# Copyright Contributors to the Pyro project.
# SPDX-License-Identifier: Apache-2.0
from abc import ABC, abstractmethod
from functools import partial
from operator import attrgetter
import os
import warnings
import numpy as np
from jax import jit, lax, local_device_count, pmap, random, vmap
import jax.numpy as jnp
from jax.tree_util import tree_flatten, tree_map
from numpyro.diagnostics import print_summary
from numpyro.util import (
cached_by,
find_stack_level,
fori_collect,
identity,
is_prng_key,
)
__all__ = [
"MCMCKernel",
"MCMC",
]
[docs]class MCMCKernel(ABC):
"""
Defines the interface for the Markov transition kernel that is
used for :class:`~numpyro.infer.mcmc.MCMC` inference.
**Example:**
.. doctest::
>>> from collections import namedtuple
>>> from jax import random
>>> import jax.numpy as jnp
>>> import numpyro
>>> import numpyro.distributions as dist
>>> from numpyro.infer import MCMC
>>> MHState = namedtuple("MHState", ["u", "rng_key"])
>>> class MetropolisHastings(numpyro.infer.mcmc.MCMCKernel):
... sample_field = "u"
...
... def __init__(self, potential_fn, step_size=0.1):
... self.potential_fn = potential_fn
... self.step_size = step_size
...
... def init(self, rng_key, num_warmup, init_params, model_args, model_kwargs):
... return MHState(init_params, rng_key)
...
... def sample(self, state, model_args, model_kwargs):
... u, rng_key = state
... rng_key, key_proposal, key_accept = random.split(rng_key, 3)
... u_proposal = dist.Normal(u, self.step_size).sample(key_proposal)
... accept_prob = jnp.exp(self.potential_fn(u) - self.potential_fn(u_proposal))
... u_new = jnp.where(dist.Uniform().sample(key_accept) < accept_prob, u_proposal, u)
... return MHState(u_new, rng_key)
>>> def f(x):
... return ((x - 2) ** 2).sum()
>>> kernel = MetropolisHastings(f)
>>> mcmc = MCMC(kernel, num_warmup=1000, num_samples=1000)
>>> mcmc.run(random.PRNGKey(0), init_params=jnp.array([1., 2.]))
>>> posterior_samples = mcmc.get_samples()
>>> mcmc.print_summary() # doctest: +SKIP
"""
[docs] def postprocess_fn(self, model_args, model_kwargs):
"""
Get a function that transforms unconstrained values at sample sites to values
constrained to the site's support, in addition to returning deterministic
sites in the model.
:param model_args: Arguments to the model.
:param model_kwargs: Keyword arguments to the model.
"""
return identity
[docs] @abstractmethod
def init(self, rng_key, num_warmup, init_params, model_args, model_kwargs):
"""
Initialize the `MCMCKernel` and return an initial state to begin sampling
from.
:param random.PRNGKey rng_key: Random number generator key to initialize
the kernel.
:param int num_warmup: Number of warmup steps. This can be useful
when doing adaptation during warmup.
:param tuple init_params: Initial parameters to begin sampling. The type must
be consistent with the input type to `potential_fn`.
:param model_args: Arguments provided to the model.
:param model_kwargs: Keyword arguments provided to the model.
:return: The initial state representing the state of the kernel. This can be
any class that is registered as a
`pytree <https://jax.readthedocs.io/en/latest/pytrees.html>`_.
"""
raise NotImplementedError
[docs] @abstractmethod
def sample(self, state, model_args, model_kwargs):
"""
Given the current `state`, return the next `state` using the given
transition kernel.
:param state: A `pytree <https://jax.readthedocs.io/en/latest/pytrees.html>`_
class representing the state for the kernel. For HMC, this is given
by :data:`~numpyro.infer.hmc.HMCState`. In general, this could be any
class that supports `getattr`.
:param model_args: Arguments provided to the model.
:param model_kwargs: Keyword arguments provided to the model.
:return: Next `state`.
"""
raise NotImplementedError
@property
def sample_field(self):
"""
The attribute of the `state` object passed to :meth:`sample` that denotes
the MCMC sample. This is used by :meth:`postprocess_fn` and for reporting
results in :meth:`MCMC.print_summary()
<numpyro.infer.mcmc.MCMC.print_summary>`.
