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from typing import Dict, List, Optional, TYPE_CHECKING, cast
if TYPE_CHECKING:
from typing import Any, Tuple
from typing import Iterable as TIterable
from collections.abc import Iterable
from collections import defaultdict
from copy import copy
import pickle
import logging
import warnings
import numpy as np
import theano.gradient as tg
from theano.tensor import Tensor
from .backends.base import BaseTrace, MultiTrace
from .backends.ndarray import NDArray
from .distributions.distribution import draw_values
from .model import modelcontext, Point, all_continuous, Model
from .step_methods import (
NUTS,
HamiltonianMC,
Metropolis,
BinaryMetropolis,
BinaryGibbsMetropolis,
CategoricalGibbsMetropolis,
Slice,
CompoundStep,
arraystep,
)
from .util import (
update_start_vals,
get_untransformed_name,
is_transformed_name,
get_default_varnames,
)
from .vartypes import discrete_types
from .exceptions import IncorrectArgumentsError
from .parallel_sampling import _cpu_count
from pymc3.step_methods.hmc import quadpotential
import pymc3 as pm
from tqdm import tqdm
import sys
sys.setrecursionlimit(10000)
__all__ = [
"sample",
"iter_sample",
"sample_posterior_predictive",
"sample_posterior_predictive_w",
"init_nuts",
"sample_prior_predictive",
"sample_ppc",
"sample_ppc_w",
]
STEP_METHODS = (
NUTS,
HamiltonianMC,
Metropolis,
BinaryMetropolis,
BinaryGibbsMetropolis,
Slice,
CategoricalGibbsMetropolis,
)
_log = logging.getLogger("pymc3")
def instantiate_steppers(model, steps, selected_steps, step_kwargs=None):
"""Instantiates steppers assigned to the model variables.
This function is intended to be called automatically from ``sample()``, but
may be called manually.
Parameters
----------
model : Model object
A fully-specified model object
step : step function or vector of step functions
One or more step functions that have been assigned to some subset of
the model's parameters. Defaults to None (no assigned variables).
selected_steps: dictionary of step methods and variables
The step methods and the variables that have were assigned to them.
step_kwargs : dict
Parameters for the samplers. Keys are the lower case names of
the step method, values a dict of arguments.
Returns
-------
methods : list
List of step methods associated with the model's variables.
"""
if step_kwargs is None:
step_kwargs = {}
used_keys = set()
for step_class, vars in selected_steps.items():
if len(vars) == 0:
continue
args = step_kwargs.get(step_class.name, {})
used_keys.add(step_class.name)
step = step_class(vars=vars, **args)
steps.append(step)
unused_args = set(step_kwargs).difference(used_keys)
if unused_args:
raise ValueError("Unused step method arguments: %s" % unused_args)
if len(steps) == 1:
steps = steps[0]
return steps
def assign_step_methods(model, step=None, methods=STEP_METHODS, step_kwargs=None):
"""Assign model variables to appropriate step methods.
Passing a specified model will auto-assign its constituent stochastic
variables to step methods based on the characteristics of the variables.
This function is intended to be called automatically from ``sample()``, but
may be called manually. Each step method passed should have a
``competence()`` method that returns an ordinal competence value
corresponding to the variable passed to it. This value quantifies the
appropriateness of the step method for sampling the variable.
Parameters
----------
model : Model object
A fully-specified model object
step : step function or vector of step functions
One or more step functions that have been assigned to some subset of
the model's parameters. Defaults to ``None`` (no assigned variables).
methods : vector of step method classes
The set of step methods from which the function may choose. Defaults
to the main step methods provided by PyMC3.
step_kwargs : dict
Parameters for the samplers. Keys are the lower case names of
the step method, values a dict of arguments.
Returns
-------
methods : list
List of step methods associated with the model's variables.
"""
steps = []
assigned_vars = set()
if step is not None:
try:
steps += list(step)
except TypeError:
steps.append(step)
for step in steps:
try:
assigned_vars = assigned_vars.union(set(step.vars))
except AttributeError:
for method in step.methods:
assigned_vars = assigned_vars.union(set(method.vars))
# Use competence classmethods to select step methods for remaining
# variables
selected_steps = defaultdict(list)
for var in model.free_RVs:
if var not in assigned_vars:
# determine if a gradient can be computed
has_gradient = var.dtype not in discrete_types
if has_gradient:
try:
tg.grad(model.logpt, var)
except (AttributeError, NotImplementedError, tg.NullTypeGradError):
has_gradient = False
# select the best method
selected = max(
methods,
key=lambda method, var=var, has_gradient=has_gradient: method._competence(
var, has_gradient
),
)
selected_steps[selected].append(var)
return instantiate_steppers(model, steps, selected_steps, step_kwargs)
def _print_step_hierarchy(s, level=0):
if isinstance(s, (list, tuple)):
_log.info(">" * level + "list")
for i in s:
_print_step_hierarchy(i, level + 1)
elif isinstance(s, CompoundStep):
_log.info(">" * level + "CompoundStep")
for i in s.methods:
_print_step_hierarchy(i, level + 1)
else:
varnames = ", ".join(
[
get_untransformed_name(v.name) if is_transformed_name(v.name) else v.name
for v in s.vars
]
)
_log.info(">" * level + "{}: [{}]".format(s.__class__.__name__, varnames))
def sample(
draws=500,
step=None,
init="auto",
n_init=200000,
start=None,
trace=None,
chain_idx=0,
chains=None,
cores=None,
tune=500,
progressbar=True,
model=None,
random_seed=None,
discard_tuned_samples=True,
compute_convergence_checks=True,
**kwargs
):
"""Draw samples from the posterior using the given step methods.
Multiple step methods are supported via compound step methods.
Parameters
----------
draws : int
The number of samples to draw. Defaults to 500. The number of tuned samples are discarded
by default. See ``discard_tuned_samples``.
init : str
Initialization method to use for auto-assigned NUTS samplers.
* auto : Choose a default initialization method automatically.
Currently, this is ``'jitter+adapt_diag'``, but this can change in the future.
If you depend on the exact behaviour, choose an initialization method explicitly.
* adapt_diag : Start with a identity mass matrix and then adapt a diagonal based on the
variance of the tuning samples. All chains use the test value (usually the prior mean)
as starting point.
