state** - A ``HMCAdaptState`` namedtuple which contains adaptation information
during warmup:
+ **step_size** - Step size to be used by the integrator in the next iteration.
+ **inverse_mass_matrix** - The inverse mass matrix to be used for the next
iteration.
+ **mass_matrix_sqrt** - The square root of mass matrix to be used for the next
iteration. In case of dense mass, this is the Cholesky factorization of the
mass matrix.
- **rng_key** - random number generator seed used for the iteration.
"""
def _get_num_steps(step_size, trajectory_length):
num_steps = jnp.clip(trajectory_length / step_size, a_min=1)
# NB: casting to jnp.int64 does not take effect (returns jnp.int32 instead)
# if jax_enable_x64 is False
return num_steps.astype(canonicalize_dtype(jnp.int64))
def momentum_generator(prototype_r, mass_matrix_sqrt, rng_key):
_, unpack_fn = ravel_pytree(prototype_r)
eps = random.normal(rng_key, jnp.shape(mass_matrix_sqrt)[:1])
if mass_matrix_sqrt.ndim == 1:
r = jnp.multiply(mass_matrix_sqrt, eps)
return unpack_fn(r)
elif mass_matrix_sqrt.ndim == 2:
r = jnp.dot(mass_matrix_sqrt, eps)
return unpack_fn(r)
else:
raise ValueError("Mass matrix has incorrect number of dims.")
[docs]def hmc(potential_fn=None, potential_fn_gen=None, kinetic_fn=None, algo='NUTS'):
r"""
Hamiltonian Monte Carlo inference, using either fixed number of
steps or the No U-Turn Sampler (NUTS) with adaptive path length.
**References:**
1. *MCMC Using Hamiltonian Dynamics*,
Radford M. Neal
2. *The No-U-turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo*,
Matthew D. Hoffman, and Andrew Gelman.
3. *A Conceptual Introduction to Hamiltonian Monte Carlo`*,
Michael Betancourt
:param potential_fn: Python callable that computes the potential energy
given input parameters. The input parameters to `potential_fn` can be
any python collection type, provided that `init_params` argument to
`init_kernel` has the same type.
:param potential_fn_gen: Python callable that when provided with model
arguments / keyword arguments returns `potential_fn`. This
may be provided to do inference on the same model with changing data.
If the data shape remains the same, we can compile `sample_kernel`
once, and use the same for multiple inference runs.
:param kinetic_fn: Python callable that returns the kinetic energy given
inverse mass matrix and momentum. If not provided, the default is
euclidean kinetic energy.
:param str algo: Whether to run ``HMC`` with fixed number of steps or ``NUTS``
with adaptive path length. Default is ``NUTS``.
:return: a tuple of callables (`init_kernel`, `sample_kernel`), the first
one to initialize the sampler, and the second one to generate samples
given an existing one.
.. warning::
Instead of using this interface directly, we would highly recommend you
to use the higher level :class:`numpyro.infer.MCMC` API instead.
**Example**
.. doctest::
>>> import jax
>>> from jax import random
>>> import jax.numpy as jnp
>>> import numpyro
>>> import numpyro.distributions as dist
>>> from numpyro.infer.hmc import hmc
>>> from numpyro.infer.util import initialize_model
>>> from numpyro.util import fori_collect
>>> true_coefs = jnp.array([1., 2., 3.])
>>> data = random.normal(random.PRNGKey(2), (2000, 3))
>>> labels = dist.Bernoulli(logits=(true_coefs * data).sum(-1)).sample(random.PRNGKey(3))
>>>
>>> def model(data, labels):
... coefs = numpyro.sample('coefs', dist.Normal(jnp.zeros(3), jnp.ones(3)))
... intercept = numpyro.sample('intercept', dist.Normal(0., 10.))
