def test_simple_operation(self):
fake_kernel = test_fixtures.TestTransitionKernel()
final_state, kernel_results = step_kernel(
num_steps=2,
current_state=0,
kernel=fake_kernel,
return_final_kernel_results=True)
final_state, kernel_results = self.evaluate(
[final_state, kernel_results])
self.assertEqual(final_state, 2)
self.assertEqual(kernel_results.counter_1, 2)
self.assertEqual(kernel_results.counter_2, 4)
def test_defined_pkr(self):
fake_kernel = test_fixtures.TestTransitionKernel()
init_pkr = test_fixtures.TestTransitionKernelResults(
tf.constant(2, dtype=tf.int32), tf.constant(3, dtype=tf.int32))
final_state, kernel_results = step_kernel(
num_steps=2,
current_state=0,
previous_kernel_results=init_pkr,
kernel=fake_kernel,
return_final_kernel_results=True)
final_state, kernel_results = self.evaluate(
[final_state, kernel_results])
self.assertEqual(final_state, 2)
self.assertEqual(kernel_results.counter_1, 4)
self.assertEqual(kernel_results.counter_2, 7)
def sample(self, num_steps, current_state, previous_kernel_results=None):
"""Sample from the configured kernel.
Args:
num_steps: Integer number of Markov chain steps.
current_state: `Tensor` or Python `list` of `Tensor`s representing the
current state(s) of the Markov chain(s).
previous_kernel_results: A `Tensor` or a nested collection of `Tensor`s.
Warm-start for the auxiliary state needed by the given `kernel`.
If not supplied, `step_kernel` will cold-start with
`kernel.bootstrap_results`.
Returns:
outputs: A `KernelOutputs` object containing the states, trace, etc.
"""
kernel = self.build(num_steps)
state, results = step.step_kernel(
num_steps=num_steps,
current_state=current_state,
previous_kernel_results=previous_kernel_results,
kernel=kernel,
return_final_kernel_results=True)
return kernel_outputs.KernelOutputs(kernel, state, results)
def sample_chain(
kernel,
num_results,
current_state,
previous_kernel_results=None,
reducer=(),
previous_reducer_state=None,
trace_fn=_trace_everything,
parallel_iterations=10,
seed=None,
name=None,
):
"""Runs a Markov chain defined by the given `TransitionKernel`.
This is meant as a (more) helpful frontend to the low-level
`TransitionKernel`-based MCMC API, supporting several main features:
- Running a batch of multiple independent chains using SIMD parallelism
- Tracing the history of the chains, or not tracing it to save memory
- Computing reductions over chain history, whether it is also traced or not
- Warm (re-)start, including auxiliary state
This function samples from a Markov chain at `current_state` whose
stationary distribution is governed by the supplied `TransitionKernel`
instance (`kernel`).
The `current_state` can be represented as a single `Tensor` or a `list` of
`Tensors` which collectively represent the current state.
This function can sample from multiple chains, in parallel. Whether or not
there are multiple chains is dictated by how the `kernel` treats its inputs.
Typically, the shape of the independent chains is shape of the result of the
`target_log_prob_fn` used by the `kernel` when applied to the given
`current_state`.
This function can compute reductions over the samples in tandem with sampling,
for example to return summary statistics without materializing all the
samples. To request reductions, pass a `Reducer` object, or a nested
structure of `Reducer` objects, as the `reducer=` argument.
In addition to the chain state, this function supports tracing of auxiliary
variables used by the kernel, as well as intermediate values of any supplied
reductions. The traced values are selected by specifying `trace_fn`. The
`trace_fn` must be a callable accepting three arguments: the chain state, the
kernel_results of the `kernel`, and the current results of the reductions, if
any are supplied. The return value of `trace_fn` (which may be a `Tensor` or
a nested structure of `Tensor`s) is accumulated, such that each `Tensor` gains
a new outmost dimension representing time in the chain history.
Since MCMC states are correlated, it is sometimes desirable to produce
additional intermediate states, and then discard them, ending up with a set of
states with decreased autocorrelation. See [Owen (2017)][1]. Such 'thinning'
is made possible by setting `num_steps_between_results > 0`. The chain then
takes `num_steps_between_results` extra steps between the steps that make it
into the results, or are shown to any supplied reductions. The extra steps
are never materialized, and thus do not increase memory requirements.