* jitter+adapt_diag : Same as ``adapt_diag``\, but add uniform jitter in [-1, 1] to the
starting point in each chain.
* advi+adapt_diag : Run ADVI and then adapt the resulting diagonal mass matrix based on the
sample variance of the tuning samples.
* advi+adapt_diag_grad : Run ADVI and then adapt the resulting diagonal mass matrix based
on the variance of the gradients during tuning. This is **experimental** and might be
removed in a future release.
* advi : Run ADVI to estimate posterior mean and diagonal mass matrix.
* advi_map: Initialize ADVI with MAP and use MAP as starting point.
* map : Use the MAP as starting point. This is discouraged.
* nuts : Run NUTS and estimate posterior mean and mass matrix from the trace.
step : function or iterable of functions
A step function or collection of functions. If there are variables without step methods,
step methods for those variables will be assigned automatically. By default the NUTS step
method will be used, if appropriate to the model; this is a good default for beginning
users.
n_init : int
Number of iterations of initializer. Only works for 'nuts' and 'ADVI'.
If 'ADVI', number of iterations, if 'nuts', number of draws.
start : dict, or array of dict
Starting point in parameter space (or partial point)
Defaults to ``trace.point(-1))`` if there is a trace provided and model.test_point if not
(defaults to empty dict). Initialization methods for NUTS (see ``init`` keyword) can
overwrite the default.
trace : backend, list, or MultiTrace
This should be a backend instance, a list of variables to track, or a MultiTrace object
with past values. If a MultiTrace object is given, it must contain samples for the chain
number ``chain``. If None or a list of variables, the NDArray backend is used.
Passing either "text" or "sqlite" is taken as a shortcut to set up the corresponding
backend (with "mcmc" used as the base name).
chain_idx : int
Chain number used to store sample in backend. If ``chains`` is greater than one, chain
numbers will start here.
chains : int
The number of chains to sample. Running independent chains is important for some
convergence statistics and can also reveal multiple modes in the posterior. If ``None``,
then set to either ``cores`` or 2, whichever is larger.
cores : int
The number of chains to run in parallel. If ``None``, set to the number of CPUs in the
system, but at most 4.
tune : int
Number of iterations to tune, defaults to 500. Samplers adjust the step sizes, scalings or
similar during tuning. Tuning samples will be drawn in addition to the number specified in
the ``draws`` argument, and will be discarded unless ``discard_tuned_samples`` is set to
False.
progressbar : bool
Whether or not to display a progress bar in the command line. The bar shows the percentage
of completion, the sampling speed in samples per second (SPS), and the estimated remaining
time until completion ("expected time of arrival"; ETA).
model : Model (optional if in ``with`` context)
random_seed : int or list of ints
A list is accepted if ``cores`` is greater than one.
discard_tuned_samples : bool
Whether to discard posterior samples of the tune interval.
compute_convergence_checks : bool, default=True
Whether to compute sampler statistics like Gelman-Rubin and ``effective_n``.
Returns
-------
trace : pymc3.backends.base.MultiTrace
A ``MultiTrace`` object that contains the samples.
Notes
-----
Optional keyword arguments can be passed to ``sample`` to be delivered to the
``step_method``s used during sampling. In particular, the NUTS step method accepts
a number of arguments. Common options are:
* target_accept: float in [0, 1]. The step size is tuned such that we approximate this
acceptance rate. Higher values like 0.9 or 0.95 often work better for problematic
posteriors.
* max_treedepth: The maximum depth of the trajectory tree.
* step_scale: float, default 0.25
The initial guess for the step size scaled down by :math:`1/n**(1/4)`
You can find a full list of arguments in the docstring of the step methods.
Examples
--------
.. code:: ipython
>>> import pymc3 as pm
... n = 100
... h = 61
... alpha = 2
... beta = 2
.. code:: ipython
>>> with pm.Model() as model: # context management
... p = pm.Beta('p', alpha=alpha, beta=beta)
... y = pm.Binomial('y', n=n, p=p, observed=h)
... trace = pm.sample(2000, tune=1000, cores=4)
>>> pm.summary(trace)
mean sd mc_error hpd_2.5 hpd_97.5
p 0.604625 0.047086 0.00078 0.510498 0.694774
"""
model = modelcontext(model)
nuts_kwargs = kwargs.pop("nuts_kwargs", None)
if nuts_kwargs is not None:
warnings.warn(
"The nuts_kwargs argument has been deprecated. Pass step "
"method arguments directly to sample instead",
DeprecationWarning,
)
kwargs.update(nuts_kwargs)
step_kwargs = kwargs.pop("step_kwargs", None)
if step_kwargs is not None:
warnings.warn(
"The step_kwargs argument has been deprecated. Pass step "
"method arguments directly to sample instead",
DeprecationWarning,
)
kwargs.update(step_kwargs)
if cores is None:
cores = min(4, _cpu_count())
if "njobs" in kwargs:
cores = kwargs["njobs"]
warnings.warn(
"The njobs argument has been deprecated. Use cores instead.", DeprecationWarning
)
if "nchains" in kwargs:
chains = kwargs["nchains"]
warnings.warn(
"The nchains argument has been deprecated. Use chains instead.", DeprecationWarning
)
if chains is None:
chains = max(2, cores)
if isinstance(start, dict):
start = [start] * chains
if random_seed == -1:
random_seed = None
if chains == 1 and isinstance(random_seed, int):
random_seed = [random_seed]
if random_seed is None or isinstance(random_seed, int):
if random_seed is not None:
np.random.seed(random_seed)
random_seed = [np.random.randint(2 ** 30) for _ in range(chains)]
if not isinstance(random_seed, Iterable):
raise TypeError("Invalid value for `random_seed`. Must be tuple, list or int")
if "chain" in kwargs:
chain_idx = kwargs["chain"]
warnings.warn(
"The chain argument has been deprecated. Use chain_idx instead.", DeprecationWarning
)
if start is not None:
for start_vals in start:
_check_start_shape(model, start_vals)
# small trace warning
if draws == 0:
msg = "Tuning was enabled throughout the whole trace."