... return numpyro.sample('y', dist.Bernoulli(logits=(coefs * data + intercept).sum(-1)), obs=labels)
>>>
>>> model_info = initialize_model(random.PRNGKey(0), model, model_args=(data, labels,))
>>> init_kernel, sample_kernel = hmc(model_info.potential_fn, algo='NUTS')
>>> hmc_state = init_kernel(model_info.param_info,
... trajectory_length=10,
... num_warmup=300)
>>> samples = fori_collect(0, 500, sample_kernel, hmc_state,
... transform=lambda state: model_info.postprocess_fn(state.z))
>>> print(jnp.mean(samples['coefs'], axis=0)) # doctest: +SKIP
[0.9153987 2.0754058 2.9621222]
"""
if kinetic_fn is None:
kinetic_fn = euclidean_kinetic_energy
vv_update = None
trajectory_len = None
max_treedepth = None
wa_update = None
wa_steps = None
forward_mode_ad = False
max_delta_energy = 1000.
if algo not in {'HMC', 'NUTS'}:
raise ValueError('`algo` must be one of `HMC` or `NUTS`.')
def init_kernel(init_params,
num_warmup,
step_size=1.0,
inverse_mass_matrix=None,
adapt_step_size=True,
adapt_mass_matrix=True,
dense_mass=False,
target_accept_prob=0.8,
trajectory_length=2*math.pi,
max_tree_depth=10,
find_heuristic_step_size=False,
forward_mode_differentiation=False,
model_args=(),
model_kwargs=None,
rng_key=random.PRNGKey(0)):
"""
Initializes the HMC sampler.
:param init_params: Initial parameters to begin sampling. The type must
be consistent with the input type to `potential_fn`.
:param int num_warmup: Number of warmup steps; samples generated
during warmup are discarded.
:param float step_size: Determines the size of a single step taken by the
verlet integrator while computing the trajectory using Hamiltonian
dynamics. If not specified, it will be set to 1.
:param numpy.ndarray inverse_mass_matrix: Initial value for inverse mass matrix.
This may be adapted during warmup if adapt_mass_matrix = True.
If no value is specified, then it is initialized to the identity matrix.
:param bool adapt_step_size: A flag to decide if we want to adapt step_size
during warm-up phase using Dual Averaging scheme.
:param bool adapt_mass_matrix: A flag to decide if we want to adapt mass
matrix during warm-up phase using Welford scheme.
:param bool dense_mass: A flag to decide if mass matrix is dense or
diagonal (default when ``dense_mass=False``)
:param float target_accept_prob: Target acceptance probability for step size
adaptation using Dual Averaging. Increasing this value will lead to a smaller
step size, hence the sampling will be slower but more robust. Default to 0.8.
:param float trajectory_length: Length of a MCMC trajectory for HMC. Default
value is :math:`2\\pi`.
:param int max_tree_depth: Max depth of the binary tree created during the doubling
scheme of NUTS sampler. Defaults to 10.
:param bool find_heuristic_step_size: whether to a heuristic function to adjust the
step size at the beginning of each adaptation window. Defaults to False.
:param tuple model_args: Model arguments if `potential_fn_gen` is specified.
:param dict model_kwargs: Model keyword arguments if `potential_fn_gen` is specified.
:param jax.random.PRNGKey rng_key: random key to be used as the source of
randomness.
"""
step_size = lax.convert_element_type(step_size, canonicalize_dtype(jnp.float64))
nonlocal wa_update, trajectory_len, max_treedepth, vv_update, wa_steps, forward_mode_ad
forward_mode_ad = forward_mode_differentiation
wa_steps = num_warmup
trajectory_len = trajectory_length
max_treedepth = max_tree_depth
if isinstance(init_params, ParamInfo):
z, pe, z_grad = init_params
else:
z, pe, z_grad = init_params, None, None
pe_fn = potential_fn
if potential_fn_gen:
if pe_fn is not None:
raise ValueError('Only one of `potential_fn` or `potential_fn_gen` must be provided.')