Args:
kernel: An instance of `tfp.mcmc.TransitionKernel` which implements one step
of the Markov chain.
num_results: Integer number of (non-discarded) Markov chain draws to
compute.
current_state: `Tensor` or Python `list` of `Tensor`s representing the
initial state(s) of the Markov chain(s).
previous_kernel_results: A `Tensor` or a nested collection of `Tensor`s
representing internal calculations made within the previous call to this
function (or as returned by `bootstrap_results`).
reducer: A (possibly nested) structure of `Reducer`s to be evaluated
on the `kernel`'s samples. If no reducers are given (`reducer=None`),
their states will not be passed to any supplied `trace_fn`.
previous_reducer_state: A (possibly nested) structure of running states
corresponding to the structure in `reducer`. For resuming streaming
reduction computations begun in a previous run.
trace_fn: A callable that takes in the current chain state, the current
auxiliary kernel state, and the current result of any reducers, and
returns a `Tensor` or a nested collection of `Tensor`s that is then
traced. If `None`, nothing is traced.
parallel_iterations: The number of iterations allowed to run in parallel. It
must be a positive integer. See `tf.while_loop` for more details.
seed: PRNG seed; see `tfp.random.sanitize_seed` for details.
name: Python `str` name prefixed to Ops created by this function.
Default value: `None` (i.e., 'mcmc_sample_chain').
Returns:
result: A `SampleChainResults` instance containing information about the
sampling run. Main fields are `trace`, the history of outputs of
`trace_fn`, and `reduction_results`, the final outputs of all supplied
`Reducer`s. See `SampleChainResults` for contents of other fields.
"""
# Features omitted for simplicity:
# - Can only warm start either all the reducers or none of them, not
# piecemeal.
#
# Defects admitted for simplicity:
# - All reducers are finalized internally at every step, whether the user
# wished to trace them or not. We expect graph mode TF to avoid that unused
# computation, but eager mode will not.
# - The user is not given the opportunity to trace the running state of
# reducers. For example, the user cannot trace the sum and count of a
# running mean, only the running mean itself. Arguably this is a feature,
# because the sum and count can be considered implementation details, the
# hiding of which is the purpose of the `finalize` method.
with tf.name_scope(name or 'mcmc_sample_chain'):
if not kernel.is_calibrated:
warnings.warn(
'supplied `TransitionKernel` is not calibrated. Markov '
'chain may not converge to intended target distribution.')
if trace_fn is None:
trace_fn = lambda *args: ()
# Form kernel onion
reduction_kernel = with_reductions.WithReductions(inner_kernel=kernel,
reducer=reducer)
# User trace function should be called with
# - current chain state
# - kernel results structure of the passed-in kernel
# - if there were any reducers, their intermediate results
#
# `WithReductions` will show the TracingReducer the intermediate state as
# the kernel results of the onion named `reduction_kernel` above. This
# wrapper converts from that to what the user-supplied trace function needs
# to see.
def internal_trace_fn(curr_state, kr):
if reducer:
def fin(reducer, red_state):
return reducer.finalize(red_state)
# Extra level of list will be unwrapped by *reduction_args, below.
reduction_args = [
nest.map_structure_up_to(reducer, fin, reducer,
kr.reduction_results)
]
else:
reduction_args = []
return trace_fn(curr_state, kr.inner_results, *reduction_args)
trace_reducer = tracing_reducer.TracingReducer(
trace_fn=internal_trace_fn, size=num_results)
tracing_kernel = with_reductions.WithReductions(
inner_kernel=reduction_kernel,
reducer=trace_reducer,
)
# Bootstrap corresponding warm start
if previous_kernel_results is None:
previous_kernel_results = kernel.bootstrap_results(current_state)
reduction_pkr = reduction_kernel.bootstrap_results(
current_state, previous_kernel_results, previous_reducer_state)
tracing_pkr = tracing_kernel.bootstrap_results(current_state,
reduction_pkr)
# pylint: disable=unbalanced-tuple-unpacking
final_state, tracing_kernel_results = step.step_kernel(
num_steps=num_results,
current_state=current_state,
previous_kernel_results=tracing_pkr,
kernel=tracing_kernel,
return_final_kernel_results=True,
parallel_iterations=parallel_iterations,
seed=seed,
name=name,
)
trace = trace_reducer.finalize(
tracing_kernel_results.reduction_results)
reduction_kernel_results = tracing_kernel_results.inner_results
reduction_results = nest.map_structure_up_to(
reducer,
lambda r, s: r.finalize(s),
reducer,
reduction_kernel_results.reduction_results,
check_types=False)
user_kernel_results = reduction_kernel_results.inner_results
resume_kwargs = {
'current_state': final_state,
'previous_kernel_results': user_kernel_results,
'kernel': kernel,
'reducer': reducer,
'previous_reducer_state':
reduction_kernel_results.reduction_results,
}
return SampleChainResults(trace=trace,
reduction_results=reduction_results,
final_state=final_state,
final_kernel_results=user_kernel_results,
resume_kwargs=resume_kwargs)
def sample_fold(
num_steps,
current_state,
previous_kernel_results=None,
kernel=None,
reducer=None,
previous_reducer_state=None,
return_final_reducer_states=False,
num_burnin_steps=0,
num_steps_between_results=0,
parallel_iterations=10,
seed=None,
name=None,
):
"""Computes the requested reductions over the `kernel`'s samples.