_log.warning(msg)
elif draws < 500:
msg = "Only %s samples in chain." % draws
_log.warning(msg)
draws += tune
if model.ndim == 0:
raise ValueError("The model does not contain any free variables.")
if step is None and init is not None and all_continuous(model.vars):
try:
# By default, try to use NUTS
_log.info("Auto-assigning NUTS sampler...")
start_, step = init_nuts(
init=init,
chains=chains,
n_init=n_init,
model=model,
random_seed=random_seed,
progressbar=progressbar,
**kwargs
)
if start is None:
start = start_
except (AttributeError, NotImplementedError, tg.NullTypeGradError):
# gradient computation failed
_log.info("Initializing NUTS failed. " "Falling back to elementwise auto-assignment.")
_log.debug("Exception in init nuts", exec_info=True)
step = assign_step_methods(model, step, step_kwargs=kwargs)
else:
step = assign_step_methods(model, step, step_kwargs=kwargs)
if isinstance(step, list):
step = CompoundStep(step)
if start is None:
start = {}
if isinstance(start, dict):
start = [start] * chains
sample_args = {
"draws": draws,
"step": step,
"start": start,
"trace": trace,
"chain": chain_idx,
"chains": chains,
"tune": tune,
"progressbar": progressbar,
"model": model,
"random_seed": random_seed,
"cores": cores,
}
sample_args.update(kwargs)
has_population_samplers = np.any(
[
isinstance(m, arraystep.PopulationArrayStepShared)
for m in (step.methods if isinstance(step, CompoundStep) else [step])
]
)
parallel = cores > 1 and chains > 1 and not has_population_samplers
if parallel:
_log.info("Multiprocess sampling ({} chains in {} jobs)".format(chains, cores))
_print_step_hierarchy(step)
try:
trace = _mp_sample(**sample_args)
except pickle.PickleError:
_log.warning("Could not pickle model, sampling singlethreaded.")
_log.debug("Pickling error:", exec_info=True)
parallel = False
except AttributeError as e:
if str(e).startswith("AttributeError: Can't pickle"):
_log.warning("Could not pickle model, sampling singlethreaded.")
_log.debug("Pickling error:", exec_info=True)
parallel = False
else:
raise
if not parallel:
if has_population_samplers:
_log.info("Population sampling ({} chains)".format(chains))
_print_step_hierarchy(step)
trace = _sample_population(**sample_args, parallelize=cores > 1)
else:
_log.info("Sequential sampling ({} chains in 1 job)".format(chains))
_print_step_hierarchy(step)
trace = _sample_many(**sample_args)
discard = tune if discard_tuned_samples else 0
trace = trace[discard:]
if compute_convergence_checks:
if draws - tune < 100:
warnings.warn("The number of samples is too small to check convergence reliably.")
else:
trace.report._run_convergence_checks(trace, model)
trace.report._log_summary()
return trace
def _check_start_shape(model, start):
if not isinstance(start, dict):
raise TypeError("start argument must be a dict or an array-like of dicts")
e = ""
for var in model.vars:
if var.name in start.keys():
var_shape = var.shape.tag.test_value
start_var_shape = np.shape(start[var.name])
if start_var_shape:
if not np.array_equal(var_shape, start_var_shape):
e += "\nExpected shape {} for var '{}', got: {}".format(
tuple(var_shape), var.name, start_var_shape
)
# if start var has no shape
else:
# if model var has a specified shape
if var_shape.size > 0:
e += "\nExpected shape {} for var " "'{}', got scalar {}".format(
tuple(var_shape), var.name, start[var.name]
)
if e != "":
raise ValueError("Bad shape for start argument:{}".format(e))
def _sample_many(draws, chain, chains, start, random_seed, step, **kwargs):
traces = []
for i in range(chains):
trace = _sample(
draws=draws,
chain=chain + i,
start=start[i],
step=step,
random_seed=random_seed[i],
**kwargs
)
if trace is None:
if len(traces) == 0:
raise ValueError("Sampling stopped before a sample was created.")
else:
break
elif len(trace) < draws:
if len(traces) == 0:
traces.append(trace)
break
else:
traces.append(trace)
return MultiTrace(traces)
def _sample_population(
draws,
chain,
chains,
start,
random_seed,
step,
tune,
model,
progressbar=None,
parallelize=False,
**kwargs
):
# create the generator that iterates all chains in parallel
chains = [chain + c for c in range(chains)]
sampling = _prepare_iter_population(
draws, chains, step, start, parallelize, tune=tune, model=model, random_seed=random_seed
)
if progressbar:
sampling = tqdm(sampling, total=draws)
latest_traces = None
for it, traces in enumerate(sampling):
latest_traces = traces
return MultiTrace(latest_traces)
def _sample(
chain,
progressbar,
random_seed,
start,
draws=None,
step=None,
trace=None,
tune=None,
model=None,
**kwargs
):
skip_first = kwargs.get("skip_first", 0)
sampling = _iter_sample(draws, step, start, trace, chain, tune, model, random_seed)
_pbar_data = None
if progressbar:
_pbar_data = {"chain": chain, "divergences": 0}
_desc = "Sampling chain {chain:d}, {divergences:,d} divergences"
sampling = tqdm(sampling, total=draws, desc=_desc.format(**_pbar_data))
try:
strace = None
for it, (strace, diverging) in enumerate(sampling):
if it >= skip_first:
trace = MultiTrace([strace])
if diverging and _pbar_data is not None:
_pbar_data["divergences"] += 1
sampling.set_description(_desc.format(**_pbar_data))
except KeyboardInterrupt:
pass
finally:
if progressbar:
sampling.close()
return strace
def iter_sample(
draws, step, start=None, trace=None, chain=0, tune=None, model=None, random_seed=None
):
"""Generator that returns a trace on each iteration using the given
step method. Multiple step methods supported via compound step
method returns the amount of time taken.