else:
kwargs = {} if model_kwargs is None else model_kwargs
pe_fn = potential_fn_gen(*model_args, **kwargs)
find_reasonable_ss = None
if find_heuristic_step_size:
find_reasonable_ss = partial(find_reasonable_step_size,
pe_fn,
kinetic_fn,
momentum_generator)
wa_init, wa_update = warmup_adapter(num_warmup,
adapt_step_size=adapt_step_size,
adapt_mass_matrix=adapt_mass_matrix,
dense_mass=dense_mass,
target_accept_prob=target_accept_prob,
find_reasonable_step_size=find_reasonable_ss)
rng_key_hmc, rng_key_wa, rng_key_momentum = random.split(rng_key, 3)
z_info = IntegratorState(z=z, potential_energy=pe, z_grad=z_grad)
wa_state = wa_init(z_info, rng_key_wa, step_size,
inverse_mass_matrix=inverse_mass_matrix,
mass_matrix_size=jnp.size(ravel_pytree(z)[0]))
r = momentum_generator(z, wa_state.mass_matrix_sqrt, rng_key_momentum)
vv_init, vv_update = velocity_verlet(pe_fn, kinetic_fn, forward_mode_ad)
vv_state = vv_init(z, r, potential_energy=pe, z_grad=z_grad)
energy = kinetic_fn(wa_state.inverse_mass_matrix, vv_state.r)
hmc_state = HMCState(0, vv_state.z, vv_state.z_grad, vv_state.potential_energy, energy,
0, 0., 0., False, wa_state, rng_key_hmc)
return device_put(hmc_state)
def _hmc_next(step_size, inverse_mass_matrix, vv_state,
model_args, model_kwargs, rng_key):
if potential_fn_gen:
nonlocal vv_update, forward_mode_ad
pe_fn = potential_fn_gen(*model_args, **model_kwargs)
_, vv_update = velocity_verlet(pe_fn, kinetic_fn, forward_mode_ad)
num_steps = _get_num_steps(step_size, trajectory_len)
vv_state_new = fori_loop(0, num_steps,
lambda i, val: vv_update(step_size, inverse_mass_matrix, val),
vv_state)
energy_old = vv_state.potential_energy + kinetic_fn(inverse_mass_matrix, vv_state.r)
energy_new = vv_state_new.potential_energy + kinetic_fn(inverse_mass_matrix, vv_state_new.r)
delta_energy = energy_new - energy_old
delta_energy = jnp.where(jnp.isnan(delta_energy), jnp.inf, delta_energy)
accept_prob = jnp.clip(jnp.exp(-delta_energy), a_max=1.0)
diverging = delta_energy > max_delta_energy
transition = random.bernoulli(rng_key, accept_prob)
vv_state, energy = cond(transition,
(vv_state_new, energy_new), identity,
(vv_state, energy_old), identity)
return vv_state, energy, num_steps, accept_prob, diverging
def _nuts_next(step_size, inverse_mass_matrix, vv_state,
model_args, model_kwargs, rng_key):
if potential_fn_gen:
nonlocal vv_update, forward_mode_ad
pe_fn = potential_fn_gen(*model_args, **model_kwargs)
_, vv_update = velocity_verlet(pe_fn, kinetic_fn, forward_mode_ad)
binary_tree = build_tree(vv_update, kinetic_fn, vv_state,
inverse_mass_matrix, step_size, rng_key,
max_delta_energy=max_delta_energy,
max_tree_depth=max_treedepth)
accept_prob = binary_tree.sum_accept_probs / binary_tree.num_proposals
num_steps = binary_tree.num_proposals
vv_state = IntegratorState(z=binary_tree.z_proposal,
r=vv_state.r,
potential_energy=binary_tree.z_proposal_pe,
z_grad=binary_tree.z_proposal_grad)
return vv_state, binary_tree.z_proposal_energy, num_steps, accept_prob, binary_tree.diverging
_next = _nuts_next if algo == 'NUTS' else _hmc_next
def sample_kernel(hmc_state, model_args=(), model_kwargs=None):
"""
Given an existing :data:`~numpyro.infer.mcmc.HMCState`, run HMC with fixed (possibly adapted)
step size and return a new :data:`~numpyro.infer.mcmc.HMCState`.
:param hmc_state: Current sample (and associated state).
:param tuple model_args: Model arguments if `potential_fn_gen` is specified.
:param dict model_kwargs: Model keyword arguments if `potential_fn_gen` is specified.
:return: new proposed :data:`~numpyro.infer.mcmc.HMCState` from simulating
Hamiltonian dynamics given existing state.
