# Copyright (c) 2017-2019 Uber Technologies, Inc.
# SPDX-License-Identifier: Apache-2.0
import math
from collections import OrderedDict
import torch
import pyro
import pyro.distributions as dist
from pyro.distributions.util import eye_like, scalar_like
from pyro.infer.mcmc.adaptation import WarmupAdapter
from pyro.infer.mcmc.mcmc_kernel import MCMCKernel
from pyro.infer.mcmc.util import initialize_model
from pyro.ops.integrator import velocity_verlet
from pyro.util import optional, torch_isnan
[docs]class HMC(MCMCKernel):
r"""
Simple Hamiltonian Monte Carlo kernel, where ``step_size`` and ``num_steps``
need to be explicitly specified by the user.
**References**
[1] `MCMC Using Hamiltonian Dynamics`,
Radford M. Neal
:param model: Python callable containing Pyro primitives.
:param potential_fn: Python callable calculating potential energy with input
is a dict of real support parameters.
: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 float trajectory_length: Length of a MCMC trajectory. If not
specified, it will be set to ``step_size x num_steps``. In case
``num_steps`` is not specified, it will be set to :math:`2\pi`.
:param int num_steps: The number of discrete steps over which to simulate
Hamiltonian dynamics. The state at the end of the trajectory is
returned as the proposal. This value is always equal to
``int(trajectory_length / step_size)``.
: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 full_mass: A flag to decide if mass matrix is dense or diagonal.
:param dict transforms: Optional dictionary that specifies a transform
for a sample site with constrained support to unconstrained space. The
transform should be invertible, and implement `log_abs_det_jacobian`.
If not specified and the model has sites with constrained support,
automatic transformations will be applied, as specified in
:mod:`torch.distributions.constraint_registry`.
:param int max_plate_nesting: Optional bound on max number of nested
:func:`pyro.plate` contexts. This is required if model contains
discrete sample sites that can be enumerated over in parallel.
:param bool jit_compile: Optional parameter denoting whether to use
the PyTorch JIT to trace the log density computation, and use this
optimized executable trace in the integrator.
:param dict jit_options: A dictionary contains optional arguments for
:func:`torch.jit.trace` function.
:param bool ignore_jit_warnings: Flag to ignore warnings from the JIT
tracer when ``jit_compile=True``. Default is False.
:param float target_accept_prob: Increasing this value will lead to a smaller
step size, hence the sampling will be slower and more robust. Default to 0.8.
.. note:: Internally, the mass matrix will be ordered according to the order
of the names of latent variables, not the order of their appearance in
the model.
Example:
>>> true_coefs = torch.tensor([1., 2., 3.])
>>> data = torch.randn(2000, 3)
>>> dim = 3
>>> labels = dist.Bernoulli(logits=(true_coefs * data).sum(-1)).sample()
>>>
>>> def model(data):
... coefs_mean = torch.zeros(dim)
... coefs = pyro.sample('beta', dist.Normal(coefs_mean, torch.ones(3)))
... y = pyro.sample('y', dist.Bernoulli(logits=(coefs * data).sum(-1)), obs=labels)
... return y
>>>
>>> hmc_kernel = HMC(model, step_size=0.0855, num_steps=4)
>>> mcmc = MCMC(hmc_kernel, num_samples=500, warmup_steps=100)
>>> mcmc.run(data)
>>> mcmc.get_samples()['beta'].mean(0) # doctest: +SKIP
tensor([ 0.9819, 1.9258, 2.9737])
"""
def __init__(self,
model=None,
potential_fn=None,
step_size=1,
trajectory_length=None,
num_steps=None,
adapt_step_size=True,
adapt_mass_matrix=True,
full_mass=False,
transforms=None,
max_plate_nesting=None,
jit_compile=False,
jit_options=None,
ignore_jit_warnings=False,
target_accept_prob=0.8):
if not ((model is None) ^ (potential_fn is None)):
raise ValueError("Only one of `model` or `potential_fn` must be specified.")