Parameters
----------
draws : int
The number of samples to draw
step : function
Step function
start : dict
Starting point in parameter space (or partial point). Defaults to trace.point(-1)) if
there is a trace provided and model.test_point if not (defaults to empty dict)
trace : backend, list, or MultiTrace
This should be a backend instance, a list of variables to track, or a MultiTrace object
with past values. If a MultiTrace object is given, it must contain samples for the chain
number ``chain``. If None or a list of variables, the NDArray backend is used.
chain : int
Chain number used to store sample in backend. If ``cores`` is greater than one, chain numbers
will start here.
tune : int
Number of iterations to tune, if applicable (defaults to None)
model : Model (optional if in ``with`` context)
random_seed : int or list of ints
A list is accepted if more if ``cores`` is greater than one.
Examples
--------
::
for trace in iter_sample(500, step):
...
"""
sampling = _iter_sample(draws, step, start, trace, chain, tune, model, random_seed)
for i, (strace, _) in enumerate(sampling):
yield MultiTrace([strace[: i + 1]])
def _iter_sample(
draws, step, start=None, trace=None, chain=0, tune=None, model=None, random_seed=None
):
model = modelcontext(model)
draws = int(draws)
if random_seed is not None:
np.random.seed(random_seed)
if draws < 1:
raise ValueError("Argument `draws` must be greater than 0.")
if start is None:
start = {}
strace = _choose_backend(trace, chain, model=model)
if len(strace) > 0:
update_start_vals(start, strace.point(-1), model)
else:
update_start_vals(start, model.test_point, model)
try:
step = CompoundStep(step)
except TypeError:
pass
point = Point(start, model=model)
if step.generates_stats and strace.supports_sampler_stats:
strace.setup(draws, chain, step.stats_dtypes)
else:
strace.setup(draws, chain)
try:
step.tune = bool(tune)
for i in range(draws):
if i == 0 and hasattr(step, "iter_count"):
step.iter_count = 0
if i == tune:
step = stop_tuning(step)
if step.generates_stats:
point, stats = step.step(point)
if strace.supports_sampler_stats:
strace.record(point, stats)
diverging = i > tune and stats and stats[0].get("diverging")
else:
strace.record(point)
else:
point = step.step(point)
strace.record(point)
diverging = False
yield strace, diverging
except KeyboardInterrupt:
strace.close()
if hasattr(step, "warnings"):
warns = step.warnings()
strace._add_warnings(warns)
raise
except BaseException:
strace.close()
raise
else:
strace.close()
if hasattr(step, "warnings"):
warns = step.warnings()
strace._add_warnings(warns)
class PopulationStepper:
def __init__(self, steppers, parallelize):
"""Tries to use multiprocessing to parallelize chains.
Falls back to sequential evaluation if multiprocessing fails.
In the multiprocessing mode of operation, a new process is started for each
chain/stepper and Pipes are used to communicate with the main process.
Parameters
----------
steppers : list
A collection of independent step methods, one for each chain.
parallelize : bool
Indicates if chain parallelization is desired
"""
self.nchains = len(steppers)
self.is_parallelized = False
self._master_ends = []
self._processes = []
self._steppers = steppers
if parallelize:
try:
# configure a child process for each stepper
_log.info(
"Attempting to parallelize chains to all cores. You can turn this off with `pm.sample(cores=1)`."
)
import multiprocessing
for c, stepper in enumerate(tqdm(steppers)):
slave_end, master_end = multiprocessing.Pipe()
stepper_dumps = pickle.dumps(stepper, protocol=4)
process = multiprocessing.Process(
target=self.__class__._run_slave,
args=(c, stepper_dumps, slave_end),
name="ChainWalker{}".format(c),
)
# we want the child process to exit if the parent is terminated
process.daemon = True
# Starting the process might fail and takes time.
# By doing it in the constructor, the sampling progress bar
# will not be confused by the process start.
process.start()
self._master_ends.append(master_end)
self._processes.append(process)
self.is_parallelized = True
except Exception:
_log.info(
"Population parallelization failed. "
"Falling back to sequential stepping of chains."
)
_log.debug("Error was: ", exec_info=True)
else:
_log.info(
"Chains are not parallelized. You can enable this by passing "
"`pm.sample(cores=n)`, where n > 1."
)
return super().__init__()
def __enter__(self):
"""Does nothing because processes are already started in __init__."""
return
def __exit__(self, exc_type, exc_val, exc_tb):
if len(self._processes) > 0:
try:
for master_end in self._master_ends:
master_end.send(None)
for process in self._processes:
process.join(timeout=3)
except Exception:
_log.warning("Termination failed.")
return
@staticmethod
def _run_slave(c, stepper_dumps, slave_end):
"""Started on a separate process to perform stepping of a chain.
Parameters
----------
c : int
number of this chain
stepper : BlockedStep
a step method such as CompoundStep
slave_end : multiprocessing.connection.PipeConnection
This is our connection to the main process
"""
# re-seed each child process to make them unique
np.random.seed(None)
try:
stepper = pickle.loads(stepper_dumps)
# the stepper is not necessarily a PopulationArraySharedStep itself,
# but rather a CompoundStep. PopulationArrayStepShared.population
# has to be updated, therefore we identify the substeppers first.
population_steppers = []
for sm in stepper.methods if isinstance(stepper, CompoundStep) else [stepper]:
if isinstance(sm, arraystep.PopulationArrayStepShared):
population_steppers.append(sm)
while True:
incoming = slave_end.recv()
# receiving a None is the signal to exit
if incoming is None:
break
tune_stop, population = incoming
if tune_stop:
stop_tuning(stepper)
# forward the population to the PopulationArrayStepShared objects
# This is necessary because due to the process fork, the population
# object is no longer shared between the steppers.
for popstep in population_steppers:
popstep.population = population
update = stepper.step(population[c])
slave_end.send(update)
except Exception:
_log.exception("ChainWalker{}".format(c))
return
def step(self, tune_stop, population):
"""Steps the entire population of chains.
Parameters
----------
tune_stop : bool
Indicates if the condition (i == tune) is fulfilled
population : list
Current Points of all chains
Returns
-------
update : Point
The new positions of the chains
"""
updates = [None] * self.nchains
if self.is_parallelized:
for c in range(self.nchains):
self._master_ends[c].send((tune_stop, population))
# Blockingly get the step outcomes
for c in range(self.nchains):
updates[c] = self._master_ends[c].recv()
else:
for c in range(self.nchains):
if tune_stop:
self._steppers[c] = stop_tuning(self._steppers[c])
updates[c] = self._steppers[c].step(population[c])
return updates
def _prepare_iter_population(
draws, chains, step, start, parallelize, tune=None, model=None, random_seed=None
):
"""Prepares a PopulationStepper and traces for population sampling.