"""
model_kwargs = {} if model_kwargs is None else model_kwargs
rng_key, rng_key_momentum, rng_key_transition = random.split(hmc_state.rng_key, 3)
r = momentum_generator(hmc_state.z, hmc_state.adapt_state.mass_matrix_sqrt, rng_key_momentum)
vv_state = IntegratorState(hmc_state.z, r, hmc_state.potential_energy, hmc_state.z_grad)
vv_state, energy, num_steps, accept_prob, diverging = _next(hmc_state.adapt_state.step_size,
hmc_state.adapt_state.inverse_mass_matrix,
vv_state,
model_args,
model_kwargs,
rng_key_transition)
# not update adapt_state after warmup phase
adapt_state = cond(hmc_state.i < wa_steps,
(hmc_state.i, accept_prob, vv_state, hmc_state.adapt_state),
lambda args: wa_update(*args),
hmc_state.adapt_state,
identity)
itr = hmc_state.i + 1
n = jnp.where(hmc_state.i < wa_steps, itr, itr - wa_steps)
mean_accept_prob = hmc_state.mean_accept_prob + (accept_prob - hmc_state.mean_accept_prob) / n
return HMCState(itr, vv_state.z, vv_state.z_grad, vv_state.potential_energy, energy, num_steps,
accept_prob, mean_accept_prob, diverging, adapt_state, rng_key)
# Make `init_kernel` and `sample_kernel` visible from the global scope once
# `hmc` is called for sphinx doc generation.
if 'SPHINX_BUILD' in os.environ:
hmc.init_kernel = init_kernel
hmc.sample_kernel = sample_kernel
return init_kernel, sample_kernel
[docs]class HMC(MCMCKernel):
"""
Hamiltonian Monte Carlo inference, using fixed trajectory length, with
provision for step size and mass matrix adaptation.
**References:**
1. *MCMC Using Hamiltonian Dynamics*,
Radford M. Neal
:param model: Python callable containing Pyro :mod:`~numpyro.primitives`.
If model is provided, `potential_fn` will be inferred using the model.
:param potential_fn: Python callable that computes the potential energy
given input parameters. The input parameters to `potential_fn` can be
any python collection type, provided that `init_params` argument to
:meth:`init` has the same type.
:param kinetic_fn: Python callable that returns the kinetic energy given
inverse mass matrix and momentum. If not provided, the default is
euclidean kinetic energy.
:param float step_size: Determines the size of a single step taken by the
verlet integrator while computing the trajectory using Hamiltonian
dynamics. If not specified, it will be set to 1.
:param bool adapt_step_size: A flag to decide if we want to adapt step_size
during warm-up phase using Dual Averaging scheme.
:param bool adapt_mass_matrix: A flag to decide if we want to adapt mass
matrix during warm-up phase using Welford scheme.
:param bool dense_mass: A flag to decide if mass matrix is dense or
diagonal (default when ``dense_mass=False``)
:param float target_accept_prob: Target acceptance probability for step size
adaptation using Dual Averaging. Increasing this value will lead to a smaller
step size, hence the sampling will be slower but more robust. Default to 0.8.
:param float trajectory_length: Length of a MCMC trajectory for HMC. Default
value is :math:`2\\pi`.
:param callable init_strategy: a per-site initialization function.
See :ref:`init_strategy` section for available functions.
:param bool find_heuristic_step_size: whether to a heuristic function to adjust the
step size at the beginning of each adaptation window. Defaults to False.
:param bool forward_mode_differentiation: whether to use forward-mode differentiation
or reverse-mode differentiation. By default, we use reverse mode but the forward
mode can be useful in some cases to improve the performance. In addition, some
control flow utility on JAX such as `jax.lax.while_loop` or `jax.lax.fori_loop`
only supports forward-mode differentiation. See
`JAX's The Autodiff Cookbook <https://jax.readthedocs.io/en/latest/notebooks/autodiff_cookbook.html>`_
for more information.