# NB: deprecating args - model, transforms
self.model = model
self.transforms = transforms
self._max_plate_nesting = max_plate_nesting
self._jit_compile = jit_compile
self._jit_options = jit_options
self._ignore_jit_warnings = ignore_jit_warnings
self.potential_fn = potential_fn
if trajectory_length is not None:
self.trajectory_length = trajectory_length
elif num_steps is not None:
self.trajectory_length = step_size * num_steps
else:
self.trajectory_length = 2 * math.pi # from Stan
# The following parameter is used in find_reasonable_step_size method.
# In NUTS paper, this threshold is set to a fixed log(0.5).
# After https://github.com/stan-dev/stan/pull/356, it is set to a fixed log(0.8).
self._direction_threshold = math.log(0.8) # from Stan
self._max_sliced_energy = 1000
self._reset()
self._adapter = WarmupAdapter(step_size,
adapt_step_size=adapt_step_size,
adapt_mass_matrix=adapt_mass_matrix,
target_accept_prob=target_accept_prob,
is_diag_mass=not full_mass)
super(HMC, self).__init__()
def _kinetic_energy(self, r):
r_flat = torch.cat([r[site_name].reshape(-1) for site_name in sorted(r)])
if self.inverse_mass_matrix.dim() == 2:
return 0.5 * self.inverse_mass_matrix.matmul(r_flat).dot(r_flat)
else:
return 0.5 * self.inverse_mass_matrix.dot(r_flat ** 2)
def _energy(self, z, r):
return self._kinetic_energy(r) + self.potential_fn(z)
def _reset(self):
self._t = 0
self._accept_cnt = 0
self._mean_accept_prob = 0.
self._divergences = []
self._prototype_trace = None
self._initial_params = None
self._z_last = None
self._potential_energy_last = None
self._z_grads_last = None
self._warmup_steps = None
def _find_reasonable_step_size(self, z):
step_size = self.step_size
# We are going to find a step_size which make accept_prob (Metropolis correction)
# near the target_accept_prob. If accept_prob:=exp(-delta_energy) is small,
# then we have to decrease step_size; otherwise, increase step_size.
potential_energy = self.potential_fn(z)
r, _ = self._sample_r(name="r_presample_0")
energy_current = self._kinetic_energy(r) + potential_energy
z_new, r_new, z_grads_new, potential_energy_new = velocity_verlet(
z, r, self.potential_fn, self.inverse_mass_matrix, step_size)
energy_new = self._kinetic_energy(r_new) + potential_energy_new
delta_energy = energy_new - energy_current
# direction=1 means keep increasing step_size, otherwise decreasing step_size.
# Note that the direction is -1 if delta_energy is `NaN` which may be the
# case for a diverging trajectory (e.g. in the case of evaluating log prob
# of a value simulated using a large step size for a constrained sample site).
direction = 1 if self._direction_threshold < -delta_energy else -1
# define scale for step_size: 2 for increasing, 1/2 for decreasing
step_size_scale = 2 ** direction
direction_new = direction
# keep scale step_size until accept_prob crosses its target
# TODO: make thresholds for too small step_size or too large step_size
t = 0
while direction_new == direction:
t += 1
step_size = step_size_scale * step_size
r, _ = self._sample_r(name="r_presample_{}".format(t))
energy_current = self._kinetic_energy(r) + potential_energy
z_new, r_new, z_grads_new, potential_energy_new = velocity_verlet(
z, r, self.potential_fn, self.inverse_mass_matrix, step_size)
energy_new = self._kinetic_energy(r_new) + potential_energy_new
delta_energy = energy_new - energy_current
direction_new = 1 if self._direction_threshold < -delta_energy else -1
return step_size
def _sample_r(self, name):
r_dist = self._adapter.r_dist
r_flat = pyro.sample(name, r_dist)
r = {}
pos = 0
for name, param in sorted(self.initial_params.items()):
next_pos = pos + param.numel()
r[name] = r_flat[pos:next_pos].reshape(param.shape)
pos = next_pos
assert pos == r_flat.size(0)
return r, r_flat
@property
def inverse_mass_matrix(self):
return self._adapter.inverse_mass_matrix
@property
def step_size(self):
return self._adapter.step_size
@property
def num_steps(self):
return max(1, int(self.trajectory_length / self.step_size))
@property
def initial_params(self):
return self._initial_params
@initial_params.setter