Returns
-------
_iter_population : generator
The generator the yields traces of all chains at the same time
"""
# chains contains the chain numbers, but for indexing we need indices...
nchains = len(chains)
model = modelcontext(model)
draws = int(draws)
if random_seed is not None:
np.random.seed(random_seed)
if draws < 1:
raise ValueError("Argument `draws` should be above 0.")
# The initialization of traces, samplers and points must happen in the right order:
# 1. traces are initialized and update_start_vals configures variable transforms
# 2. population of points is created
# 3. steppers are initialized and linked to the points object
# 4. traces are configured to track the sampler stats
# 5. a PopulationStepper is configured for parallelized stepping
# 1. prepare a BaseTrace for each chain
traces = [_choose_backend(None, chain, model=model) for chain in chains]
for c, strace in enumerate(traces):
# initialize the trace size and variable transforms
if len(strace) > 0:
update_start_vals(start[c], strace.point(-1), model)
else:
update_start_vals(start[c], model.test_point, model)
# 2. create a population (points) that tracks each chain
# it is updated as the chains are advanced
population = [Point(start[c], model=model) for c in range(nchains)]
# 3. Set up the steppers
steppers = [None] * nchains
for c in range(nchains):
# need indepenent samplers for each chain
# it is important to copy the actual steppers (but not the delta_logp)
if isinstance(step, CompoundStep):
chainstep = CompoundStep([copy(m) for m in step.methods])
else:
chainstep = copy(step)
# link population samplers to the shared population state
for sm in chainstep.methods if isinstance(step, CompoundStep) else [chainstep]:
if isinstance(sm, arraystep.PopulationArrayStepShared):
sm.link_population(population, c)
steppers[c] = chainstep
# 4. configure tracking of sampler stats
for c in range(nchains):
if steppers[c].generates_stats and traces[c].supports_sampler_stats:
traces[c].setup(draws, c, steppers[c].stats_dtypes)
else:
traces[c].setup(draws, c)
# 5. configure the PopulationStepper (expensive call)
popstep = PopulationStepper(steppers, parallelize)
# Because the preparations above are expensive, the actual iterator is
# in another method. This way the progbar will not be disturbed.
return _iter_population(draws, tune, popstep, steppers, traces, population)
def _iter_population(draws, tune, popstep, steppers, traces, points):
"""Generator that iterates a PopulationStepper.
Parameters
----------
draws : int
number of draws per chain
tune : int
number of tuning steps
popstep : PopulationStepper
the helper object for (parallelized) stepping of chains
steppers : list
The step methods for each chain
traces : list
Traces for each chain
points : list
population of chain states
"""
try:
with popstep:
# iterate draws of all chains
for i in range(draws):
updates = popstep.step(i == tune, points)
# apply the update to the points and record to the traces
for c, strace in enumerate(traces):
if steppers[c].generates_stats:
points[c], stats = updates[c]
if strace.supports_sampler_stats:
strace.record(points[c], stats)
else:
strace.record(points[c])
else:
points[c] = updates[c]
strace.record(points[c])
# yield the state of all chains in parallel
yield traces
except KeyboardInterrupt:
for c, strace in enumerate(traces):
strace.close()
if hasattr(steppers[c], "report"):
steppers[c].report._finalize(strace)
raise
except BaseException:
for c, strace in enumerate(traces):
strace.close()
raise
else:
for c, strace in enumerate(traces):
strace.close()
if hasattr(steppers[c], "report"):
steppers[c].report._finalize(strace)
def _choose_backend(trace, chain, shortcuts=None, **kwds):
if isinstance(trace, BaseTrace):
return trace
if isinstance(trace, MultiTrace):
return trace._straces[chain]
if trace is None:
return NDArray(**kwds)
if shortcuts is None:
shortcuts = pm.backends._shortcuts
try:
backend = shortcuts[trace]["backend"]
name = shortcuts[trace]["name"]
return backend(name, **kwds)
except TypeError:
return NDArray(vars=trace, **kwds)
except KeyError:
raise ValueError("Argument `trace` is invalid.")
def _mp_sample(
draws,
tune,
step,
chains,
cores,
chain,
random_seed,
start,
progressbar,
trace=None,
model=None,
**kwargs
):
import pymc3.parallel_sampling as ps
# We did draws += tune in pm.sample
draws -= tune
traces = []
for idx in range(chain, chain + chains):
if trace is not None:
strace = _choose_backend(copy(trace), idx, model=model)
else:
strace = _choose_backend(None, idx, model=model)
# for user supply start value, fill-in missing value if the supplied
# dict does not contain all parameters
update_start_vals(start[idx - chain], model.test_point, model)
if step.generates_stats and strace.supports_sampler_stats:
strace.setup(draws + tune, idx + chain, step.stats_dtypes)
else:
strace.setup(draws + tune, idx + chain)
traces.append(strace)
sampler = ps.ParallelSampler(
draws, tune, chains, cores, random_seed, start, step, chain, progressbar
)
try:
try:
with sampler:
for draw in sampler:
trace = traces[draw.chain - chain]
if trace.supports_sampler_stats and draw.stats is not None:
trace.record(draw.point, draw.stats)
else:
trace.record(draw.point)
if draw.is_last:
trace.close()
if draw.warnings is not None:
trace._add_warnings(draw.warnings)
except ps.ParallelSamplingError as error:
trace = traces[error._chain - chain]
trace._add_warnings(error._warnings)
for trace in traces:
trace.close()
multitrace = MultiTrace(traces)
multitrace._report._log_summary()
raise
return MultiTrace(traces)
except KeyboardInterrupt:
traces, length = _choose_chains(traces, tune)
return MultiTrace(traces)[:length]
finally:
for trace in traces:
trace.close()
def _choose_chains(traces, tune):
if tune is None:
tune = 0
if not traces:
return []
lengths = [max(0, len(trace) - tune) for trace in traces]
if not sum(lengths):
raise ValueError("Not enough samples to build a trace.")
idxs = np.argsort(lengths)[::-1]
l_sort = np.array(lengths)[idxs]
final_length = l_sort[0]
last_total = 0
for i, length in enumerate(l_sort):
total = (i + 1) * length
if total < last_total:
use_until = i
break
last_total = total
final_length = length
else:
use_until = len(lengths)
return [traces[idx] for idx in idxs[:use_until]], final_length + tune
def stop_tuning(step):
""" stop tuning the current step method """
step.stop_tuning()
return step
class _DefaultTrace:
"""
This class is a utility for collecting a number of samples
into a dictionary. Name comes from its similarity to `defaultdict` --
entries are lazily created.