"""
def __init__(self,
model=None,
potential_fn=None,
kinetic_fn=None,
step_size=1.0,
adapt_step_size=True,
adapt_mass_matrix=True,
dense_mass=False,
target_accept_prob=0.8,
trajectory_length=2 * math.pi,
init_strategy=init_to_uniform,
find_heuristic_step_size=False,
forward_mode_differentiation=False):
if not (model is None) ^ (potential_fn is None):
raise ValueError('Only one of `model` or `potential_fn` must be specified.')
self._model = model
self._potential_fn = potential_fn
self._kinetic_fn = kinetic_fn if kinetic_fn is not None else euclidean_kinetic_energy
self._step_size = step_size
self._adapt_step_size = adapt_step_size
self._adapt_mass_matrix = adapt_mass_matrix
self._dense_mass = dense_mass
self._target_accept_prob = target_accept_prob
self._trajectory_length = trajectory_length
self._algo = 'HMC'
self._max_tree_depth = 10
self._init_strategy = init_strategy
self._find_heuristic_step_size = find_heuristic_step_size
self._forward_mode_differentiation = forward_mode_differentiation
# Set on first call to init
self._init_fn = None
self._potential_fn_gen = None
self._postprocess_fn = None
self._sample_fn = None
def _init_state(self, rng_key, model_args, model_kwargs, init_params):
if self._model is not None:
init_params, potential_fn, postprocess_fn, model_trace = initialize_model(
rng_key,
self._model,
dynamic_args=True,
init_strategy=self._init_strategy,
model_args=model_args,
model_kwargs=model_kwargs,
forward_mode_differentiation=self._forward_mode_differentiation)
if self._init_fn is None:
self._init_fn, self._sample_fn = hmc(potential_fn_gen=potential_fn,
kinetic_fn=self._kinetic_fn,
algo=self._algo)
self._potential_fn_gen = potential_fn
self._postprocess_fn = postprocess_fn
elif self._init_fn is None:
self._init_fn, self._sample_fn = hmc(potential_fn=self._potential_fn,
kinetic_fn=self._kinetic_fn,
algo=self._algo)
return init_params
@property
def model(self):
return self._model
@property
def sample_field(self):
return 'z'
@property
def default_fields(self):
return ('z', 'diverging')
[docs] def get_diagnostics_str(self, state):
return '{} steps of size {:.2e}. acc. prob={:.2f}'.format(state.num_steps,
state.adapt_state.step_size,
state.mean_accept_prob)
[docs] def init(self, rng_key, num_warmup, init_params=None, model_args=(), model_kwargs={}):
# non-vectorized
if rng_key.ndim == 1:
rng_key, rng_key_init_model = random.split(rng_key)
# vectorized
else:
rng_key, rng_key_init_model = jnp.swapaxes(vmap(random.split)(rng_key), 0, 1)
init_params = self._init_state(rng_key_init_model, model_args, model_kwargs, init_params)
if self._potential_fn and init_params is None:
raise ValueError('Valid value of `init_params` must be provided with'
' `potential_fn`.')
hmc_init_fn = lambda init_params, rng_key: self._init_fn( # noqa: E731
init_params,
num_warmup=num_warmup,
step_size=self._step_size,
adapt_step_size=self._adapt_step_size,
adapt_mass_matrix=self._adapt_mass_matrix,
dense_mass=self._dense_mass,
target_accept_prob=self._target_accept_prob,
trajectory_length=self._trajectory_length,
max_tree_depth=self._max_tree_depth,
find_heuristic_step_size=self._find_heuristic_step_size,
forward_mode_differentiation=self._forward_mode_differentiation,
model_args=model_args,
model_kwargs=model_kwargs,
rng_key=rng_key,
)
if rng_key.ndim == 1:
init_state = hmc_init_fn(init_params, rng_key)
else:
# XXX it is safe to run hmc_init_fn under vmap despite that hmc_init_fn changes some
# nonlocal variables: momentum_generator, wa_update, trajectory_len, max_treedepth,
# wa_steps because those variables do not depend on traced args: init_params, rng_key.
init_state = vmap(hmc_init_fn)(init_params, rng_key)
sample_fn = vmap(self._sample_fn, in_axes=(0, None, None))
self._sample_fn = sample_fn
return init_state
[docs] def postprocess_fn(self, args, kwargs):
if self._postprocess_fn is None:
return identity
return self._postprocess_fn(*args, **kwargs)
[docs] def sample(self, state, model_args, model_kwargs):
"""
Run HMC from the given :data:`~numpyro.infer.hmc.HMCState` and return the resulting
:data:`~numpyro.infer.hmc.HMCState`.