"""
raise NotImplementedError
@property
def default_fields(self):
"""
The attributes of the `state` object to be collected by default during
the MCMC run (when :meth:`MCMC.run() <numpyro.infer.MCMC.run>` is called).
"""
return (self.sample_field,)
[docs] def get_diagnostics_str(self, state):
"""
Given the current `state`, returns the diagnostics string to
be added to progress bar for diagnostics purpose.
"""
return ""
def _get_progbar_desc_str(num_warmup, phase, i):
if phase is not None:
return phase
return "warmup" if i < num_warmup else "sample"
def _get_value_from_index(xs, i):
return tree_map(lambda x: x[i], xs)
def _laxmap(f, xs):
n = tree_flatten(xs)[0][0].shape[0]
ys = []
for i in range(n):
x = jit(_get_value_from_index)(xs, i)
ys.append(f(x))
return tree_map(lambda *args: jnp.stack(args), *ys)
def _sample_fn_jit_args(state, sampler):
hmc_state, args, kwargs = state
return sampler.sample(hmc_state, args, kwargs), args, kwargs
def _sample_fn_nojit_args(state, sampler, args, kwargs):
# state is a tuple of size 1 - containing HMCState
return (sampler.sample(state[0], args, kwargs),)
def _collect_fn(collect_fields):
@cached_by(_collect_fn, collect_fields)
def collect(x):
if collect_fields:
return attrgetter(*collect_fields)(x[0])
else:
return x[0]
return collect
# XXX: Is there a better hash key that we can use?
def _hashable(x):
# NOTE: When the arguments are JITed, ShapedArray is hashable.
if isinstance(x, (np.ndarray, jnp.ndarray)):
return id(x)
return x
[docs]class MCMC(object):
"""
Provides access to Markov Chain Monte Carlo inference algorithms in NumPyro.
.. note:: `chain_method` is an experimental arg, which might be removed in a future version.
.. note:: Setting `progress_bar=False` will improve the speed for many cases. But it might
require more memory than the other option.
.. note:: If setting `num_chains` greater than `1` in a Jupyter Notebook, then you will need to
have installed `ipywidgets <https://ipywidgets.readthedocs.io/en/latest/user_install.html>`_
in the environment from which you launced Jupyter in order for the progress bars to render
correctly. If you are using Jupyter Notebook or Jupyter Lab, please also install the
corresponding extension package like `widgetsnbextension` or `jupyterlab_widgets`.
.. note:: If your dataset is large and you have access to multiple acceleration devices,
you can distribute the computation across multiple devices. Make sure that your jax version
is v0.4.4 or newer. For example,
.. code-block:: python
import jax
from jax.experimental import mesh_utils
from jax.sharding import PositionalSharding
import numpy as np
import numpyro
import numpyro.distributions as dist
from numpyro.infer import MCMC, NUTS
X = np.random.randn(128, 3)
y = np.random.randn(128)
def model(X, y):
beta = numpyro.sample("beta", dist.Normal(0, 1).expand([3]))
numpyro.sample("obs", dist.Normal(X @ beta, 1), obs=y)
mcmc = MCMC(NUTS(model), num_warmup=10, num_samples=10)
# See https://jax.readthedocs.io/en/latest/notebooks/Distributed_arrays_and_automatic_parallelization.html
sharding = PositionalSharding(mesh_utils.create_device_mesh((8,)))
X_shard = jax.device_put(X, sharding.reshape(8, 1))
y_shard = jax.device_put(y, sharding.reshape(8))
mcmc.run(jax.random.PRNGKey(0), X_shard, y_shard)
:param MCMCKernel sampler: an instance of :class:`~numpyro.infer.mcmc.MCMCKernel` that
determines the sampler for running MCMC. Currently, only :class:`~numpyro.infer.hmc.HMC`
and :class:`~numpyro.infer.hmc.NUTS` are available.
:param int num_warmup: Number of warmup steps.
:param int num_samples: Number of samples to generate from the Markov chain.
:param int thinning: Positive integer that controls the fraction of post-warmup samples that are
retained. For example if thinning is 2 then every other sample is retained.
Defaults to 1, i.e. no thinning.
:param int num_chains: Number of MCMC chains to run. By default, chains will be
run in parallel using :func:`jax.pmap`. If there are not enough devices
available, chains will be run in sequence.