Parameters
----------
samples : int
The number of samples that will be collected, per variable,
into the trace.
Attributes
----------
trace_dict : Dict[str, np.ndarray]
A dictionary constituting a trace. Should be extracted
after a procedure has filled the `_DefaultTrace` using the
`insert()` method
"""
trace_dict = {} # type: Dict[str, np.ndarray]
_len = None # type: int
def __init__(self, samples):
self._len = samples
self.trace_dict = {}
def insert(self, k: str, v, idx: int):
"""
Insert `v` as the value of the `idx`th sample for the variable `k`.
Parameters
----------
k : str
Name of the variable.
v : anything that can go into a numpy array (including a numpy array)
The value of the `idx`th sample from variable `k`
ids : int
The index of the sample we are inserting into the trace.
"""
if hasattr(v, "shape"):
value_shape = tuple(v.shape) # type: Tuple[int, ...]
else:
value_shape = ()
# initialize if necessary
if k not in self.trace_dict:
array_shape = (self._len,) + value_shape
self.trace_dict[k] = np.empty(array_shape, dtype=np.array(v).dtype)
# do the actual insertion
if value_shape == ():
self.trace_dict[k][idx] = v
else:
self.trace_dict[k][idx, :] = v
def sample_posterior_predictive(
trace,
samples: Optional[int] = None,
model: Optional[Model] = None,
vars: Optional[TIterable[Tensor]] = None,
var_names: Optional[List[str]] = None,
size: Optional[int] = None,
keep_size: Optional[bool] = False,
random_seed=None,
progressbar: bool = True,
) -> Dict[str, np.ndarray]:
"""Generate posterior predictive samples from a model given a trace.
Parameters
----------
trace : backend, list, or MultiTrace
Trace generated from MCMC sampling. Or a list containing dicts from
find_MAP() or points
samples : int
Number of posterior predictive samples to generate. Defaults to one posterior predictive
sample per posterior sample, that is, the number of draws times the number of chains. It
is not recommended to modify this value; when modified, some chains may not be represented
in the posterior predictive sample.
model : Model (optional if in ``with`` context)
Model used to generate ``trace``
vars : iterable
Variables for which to compute the posterior predictive samples.
Deprecated: please use ``var_names`` instead.
var_names : Iterable[str]
Alternative way to specify vars to sample, to make this function orthogonal with
others.
size : int
The number of random draws from the distribution specified by the parameters in each
sample of the trace. Not recommended unless more than ndraws times nchains posterior
predictive samples are needed.
keep_size : bool, optional
Force posterior predictive sample to have the same shape as posterior and sample stats
data: ``(nchains, ndraws, ...)``. Overrides samples and size parameters.
random_seed : int
Seed for the random number generator.
progressbar : bool
Whether or not to display a progress bar in the command line. The bar shows the percentage
of completion, the sampling speed in samples per second (SPS), and the estimated remaining
time until completion ("expected time of arrival"; ETA).
Returns
-------
samples : dict
Dictionary with the variable names as keys, and values numpy arrays containing
posterior predictive samples.
"""
len_trace = len(trace)
try:
nchain = trace.nchains
except AttributeError:
nchain = 1
if keep_size and samples is not None:
raise IncorrectArgumentsError("Should not specify both keep_size and samples argukments")
if keep_size and size is not None:
raise IncorrectArgumentsError("Should not specify both keep_size and size argukments")
if samples is None:
samples = sum(len(v) for v in trace._straces.values())
if samples < len_trace * nchain:
warnings.warn(
"samples parameter is smaller than nchains times ndraws, some draws "
"and/or chains may not be represented in the returned posterior "
"predictive sample"
)
model = modelcontext(model)
if var_names is not None:
if vars is not None:
raise IncorrectArgumentsError("Should not specify both vars and var_names arguments.")
else:
vars = [model[x] for x in var_names]
elif vars is not None: # var_names is None, and vars is not.
warnings.warn("vars argument is deprecated in favor of var_names.", DeprecationWarning)
if vars is None:
vars = model.observed_RVs
if random_seed is not None:
np.random.seed(random_seed)
indices = np.arange(samples)
if progressbar:
indices = tqdm(indices, total=samples)
ppc_trace_t = _DefaultTrace(samples)
try:
for idx in indices:
if nchain > 1:
chain_idx, point_idx = np.divmod(idx, len_trace)
param = trace._straces[chain_idx % nchain].point(point_idx)
else:
param = trace[idx % len_trace]
values = draw_values(vars, point=param, size=size)
for k, v in zip(vars, values):
ppc_trace_t.insert(k.name, v, idx)
except KeyboardInterrupt:
pass
finally:
if progressbar:
indices.close()
ppc_trace = ppc_trace_t.trace_dict
if keep_size:
for k, ary in ppc_trace.items():
ppc_trace[k] = ary.reshape((nchain, len_trace, *ary.shape[1:]))
return ppc_trace
def sample_ppc(*args, **kwargs):
"""This method is deprecated. Please use :func:`~sampling.sample_posterior_predictive`"""
message = "sample_ppc() is deprecated. Please use sample_posterior_predictive()"
warnings.warn(message, DeprecationWarning, stacklevel=2)
return sample_posterior_predictive(*args, **kwargs)
def sample_posterior_predictive_w(
traces, samples=None, models=None, weights=None, random_seed=None, progressbar=True
):
"""Generate weighted posterior predictive samples from a list of models and
a list of traces according to a set of weights.