:param HMCState state: Represents the current state.
:param model_args: Arguments provided to the model.
:param model_kwargs: Keyword arguments provided to the model.
:return: Next `state` after running HMC.
"""
return self._sample_fn(state, model_args, model_kwargs)
[docs]class NUTS(HMC):
"""
Hamiltonian Monte Carlo inference, using the No U-Turn Sampler (NUTS)
with adaptive path length and mass matrix adaptation.
**References:**
1. *MCMC Using Hamiltonian Dynamics*,
Radford M. Neal
2. *The No-U-turn sampler: adaptively setting path lengths in Hamiltonian Monte Carlo*,
Matthew D. Hoffman, and Andrew Gelman.
3. *A Conceptual Introduction to Hamiltonian Monte Carlo`*,
Michael Betancourt
:param model: Python callable containing Pyro :mod:`~numpyro.primitives`.
If model is provided, `potential_fn` will be inferred using the model.
:param potential_fn: Python callable that computes the potential energy
given input parameters. The input parameters to `potential_fn` can be
any python collection type, provided that `init_params` argument to
`init_kernel` has the same type.
:param kinetic_fn: Python callable that returns the kinetic energy given
inverse mass matrix and momentum. If not provided, the default is
euclidean kinetic energy.
:param float step_size: Determines the size of a single step taken by the
verlet integrator while computing the trajectory using Hamiltonian
dynamics. If not specified, it will be set to 1.
:param bool adapt_step_size: A flag to decide if we want to adapt step_size
during warm-up phase using Dual Averaging scheme.
:param bool adapt_mass_matrix: A flag to decide if we want to adapt mass
matrix during warm-up phase using Welford scheme.
:param bool dense_mass: A flag to decide if mass matrix is dense or
diagonal (default when ``dense_mass=False``)
:param float target_accept_prob: Target acceptance probability for step size
adaptation using Dual Averaging. Increasing this value will lead to a smaller
step size, hence the sampling will be slower but more robust. Default to 0.8.
:param float trajectory_length: Length of a MCMC trajectory for HMC. This arg has
no effect in NUTS sampler.
:param int max_tree_depth: Max depth of the binary tree created during the doubling
scheme of NUTS sampler. Defaults to 10.
:param callable init_strategy: a per-site initialization function.
See :ref:`init_strategy` section for available functions.
:param bool find_heuristic_step_size: whether to a heuristic function to adjust the
step size at the beginning of each adaptation window. Defaults to False.
:param bool forward_mode_differentiation: whether to use forward-mode differentiation
or reverse-mode differentiation. By default, we use reverse mode but the forward
mode can be useful in some cases to improve the performance. In addition, some
control flow utility on JAX such as `jax.lax.while_loop` or `jax.lax.fori_loop`
only supports forward-mode differentiation. See
`JAX's The Autodiff Cookbook <https://jax.readthedocs.io/en/latest/notebooks/autodiff_cookbook.html>`_
for more information.
"""
def __init__(self,
model=None,
potential_fn=None,
kinetic_fn=None,
step_size=1.0,
adapt_step_size=True,
adapt_mass_matrix=True,
dense_mass=False,
target_accept_prob=0.8,
trajectory_length=None,
max_tree_depth=10,
init_strategy=init_to_uniform,
find_heuristic_step_size=False,
forward_mode_differentiation=False):
super(NUTS, self).__init__(potential_fn=potential_fn, model=model, kinetic_fn=kinetic_fn,
step_size=step_size, adapt_step_size=adapt_step_size,
adapt_mass_matrix=adapt_mass_matrix, dense_mass=dense_mass,
target_accept_prob=target_accept_prob,
trajectory_length=trajectory_length,
init_strategy=init_strategy,
find_heuristic_step_size=find_heuristic_step_size,
forward_mode_differentiation=forward_mode_differentiation)
self._max_tree_depth = max_tree_depth
self._algo = 'NUTS'