:param postprocess_fn: Post-processing callable - used to convert a collection of unconstrained
sample values returned from the sampler to constrained values that lie within the support
of the sample sites. Additionally, this is used to return values at deterministic sites in
the model.
:param str chain_method: One of 'parallel' (default), 'sequential', 'vectorized'. The method
'parallel' is used to execute the drawing process in parallel on XLA devices (CPUs/GPUs/TPUs),
If there are not enough devices for 'parallel', we fall back to 'sequential' method to draw
chains sequentially. 'vectorized' method is an experimental feature which vectorizes the
drawing method, hence allowing us to collect samples in parallel on a single device.
:param bool progress_bar: Whether to enable progress bar updates. Defaults to
``True``.
:param bool jit_model_args: If set to `True`, this will compile the potential energy
computation as a function of model arguments. As such, calling `MCMC.run` again
on a same sized but different dataset will not result in additional compilation cost.
Note that currently, this does not take effect for the case ``num_chains > 1``
and ``chain_method == 'parallel'``.
.. note:: It is possible to mix parallel and vectorized sampling, i.e., run vectorized chains
on multiple devices using explicit `pmap`. Currently, doing so requires disabling the
progress bar. For example,
.. code-block:: python
def do_mcmc(rng_key, n_vectorized=8):
nuts_kernel = NUTS(model)
mcmc = MCMC(
nuts_kernel,
progress_bar=False,
num_chains=n_vectorized,
chain_method='vectorized'
)
mcmc.run(
rng_key,
extra_fields=("potential_energy",),
)
return {**mcmc.get_samples(), **mcmc.get_extra_fields()}
# Number of devices to pmap over
n_parallel = jax.local_device_count()
rng_keys = jax.random.split(PRNGKey(rng_seed), n_parallel)
traces = pmap(do_mcmc)(rng_keys)
# concatenate traces along pmap'ed axis
trace = {k: np.concatenate(v) for k, v in traces.items()}
"""
def __init__(
self,
sampler,
*,
num_warmup,
num_samples,
num_chains=1,
thinning=1,
postprocess_fn=None,
chain_method="parallel",
progress_bar=True,
jit_model_args=False,
):
self.sampler = sampler
self._sample_field = sampler.sample_field
self._default_fields = sampler.default_fields
self.num_warmup = num_warmup
self.num_samples = num_samples
self.num_chains = num_chains
if not isinstance(thinning, int) or thinning < 1:
raise ValueError("thinning must be a positive integer")
self.thinning = thinning
self.postprocess_fn = postprocess_fn
if chain_method not in ["parallel", "vectorized", "sequential"]:
raise ValueError(
"Only supporting the following methods to draw chains:"
' "sequential", "parallel", or "vectorized"'
)
if chain_method == "parallel" and local_device_count() < self.num_chains:
chain_method = "sequential"
warnings.warn(
"There are not enough devices to run parallel chains: expected {} but got {}."
" Chains will be drawn sequentially. If you are running MCMC in CPU,"
" consider using `numpyro.set_host_device_count({})` at the beginning"
" of your program. You can double-check how many devices are available in"
" your system using `jax.local_device_count()`.".format(
self.num_chains, local_device_count(), self.num_chains
),
stacklevel=find_stack_level(),
)
self.chain_method = chain_method
self.progress_bar = progress_bar
if "CI" in os.environ or "PYTEST_XDIST_WORKER" in os.environ:
self.progress_bar = False
self._jit_model_args = jit_model_args
self._states = None
self._states_flat = None
# HMCState returned by last run
self._last_state = None
# HMCState returned by last warmup
self._warmup_state = None
# HMCState returned by hmc.init_kernel
self._init_state_cache = {}
self._cache = {}
self._collection_params = {}
self._set_collection_params()
def _get_cached_fns(self):
if self._jit_model_args:
args, kwargs = (None,), (None,)
else:
args = tree_map(lambda x: _hashable(x), self._args)
kwargs = tree_map(
lambda x: _hashable(x), tuple(sorted(self._kwargs.items()))
)
key = args + kwargs
try:
fns = self._cache.get(key, None)
# If unhashable arguments are provided, proceed normally
# without caching
except TypeError:
fns, key = None, None
if fns is None:
def laxmap_postprocess_fn(states, args, kwargs):