Parameters
----------
traces : list or list of lists
List of traces generated from MCMC sampling, or a list of list
containing dicts from find_MAP() or points. The number of traces should
be equal to the number of weights.
samples : int
Number of posterior predictive samples to generate. Defaults to the
length of the shorter trace in traces.
models : list
List of models used to generate the list of traces. The number of models should be equal to
the number of weights and the number of observed RVs should be the same for all models.
By default a single model will be inferred from ``with`` context, in this case results will
only be meaningful if all models share the same distributions for the observed RVs.
weights: array-like
Individual weights for each trace. Default, same weight for each model.
random_seed : int
Seed for the random number generator.
progressbar : bool
Whether or not to display a progress bar in the command line. The bar shows the percentage
of completion, the sampling speed in samples per second (SPS), and the estimated remaining
time until completion ("expected time of arrival"; ETA).
Returns
-------
samples : dict
Dictionary with the variables as keys. The values corresponding to the
posterior predictive samples from the weighted models.
"""
np.random.seed(random_seed)
if models is None:
models = [modelcontext(models)] * len(traces)
if weights is None:
weights = [1] * len(traces)
if len(traces) != len(weights):
raise ValueError("The number of traces and weights should be the same")
if len(models) != len(weights):
raise ValueError("The number of models and weights should be the same")
length_morv = len(models[0].observed_RVs)
if not all(len(i.observed_RVs) == length_morv for i in models):
raise ValueError("The number of observed RVs should be the same for all models")
weights = np.asarray(weights)
p = weights / np.sum(weights)
min_tr = min([len(i) * i.nchains for i in traces])
n = (min_tr * p).astype("int")
# ensure n sum up to min_tr
idx = np.argmax(n)
n[idx] = n[idx] + min_tr - np.sum(n)
trace = []
for i, j in enumerate(n):
tr = traces[i]
len_trace = len(tr)
try:
nchain = tr.nchains
except AttributeError:
nchain = 1
indices = np.random.randint(0, nchain * len_trace, j)
if nchain > 1:
chain_idx, point_idx = np.divmod(indices, len_trace)
for idx in zip(chain_idx, point_idx):
trace.append(tr._straces[idx[0]].point(idx[1]))
else:
for idx in indices:
trace.append(tr[idx])
obs = [x for m in models for x in m.observed_RVs]
variables = np.repeat(obs, n)
lengths = list(set([np.atleast_1d(observed).shape for observed in obs]))
if len(lengths) == 1:
size = [None for i in variables]
elif len(lengths) > 2:
raise ValueError("Observed variables could not be broadcast together")
else:
size = []
x = np.zeros(shape=lengths[0])
y = np.zeros(shape=lengths[1])
b = np.broadcast(x, y)
for var in variables:
shape = np.shape(np.atleast_1d(var.distribution.default()))
if shape != b.shape:
size.append(b.shape)
else:
size.append(None)
len_trace = len(trace)
if samples is None:
samples = len_trace
indices = np.random.randint(0, len_trace, samples)
if progressbar:
indices = tqdm(indices, total=samples)
try:
ppc = defaultdict(list)
for idx in indices:
param = trace[idx]
var = variables[idx]
# TODO sample_posterior_predictive_w is currently only work for model with
# one observed.
ppc[var.name].append(draw_values([var], point=param, size=size[idx])[0])
except KeyboardInterrupt:
pass
finally:
if progressbar:
indices.close()
return {k: np.asarray(v) for k, v in ppc.items()}
def sample_ppc_w(*args, **kwargs):
"""This method is deprecated. Please use :func:`~sampling.sample_posterior_predictive_w`"""
message = "sample_ppc() is deprecated. Please use sample_posterior_predictive_w()"
warnings.warn(message, DeprecationWarning, stacklevel=2)
return sample_posterior_predictive_w(*args, **kwargs)
def sample_prior_predictive(
samples=500,
model: Optional[Model] = None,
vars: Optional[TIterable[str]] = None,
var_names: Optional[TIterable[str]] = None,
random_seed=None,
) -> Dict[str, np.ndarray]:
"""Generate samples from the prior predictive distribution.
Parameters
----------
samples : int
Number of samples from the prior predictive to generate. Defaults to 500.
model : Model (optional if in ``with`` context)
vars : Iterable[str]
A list of names of variables for which to compute the posterior predictive
samples. *DEPRECATED* - Use ``var_names`` argument instead.
var_names : Iterable[str]
A list of names of variables for which to compute the posterior predictive
samples. Defaults to both observed and unobserved RVs.
random_seed : int
Seed for the random number generator.
Returns
-------
dict
Dictionary with variable names as keys. The values are numpy arrays of prior
samples.
"""
model = modelcontext(model)
if vars is None and var_names is None:
prior_pred_vars = model.observed_RVs
prior_vars = (
get_default_varnames(model.unobserved_RVs, include_transformed=True) + model.potentials
)
vars_ = [var.name for var in prior_vars + prior_pred_vars]
vars = set(vars_)
elif vars is None:
vars = var_names
vars_ = vars
elif vars is not None:
warnings.warn("vars argument is deprecated in favor of var_names.", DeprecationWarning)
vars_ = vars
else:
raise ValueError("Cannot supply both vars and var_names arguments.")
vars = cast(TIterable[str], vars) # tell mypy that vars cannot be None here.
if random_seed is not None:
np.random.seed(random_seed)
names = get_default_varnames(vars_, include_transformed=False)
# draw_values fails with auto-transformed variables. transform them later!
values = draw_values([model[name] for name in names], size=samples)
data = {k: v for k, v in zip(names, values)}
if data is None:
raise AssertionError("No variables sampled: attempting to sample %s" % names)
prior = {} # type: Dict[str, np.ndarray]
for var_name in vars:
if var_name in data:
prior[var_name] = data[var_name]
elif is_transformed_name(var_name):
untransformed = get_untransformed_name(var_name)
if untransformed in data:
prior[var_name] = model[untransformed].transformation.forward_val(
data[untransformed]
)
return prior
def init_nuts(
init="auto", chains=1, n_init=500000, model=None, random_seed=None, progressbar=True, **kwargs
):
"""Set up the mass matrix initialization for NUTS.
NUTS convergence and sampling speed is extremely dependent on the
choice of mass/scaling matrix. This function implements different
methods for choosing or adapting the mass matrix.