To wit, runs the given `kernel` for `num_steps` steps, and consumes
the stream of samples with the given `Reducer`s' `one_step` method(s).
This runs in constant memory (unless a given `Reducer` builds a
large structure).
The driver internally composes the correct onion of `WithReductions`
and `SampleDiscardingKernel` to implement the requested optionally
thinned reduction; however, the kernel results of those applied
Transition Kernels will not be returned. Hence, if warm-restarting
reductions is desired, one should manually build the Transition Kernel
onion and use `tfp.experimental.mcmc.step_kernel`.
An arbitrary collection of `reducer` can be provided, and the resulting
finalized statistic(s) will be returned in an identical structure.
This function can sample from and reduce over multiple chains, in parallel.
Whether or not there are multiple chains is dictated by how the `kernel`
treats its inputs. Typically, the shape of the independent chains is shape of
the result of the `target_log_prob_fn` used by the `kernel` when applied to
the given `current_state`.
Args:
num_steps: Integer or scalar `Tensor` representing the number of `Reducer`
steps.
current_state: `Tensor` or Python `list` of `Tensor`s representing the
current state(s) of the Markov chain(s).
previous_kernel_results: A `Tensor` or a nested collection of `Tensor`s.
Warm-start for the auxiliary state needed by the given `kernel`.
If not supplied, `sample_fold` will cold-start with
`kernel.bootstrap_results`.
kernel: An instance of `tfp.mcmc.TransitionKernel` which implements one step
of the Markov chain.
reducer: A (possibly nested) structure of `Reducer`s to be evaluated
on the `kernel`'s samples. If no reducers are given (`reducer=None`),
then `None` will be returned in place of streaming calculations.
previous_reducer_state: A (possibly nested) structure of running states
corresponding to the structure in `reducer`. For resuming streaming
reduction computations begun in a previous run.
return_final_reducer_states: A Python `bool` giving whether to return
resumable final reducer states.
num_burnin_steps: Integer or scalar `Tensor` representing the number
of chain steps to take before starting to collect results.
Defaults to 0 (i.e., no burn-in).
num_steps_between_results: Integer or scalar `Tensor` representing
the number of chain steps between collecting a result. Only one out
of every `num_steps_between_samples + 1` steps is included in the
returned results. Defaults to 0 (i.e., no thinning).
parallel_iterations: The number of iterations allowed to run in parallel. It
must be a positive integer. See `tf.while_loop` for more details.
seed: Optional seed for reproducible sampling.
name: Python `str` name prefixed to Ops created by this function.
Default value: `None` (i.e., 'mcmc_sample_fold').
Returns:
reduction_results: A (possibly nested) structure of finalized reducer
statistics. The structure identically mimics that of `reducer`.
end_state: The final state of the Markov chain(s).
final_kernel_results: `collections.namedtuple` of internal calculations
used to advance the supplied `kernel`. These results do not include
the kernel results of `WithReductions` or `SampleDiscardingKernel`.
final_reducer_states: A (possibly nested) structure of final running reducer
states, if `return_final_reducer_states` was `True`. Can be used to
resume streaming reductions when continuing sampling.
"""
with tf.name_scope(name or 'mcmc_sample_fold'):
num_steps = tf.convert_to_tensor(num_steps,
dtype=tf.int32,
name='num_steps')
current_state = tf.nest.map_structure(
lambda x: tf.convert_to_tensor(x, name='current_state'),
current_state)
reducer_was_none = False
if reducer is None:
reducer = []
reducer_was_none = True
thinning_k = sample_discarding_kernel.SampleDiscardingKernel(
inner_kernel=kernel,
num_burnin_steps=num_burnin_steps,
num_steps_between_results=num_steps_between_results)
reduction_kernel = with_reductions.WithReductions(
inner_kernel=thinning_k,
reducer=reducer,
# Strip thinning kernel results layer
adjust_kr_fn=lambda kr: kr.inner_results,
)
if previous_kernel_results is None:
previous_kernel_results = kernel.bootstrap_results(current_state)
thinning_pkr = thinning_k.bootstrap_results(current_state,
previous_kernel_results)
reduction_pkr = reduction_kernel.bootstrap_results(
current_state, thinning_pkr, previous_reducer_state)
end_state, final_kernel_results = step.step_kernel(
num_steps=num_steps,
current_state=current_state,
previous_kernel_results=reduction_pkr,
kernel=reduction_kernel,
return_final_kernel_results=True,
parallel_iterations=parallel_iterations,
seed=seed,
name=name,
)
reduction_results = nest.map_structure_up_to(
reducer,
lambda r, s: r.finalize(s),
reducer,
final_kernel_results.reduction_results,
check_types=False)
if reducer_was_none:
reduction_results = None
# TODO(axch): Choose a friendly return value convention that
# - Doesn't burden the user with needless stuff when they don't want it
# - Supports warm restart when the user does want it
# - Doesn't trigger Pylint's unbalanced-tuple-unpacking warning.
if return_final_reducer_states:
return (reduction_results, end_state,
final_kernel_results.inner_results.inner_results,
final_kernel_results.reduction_results)
else:
return (reduction_results, end_state,
final_kernel_results.inner_results.inner_results)
def sample_chain_with_burnin(
num_results,
current_state,
previous_kernel_results=None,
kernel=None,
num_burnin_steps=0,
num_steps_between_results=0,
trace_fn=_trace_current_state,
parallel_iterations=10,
seed=None,
name=None,
):
"""Implements Markov chain Monte Carlo via repeated `TransitionKernel` steps.
This function samples from a Markov chain at `current_state` whose
stationary distribution is governed by the supplied `TransitionKernel`
instance (`kernel`).
This function can sample from multiple chains, in parallel. (Whether or not
there are multiple chains is dictated by the `kernel`.)
The `current_state` can be represented as a single `Tensor` or a `list` of
`Tensors` which collectively represent the current state.
Since MCMC states are correlated, it is sometimes desirable to produce
additional intermediate states, and then discard them, ending up with a set of
states with decreased autocorrelation. See [Owen (2017)][1]. Such 'thinning'
is made possible by setting `num_steps_between_results > 0`. The chain then
takes `num_steps_between_results` extra steps between the steps that make it
into the results. The extra steps are never materialized, and thus do not
increase memory requirements.
In addition to returning the chain state, this function supports tracing of
auxiliary variables used by the kernel. The traced values are selected by
specifying `trace_fn`. By default, all chain states but no kernel results are
traced.
Args:
num_results: Integer number of Markov chain draws.
current_state: `Tensor` or Python `list` of `Tensor`s representing the
current state(s) of the Markov chain(s).
previous_kernel_results: A `Tensor` or a nested collection of `Tensor`s
representing internal calculations made within the previous call to this
function (or as returned by `bootstrap_results`).
kernel: An instance of `tfp.mcmc.TransitionKernel` which implements one step
of the Markov chain.
num_burnin_steps: Integer number of chain steps to take before starting to
collect results.
Default value: 0 (i.e., no burn-in).
num_steps_between_results: Integer number of chain steps between collecting
a result. Only one out of every `num_steps_between_samples + 1` steps is
included in the returned results. The number of returned chain states is
still equal to `num_results`. Default value: 0 (i.e., no thinning).
trace_fn: A callable that takes in the current chain state and the previous
kernel results and return a `Tensor` or a nested collection of `Tensor`s
that is then traced along with the chain state.
parallel_iterations: The number of iterations allowed to run in parallel. It
must be a positive integer. See `tf.while_loop` for more details.
seed: Optional, a seed for reproducible sampling.
name: Python `str` name prefixed to Ops created by this function.
Default value: `None` (i.e.,
'experimental_mcmc_sample_chain_with_burnin').
Returns:
result: A `RunKernelResults` instance containing information about the
sampling run. Main field is `trace`, the history of outputs of
`trace_fn`. See `RunKernelResults` for contents of other fields.
#### References
[1]: Art B. Owen. Statistically efficient thinning of a Markov chain sampler.
_Technical Report_, 2017.
http://statweb.stanford.edu/~owen/reports/bestthinning.pdf
"""
with tf.name_scope(name or 'experimental_mcmc_sample_chain_with_burnin'):
if not kernel.is_calibrated:
warnings.warn(
'supplied `TransitionKernel` is not calibrated. Markov '
'chain may not converge to intended target distribution.')
if trace_fn is None:
trace_fn = lambda *args: ()
burnin_seed, sampling_seed = random.split_seed(seed, n=2)
# Burn-in run
chain_state, kr = step.step_kernel(
num_steps=num_burnin_steps,
current_state=current_state,
previous_kernel_results=previous_kernel_results,
kernel=kernel,
return_final_kernel_results=True,
parallel_iterations=parallel_iterations,
seed=burnin_seed,
name='burnin')
thinning_k = thinning_kernel.ThinningKernel(
kernel, num_steps_to_skip=num_steps_between_results)
# ThinningKernel doesn't wrap the kernel_results structure, so we don't need
# any of the usual munging.
results = sample.sample_chain(num_results=num_results,
current_state=chain_state,
previous_kernel_results=kr,
kernel=thinning_k,
trace_fn=trace_fn,
parallel_iterations=parallel_iterations,
seed=sampling_seed,
name='sampling')
del results.resume_kwargs['reducer']
del results.resume_kwargs['previous_reducer_state']
return results