if self.postprocess_fn is None:
body_fn = self.sampler.postprocess_fn(args, kwargs)
else:
body_fn = self.postprocess_fn
if self.chain_method == "vectorized" and self.num_chains > 1:
body_fn = vmap(body_fn)
return lax.map(body_fn, states)
if self._jit_model_args:
sample_fn = partial(_sample_fn_jit_args, sampler=self.sampler)
postprocess_fn = jit(laxmap_postprocess_fn)
else:
sample_fn = partial(
_sample_fn_nojit_args,
sampler=self.sampler,
args=self._args,
kwargs=self._kwargs,
)
postprocess_fn = jit(
partial(laxmap_postprocess_fn, args=self._args, kwargs=self._kwargs)
)
fns = sample_fn, postprocess_fn
if key is not None:
self._cache[key] = fns
return fns
def _get_cached_init_state(self, rng_key, args, kwargs):
rng_key = (_hashable(rng_key),)
args = tree_map(lambda x: _hashable(x), args)
kwargs = tree_map(lambda x: _hashable(x), tuple(sorted(kwargs.items())))
key = rng_key + args + kwargs
try:
return self._init_state_cache.get(key, None)
# If unhashable arguments are provided, return None
except TypeError:
return None
def _single_chain_mcmc(self, init, args, kwargs, collect_fields):
rng_key, init_state, init_params = init
# Check if _sample_fn is None, then we need to initialize the sampler.
if init_state is None or (getattr(self.sampler, "_sample_fn", None) is None):
new_init_state = self.sampler.init(
rng_key,
self.num_warmup,
init_params,
model_args=args,
model_kwargs=kwargs,
)
init_state = new_init_state if init_state is None else init_state
sample_fn, postprocess_fn = self._get_cached_fns()
diagnostics = (
lambda x: self.sampler.get_diagnostics_str(x[0])
if is_prng_key(rng_key)
else ""
) # noqa: E731
init_val = (init_state, args, kwargs) if self._jit_model_args else (init_state,)
lower_idx = self._collection_params["lower"]
upper_idx = self._collection_params["upper"]
phase = self._collection_params["phase"]
collection_size = self._collection_params["collection_size"]
collection_size = (
collection_size
if collection_size is None
else collection_size // self.thinning
)
collect_vals = fori_collect(
lower_idx,
upper_idx,
sample_fn,
init_val,
transform=_collect_fn(collect_fields),
progbar=self.progress_bar,
return_last_val=True,
thinning=self.thinning,
collection_size=collection_size,
progbar_desc=partial(_get_progbar_desc_str, lower_idx, phase),
diagnostics_fn=diagnostics,
num_chains=self.num_chains if self.chain_method == "parallel" else 1,
)
states, last_val = collect_vals
# Get first argument of type `HMCState`
last_state = last_val[0]
if len(collect_fields) == 1:
states = (states,)
states = dict(zip(collect_fields, states))
# Apply constraints if number of samples is non-zero
site_values = tree_flatten(states[self._sample_field])[0]
# XXX: lax.map still works if some arrays have 0 size
# so we only need to filter out the case site_value.shape[0] == 0
# (which happens when lower_idx==upper_idx)
if len(site_values) > 0 and jnp.shape(site_values[0])[0] > 0:
if self._jit_model_args:
states[self._sample_field] = postprocess_fn(
states[self._sample_field], args, kwargs
)
else:
states[self._sample_field] = postprocess_fn(states[self._sample_field])
return states, last_state
def _set_collection_params(
self, lower=None, upper=None, collection_size=None, phase=None
):
self._collection_params["lower"] = self.num_warmup if lower is None else lower
self._collection_params["upper"] = (
self.num_warmup + self.num_samples if upper is None else upper
)
self._collection_params["collection_size"] = collection_size
self._collection_params["phase"] = phase
def _compile(self, rng_key, *args, extra_fields=(), init_params=None, **kwargs):
self._set_collection_params(0, 0, self.num_samples)
self.run(
rng_key, *args, extra_fields=extra_fields, init_params=init_params, **kwargs
)
rng_key = (_hashable(rng_key),)
args = tree_map(lambda x: _hashable(x), args)
kwargs = tree_map(lambda x: _hashable(x), tuple(sorted(kwargs.items())))
key = rng_key + args + kwargs
try:
self._init_state_cache[key] = self._last_state
# If unhashable arguments are provided, return None
except TypeError:
pass
@property
def post_warmup_state(self):
"""
The state before the sampling phase. If this attribute is not None,
:meth:`run` will skip the warmup phase and start with the state
specified in this attribute.