Parameters
----------
init : str
Initialization method to use.
* auto : Choose a default initialization method automatically.
Currently, this is `'jitter+adapt_diag'`, but this can change in the future. If you
depend on the exact behaviour, choose an initialization method explicitly.
* adapt_diag : Start with a identity mass matrix and then adapt a diagonal based on the
variance of the tuning samples. All chains use the test value (usually the prior mean)
as starting point.
* jitter+adapt_diag : Same as ``adapt_diag``, but use uniform jitter in [-1, 1] as starting
point in each chain.
* advi+adapt_diag : Run ADVI and then adapt the resulting diagonal mass matrix based on the
sample variance of the tuning samples.
* advi+adapt_diag_grad : Run ADVI and then adapt the resulting diagonal mass matrix based
on the variance of the gradients during tuning. This is **experimental** and might be
removed in a future release.
* advi : Run ADVI to estimate posterior mean and diagonal mass matrix.
* advi_map: Initialize ADVI with MAP and use MAP as starting point.
* map : Use the MAP as starting point. This is discouraged.
* nuts : Run NUTS and estimate posterior mean and mass matrix from
the trace.
chains : int
Number of jobs to start.
n_init : int
Number of iterations of initializer
If 'ADVI', number of iterations, if 'nuts', number of draws.
model : Model (optional if in ``with`` context)
progressbar : bool
Whether or not to display a progressbar for advi sampling.
**kwargs : keyword arguments
Extra keyword arguments are forwarded to pymc3.NUTS.
Returns
-------
start : pymc3.model.Point
Starting point for sampler
nuts_sampler : pymc3.step_methods.NUTS
Instantiated and initialized NUTS sampler object
"""
model = modelcontext(model)
vars = kwargs.get("vars", model.vars)
if set(vars) != set(model.vars):
raise ValueError("Must use init_nuts on all variables of a model.")
if not all_continuous(vars):
raise ValueError("init_nuts can only be used for models with only " "continuous variables.")
if not isinstance(init, str):
raise TypeError("init must be a string.")
if init is not None:
init = init.lower()
if init == "auto":
init = "jitter+adapt_diag"
_log.info("Initializing NUTS using {}...".format(init))
if random_seed is not None:
random_seed = int(np.atleast_1d(random_seed)[0])
np.random.seed(random_seed)
cb = [
pm.callbacks.CheckParametersConvergence(tolerance=1e-2, diff="absolute"),
pm.callbacks.CheckParametersConvergence(tolerance=1e-2, diff="relative"),
]
if init == "adapt_diag":
start = [model.test_point] * chains
mean = np.mean([model.dict_to_array(vals) for vals in start], axis=0)
var = np.ones_like(mean)
potential = quadpotential.QuadPotentialDiagAdapt(model.ndim, mean, var, 10)
elif init == "jitter+adapt_diag":
start = []
for _ in range(chains):
mean = {var: val.copy() for var, val in model.test_point.items()}
for val in mean.values():
val[...] += 2 * np.random.rand(*val.shape) - 1
start.append(mean)
mean = np.mean([model.dict_to_array(vals) for vals in start], axis=0)
var = np.ones_like(mean)
potential = quadpotential.QuadPotentialDiagAdapt(model.ndim, mean, var, 10)
elif init == "advi+adapt_diag_grad":
approx = pm.fit(
random_seed=random_seed,
n=n_init,
method="advi",
model=model,
callbacks=cb,
progressbar=progressbar,
obj_optimizer=pm.adagrad_window,
) # type: pm.MeanField
start = approx.sample(draws=chains)
start = list(start)
stds = approx.bij.rmap(approx.std.eval())
cov = model.dict_to_array(stds) ** 2
mean = approx.bij.rmap(approx.mean.get_value())
mean = model.dict_to_array(mean)
weight = 50
potential = quadpotential.QuadPotentialDiagAdaptGrad(model.ndim, mean, cov, weight)
elif init == "advi+adapt_diag":
approx = pm.fit(
random_seed=random_seed,
n=n_init,
method="advi",
model=model,
callbacks=cb,
progressbar=progressbar,
obj_optimizer=pm.adagrad_window,
) # type: pm.MeanField
start = approx.sample(draws=chains)
start = list(start)
stds = approx.bij.rmap(approx.std.eval())
cov = model.dict_to_array(stds) ** 2
mean = approx.bij.rmap(approx.mean.get_value())
mean = model.dict_to_array(mean)
weight = 50
potential = quadpotential.QuadPotentialDiagAdapt(model.ndim, mean, cov, weight)
elif init == "advi":
approx = pm.fit(
random_seed=random_seed,
n=n_init,
method="advi",
model=model,
callbacks=cb,
progressbar=progressbar,
obj_optimizer=pm.adagrad_window,
) # type: pm.MeanField
start = approx.sample(draws=chains)
start = list(start)
stds = approx.bij.rmap(approx.std.eval())
cov = model.dict_to_array(stds) ** 2
potential = quadpotential.QuadPotentialDiag(cov)
elif init == "advi_map":
start = pm.find_MAP(include_transformed=True)
approx = pm.MeanField(model=model, start=start)
pm.fit(
random_seed=random_seed,
n=n_init,
method=pm.KLqp(approx),
callbacks=cb,
progressbar=progressbar,
obj_optimizer=pm.adagrad_window,
)
start = approx.sample(draws=chains)
start = list(start)
stds = approx.bij.rmap(approx.std.eval())
cov = model.dict_to_array(stds) ** 2
potential = quadpotential.QuadPotentialDiag(cov)
elif init == "map":
start = pm.find_MAP(include_transformed=True)
cov = pm.find_hessian(point=start)
start = [start] * chains
potential = quadpotential.QuadPotentialFull(cov)
elif init == "nuts":
init_trace = pm.sample(
draws=n_init, step=pm.NUTS(), tune=n_init // 2, random_seed=random_seed
)
cov = np.atleast_1d(pm.trace_cov(init_trace))
start = list(np.random.choice(init_trace, chains))
potential = quadpotential.QuadPotentialFull(cov)
else:
raise ValueError("Unknown initializer: {}.".format(init))
step = pm.NUTS(potential=potential, model=model, **kwargs)
return start, step
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