def initial_params(self, params):
self._initial_params = params
def _initialize_model_properties(self, model_args, model_kwargs):
init_params, potential_fn, transforms, trace = initialize_model(
self.model,
model_args,
model_kwargs,
transforms=self.transforms,
max_plate_nesting=self._max_plate_nesting,
jit_compile=self._jit_compile,
jit_options=self._jit_options,
skip_jit_warnings=self._ignore_jit_warnings,
)
self.potential_fn = potential_fn
self.transforms = transforms
if self._initial_params is None:
self._initial_params = init_params
self._prototype_trace = trace
def _initialize_adapter(self):
mass_matrix_size = sum([p.numel() for p in self.initial_params.values()])
site_value = list(self.initial_params.values())[0]
if self._adapter.is_diag_mass:
initial_mass_matrix = torch.ones(mass_matrix_size,
dtype=site_value.dtype,
device=site_value.device)
else:
initial_mass_matrix = eye_like(site_value, mass_matrix_size)
self._adapter.configure(self._warmup_steps,
inv_mass_matrix=initial_mass_matrix,
find_reasonable_step_size_fn=self._find_reasonable_step_size)
if self._adapter.adapt_step_size:
self._adapter.reset_step_size_adaptation(self._initial_params)
[docs] def setup(self, warmup_steps, *args, **kwargs):
self._warmup_steps = warmup_steps
if self.model is not None:
self._initialize_model_properties(args, kwargs)
potential_energy = self.potential_fn(self.initial_params)
self._cache(self.initial_params, potential_energy, None)
if self.initial_params:
self._initialize_adapter()
[docs] def cleanup(self):
self._reset()
def _cache(self, z, potential_energy, z_grads=None):
self._z_last = z
self._potential_energy_last = potential_energy
self._z_grads_last = z_grads
[docs] def clear_cache(self):
self._z_last = None
self._potential_energy_last = None
self._z_grads_last = None
def _fetch_from_cache(self):
return self._z_last, self._potential_energy_last, self._z_grads_last
[docs] def sample(self, params):
z, potential_energy, z_grads = self._fetch_from_cache()
# recompute PE when cache is cleared
if z is None:
z = params
potential_energy = self.potential_fn(z)
self._cache(z, potential_energy)
# return early if no sample sites
elif len(z) == 0:
self._t += 1
self._mean_accept_prob = 1.
if self._t > self._warmup_steps:
self._accept_cnt += 1
return params
r, _ = self._sample_r(name="r_t={}".format(self._t))
energy_current = self._kinetic_energy(r) + potential_energy
# Temporarily disable distributions args checking as
# NaNs are expected during step size adaptation
with optional(pyro.validation_enabled(False), self._t < self._warmup_steps):
z_new, r_new, z_grads_new, potential_energy_new = velocity_verlet(z, r, self.potential_fn,
self.inverse_mass_matrix,
self.step_size,
self.num_steps,
z_grads=z_grads)
# apply Metropolis correction.
energy_proposal = self._kinetic_energy(r_new) + potential_energy_new
delta_energy = energy_proposal - energy_current
# handle the NaN case which may be the case for a diverging trajectory
# when using a large step size.
delta_energy = scalar_like(delta_energy, float("inf")) if torch_isnan(delta_energy) else delta_energy
if delta_energy > self._max_sliced_energy and self._t >= self._warmup_steps:
self._divergences.append(self._t - self._warmup_steps)
accept_prob = (-delta_energy).exp().clamp(max=1.)
rand = pyro.sample("rand_t={}".format(self._t), dist.Uniform(scalar_like(accept_prob, 0.),
scalar_like(accept_prob, 1.)))
accepted = False
if rand < accept_prob:
accepted = True
z = z_new
self._cache(z, potential_energy_new, z_grads_new)
self._t += 1
if self._t > self._warmup_steps:
n = self._t - self._warmup_steps
if accepted:
self._accept_cnt += 1
else:
n = self._t
self._adapter.step(self._t, z, accept_prob)
self._mean_accept_prob += (accept_prob.item() - self._mean_accept_prob) / n
return z.copy()
[docs] def logging(self):
return OrderedDict([
("step size", "{:.2e}".format(self.step_size)),
("acc. prob", "{:.3f}".format(self._mean_accept_prob))
])
[docs] def diagnostics(self):
return {"divergences": self._divergences,
"acceptance rate": self._accept_cnt / (self._t - self._warmup_steps)}