.. note:: This attribute can be used to sequentially draw MCMC samples. For example,
.. code-block:: python
mcmc = MCMC(NUTS(model), num_warmup=100, num_samples=100)
mcmc.run(random.PRNGKey(0))
first_100_samples = mcmc.get_samples()
mcmc.post_warmup_state = mcmc.last_state
mcmc.run(mcmc.post_warmup_state.rng_key) # or mcmc.run(random.PRNGKey(1))
second_100_samples = mcmc.get_samples()
"""
return self._warmup_state
@post_warmup_state.setter
def post_warmup_state(self, state):
self._warmup_state = state
@property
def last_state(self):
"""
The final MCMC state at the end of the sampling phase.
"""
return self._last_state
[docs] def warmup(
self,
rng_key,
*args,
extra_fields=(),
collect_warmup=False,
init_params=None,
**kwargs,
):
"""
Run the MCMC warmup adaptation phase. After this call, `self.warmup_state` will be set
and the :meth:`run` method will skip the warmup adaptation phase. To run `warmup` again
for the new data, it is required to run :meth:`warmup` again.
:param random.PRNGKey rng_key: Random number generator key to be used for the sampling.
:param args: Arguments to be provided to the :meth:`numpyro.infer.mcmc.MCMCKernel.init` method.
These are typically the arguments needed by the `model`.
:param extra_fields: Extra fields (aside from :meth:`~numpyro.infer.mcmc.MCMCKernel.default_fields`)
from the state object (e.g. :data:`numpyro.infer.hmc.HMCState` for HMC) to collect during
the MCMC run.
:type extra_fields: tuple or list
:param bool collect_warmup: Whether to collect samples from the warmup phase. Defaults
to `False`.
:param init_params: Initial parameters to begin sampling. The type must be consistent
with the input type to `potential_fn` provided to the kernel. If the kernel is
instantiated by a numpyro model, the initial parameters here correspond to latent
values in unconstrained space.
:param kwargs: Keyword arguments to be provided to the :meth:`numpyro.infer.mcmc.MCMCKernel.init`
method. These are typically the keyword arguments needed by the `model`.
"""
self._warmup_state = None
if collect_warmup:
self._set_collection_params(0, self.num_warmup, self.num_warmup, "warmup")
else:
self._set_collection_params(
self.num_warmup, self.num_warmup, self.num_samples, "warmup"
)
self.run(
rng_key, *args, extra_fields=extra_fields, init_params=init_params, **kwargs
)
self._warmup_state = self._last_state
[docs] def run(self, rng_key, *args, extra_fields=(), init_params=None, **kwargs):
"""
Run the MCMC samplers and collect samples.
:param random.PRNGKey rng_key: Random number generator key to be used for the sampling.
For multi-chains, a batch of `num_chains` keys can be supplied. If `rng_key`
does not have batch_size, it will be split in to a batch of `num_chains` keys.
:param args: Arguments to be provided to the :meth:`numpyro.infer.mcmc.MCMCKernel.init` method.
These are typically the arguments needed by the `model`.
:param extra_fields: Extra fields (aside from `"z"`, `"diverging"`) from the
state object (e.g. :data:`numpyro.infer.hmc.HMCState` for HMC) to be collected
during the MCMC run. Note that subfields can be accessed using dots, e.g.
`"adapt_state.step_size"` can be used to collect step sizes at each step.
:type extra_fields: tuple or list of str
:param init_params: Initial parameters to begin sampling. The type must be consistent
with the input type to `potential_fn` provided to the kernel. If the kernel is
instantiated by a numpyro model, the initial parameters here correspond to latent
values in unconstrained space.
:param kwargs: Keyword arguments to be provided to the :meth:`numpyro.infer.mcmc.MCMCKernel.init`
method. These are typically the keyword arguments needed by the `model`.
.. note:: jax allows python code to continue even when the compiled code has not finished yet.
This can cause troubles when trying to profile the code for speed.
See https://jax.readthedocs.io/en/latest/async_dispatch.html and
https://jax.readthedocs.io/en/latest/profiling.html for pointers on profiling jax programs.
"""
init_params = tree_map(
lambda x: lax.convert_element_type(x, jnp.result_type(x)), init_params
)
self._args = args
self._kwargs = kwargs
init_state = self._get_cached_init_state(rng_key, args, kwargs)
if self.num_chains > 1 and is_prng_key(rng_key):
rng_key = random.split(rng_key, self.num_chains)
if self._warmup_state is not None:
self._set_collection_params(0, self.num_samples, self.num_samples, "sample")
init_state = self._warmup_state._replace(rng_key=rng_key)
if init_params is not None and self.num_chains > 1:
prototype_init_val = tree_flatten(init_params)[0][0]
if jnp.shape(prototype_init_val)[0] != self.num_chains:
raise ValueError(
"`init_params` must have the same leading dimension"
" as `num_chains`."
)
assert isinstance(extra_fields, (tuple, list))
collect_fields = tuple(
set(
(self._sample_field,)
+ tuple(self._default_fields)
+ tuple(extra_fields)
)
)
partial_map_fn = partial(
self._single_chain_mcmc,
args=args,
kwargs=kwargs,
collect_fields=collect_fields,
)
map_args = (rng_key, init_state, init_params)
if self.num_chains == 1:
states_flat, last_state = partial_map_fn(map_args)
states = tree_map(lambda x: x[jnp.newaxis, ...], states_flat)
else:
if self.chain_method == "sequential":
states, last_state = _laxmap(partial_map_fn, map_args)
elif self.chain_method == "parallel":
states, last_state = pmap(partial_map_fn)(map_args)
else:
assert self.chain_method == "vectorized"
states, last_state = partial_map_fn(map_args)
# swap num_samples x num_chains to num_chains x num_samples
states = tree_map(lambda x: jnp.swapaxes(x, 0, 1), states)
states_flat = tree_map(
# need to calculate first dimension manually; see issue #1328
lambda x: jnp.reshape(x, (x.shape[0] * x.shape[1],) + x.shape[2:]),
states,
)
self._last_state = last_state
self._states = states
self._states_flat = states_flat
self._set_collection_params()
[docs] def get_samples(self, group_by_chain=False):
"""
Get samples from the MCMC run.
:param bool group_by_chain: Whether to preserve the chain dimension. If True,
all samples will have num_chains as the size of their leading dimension.
:return: Samples having the same data type as `init_params`. The data type is a
`dict` keyed on site names if a model containing Pyro primitives is used,
but can be any :func:`jaxlib.pytree`, more generally (e.g. when defining a
`potential_fn` for HMC that takes `list` args).
**Example:**
You can then pass those samples to :class:`~numpyro.infer.util.Predictive`::
posterior_samples = mcmc.get_samples()
predictive = Predictive(model, posterior_samples=posterior_samples)
samples = predictive(rng_key1, *model_args, **model_kwargs)
"""
return (
self._states[self._sample_field]
if group_by_chain
else self._states_flat[self._sample_field]
)
[docs] def print_summary(self, prob=0.9, exclude_deterministic=True):
"""
Print the statistics of posterior samples collected during running this MCMC instance.
:param float prob: the probability mass of samples within the credible interval.
:param bool exclude_deterministic: whether or not print out the statistics
at deterministic sites.
"""
# Exclude deterministic sites by default
sites = self._states[self._sample_field]
if isinstance(sites, dict) and exclude_deterministic:
state_sample_field = attrgetter(self._sample_field)(self._last_state)
# XXX: there might be the case that state.z is not a dictionary but
# its postprocessed value `sites` is a dictionary.
# TODO: in general, when both `sites` and `state.z` are dictionaries,
# they can have different key names, not necessary due to deterministic
# behavior. We might revise this logic if needed in the future.
if isinstance(state_sample_field, dict):
sites = {
k: v
for k, v in self._states[self._sample_field].items()
if k in state_sample_field
}
print_summary(sites, prob=prob)
extra_fields = self.get_extra_fields()
if "diverging" in extra_fields:
print(
"Number of divergences: {}".format(jnp.sum(extra_fields["diverging"]))
)
def __getstate__(self):
state = self.__dict__.copy()
state["_cache"] = {}
return state