def bootstrap_results(self, init_state):
"""Returns an object with the same type as returned by `one_step`.
Args:
init_state: `Tensor` or Python `list` of `Tensor`s representing the
initial state(s) of the Markov chain(s).
Returns:
kernel_results: A (possibly nested) `tuple`, `namedtuple` or `list` of
`Tensor`s representing internal calculations made within this function.
This inculdes replica states.
"""
with tf.name_scope(
mcmc_util.make_name(self.name, 'remc', 'bootstrap_results')):
init_state, unused_is_multipart_state = mcmc_util.prepare_state_parts(
init_state)
inverse_temperatures = tf.convert_to_tensor(
self.inverse_temperatures, name='inverse_temperatures')
if self._state_includes_replicas:
it_n_replica = inverse_temperatures.shape[0]
state_n_replica = init_state[0].shape[0]
if ((it_n_replica is not None)
and (state_n_replica is not None)
and (it_n_replica != state_n_replica)):
raise ValueError(
'Number of replicas implied by initial state ({}) must equal '
'number of replicas implied by inverse_temperatures ({}), but '
'did not'.format(it_n_replica, state_n_replica))
# We will now replicate each of a possible batch of initial stats, one for
# each inverse_temperature. So if init_state=[x, y] of shapes [Sx, Sy]
# then the new shape is [(T, Sx), (T, Sy)] where (a, b) means
# concatenation and T=shape(inverse_temperature).
num_replica = ps.size0(inverse_temperatures)
replica_shape = ps.convert_to_shape_tensor([num_replica])
if self._state_includes_replicas:
replica_states = init_state
else:
replica_states = [
tf.broadcast_to( # pylint: disable=g-complex-comprehension
x,
ps.concat([replica_shape, ps.shape(x)], axis=0),
name='replica_states') for x in init_state
]
target_log_prob_for_inner_kernel = _make_replica_target_log_prob_fn(
target_log_prob_fn=self.target_log_prob_fn,
inverse_temperatures=inverse_temperatures,
untempered_log_prob_fn=self.untempered_log_prob_fn,
tempered_log_prob_fn=self.tempered_log_prob_fn,
)
# TODO(b/159636942): Clean up the helpful error msg after 2020-11-10.
try:
inner_kernel = self.make_kernel_fn( # pylint: disable=not-callable
target_log_prob_for_inner_kernel)
except TypeError as e:
if 'argument' not in str(e):
raise
raise TypeError(
'`ReplicaExchangeMC`s `make_kernel_fn` no longer receives a second '
'(`seed`) argument. `TransitionKernel` instances now receive seeds '
'via `one_step`.')
replica_results = inner_kernel.bootstrap_results(replica_states)
pre_swap_replica_target_log_prob = _get_field(
replica_results, 'target_log_prob')
replica_and_batch_shape = ps.shape(
pre_swap_replica_target_log_prob)
batch_shape = replica_and_batch_shape[1:]
inverse_temperatures = mcmc_util.left_justified_broadcast_to(
inverse_temperatures, replica_and_batch_shape)
# Pretend we did a "null swap", which will always be accepted.
swaps = mcmc_util.left_justified_broadcast_to(
tf.range(num_replica), replica_and_batch_shape)
# is_swap_accepted.shape = [n_replica, n_replica] + batch_shape.
is_swap_accepted = distribution_util.rotate_transpose(tf.eye(
num_replica, batch_shape=batch_shape, dtype=tf.bool),
shift=2)
return ReplicaExchangeMCKernelResults(
post_swap_replica_states=replica_states,
pre_swap_replica_results=replica_results,
post_swap_replica_results=_set_swapped_fields_to_nan(
replica_results),
is_swap_proposed=is_swap_accepted,
is_swap_accepted=is_swap_accepted,
is_swap_proposed_adjacent=_sub_diag(is_swap_accepted),
is_swap_accepted_adjacent=_sub_diag(is_swap_accepted),
inverse_temperatures=self.inverse_temperatures,
swaps=swaps,
step_count=tf.zeros(shape=(), dtype=tf.int32),
seed=samplers.zeros_seed(),
)
def one_step(self, current_state, previous_kernel_results, seed=None):
"""Takes one step of the TransitionKernel.
Args:
current_state: `Tensor` or Python `list` of `Tensor`s representing the
current state(s) of the Markov chain(s).
previous_kernel_results: A (possibly nested) `tuple`, `namedtuple` or
`list` of `Tensor`s representing internal calculations made within the
previous call to this function (or as returned by `bootstrap_results`).
seed: Optional, a seed for reproducible sampling.
Returns:
next_state: `Tensor` or Python `list` of `Tensor`s representing the
next state(s) of the Markov chain(s).
kernel_results: A (possibly nested) `tuple`, `namedtuple` or `list` of
`Tensor`s representing internal calculations made within this function.
This inculdes replica states.
"""
# The code below propagates one step states of shape
# [n_replica] + batch_shape + event_shape.
#
# The step is done in three parts:
# 1) Call one_step to transition states via a tempered version of
# self.target_log_prob_fn (see _replica_target_log_prob).
# 2) Permute values in states
# 3) Update state-dependent values, such as log_probs.
#
# We chose to swap states, rather than temperatures, because...
# (i) If swapping temperatures, you *still* have to swap log_probs to
# determine acceptance, as well as states (for kernel results).
# So it's just as difficult to swap temperatures.
# (ii) If swapping temperatures, you have to take care to swap any user-
# supplied temperature related things (like step size).
# A-priori, we don't know what else will need to be swapped!
# (iii)In both cases, the kernel results need to be updated in a non-trivial
# manner....so we either special-case, or use bootstrap.
with tf.name_scope(mcmc_util.make_name(self.name, 'remc', 'one_step')):
# Force a read in case the `inverse_temperatures` is a `tf.Variable`.
inverse_temperatures = tf.convert_to_tensor(
previous_kernel_results.inverse_temperatures,
name='inverse_temperatures')
target_log_prob_for_inner_kernel = _make_replica_target_log_prob_fn(
target_log_prob_fn=self.target_log_prob_fn,
inverse_temperatures=inverse_temperatures,
untempered_log_prob_fn=self.untempered_log_prob_fn,
tempered_log_prob_fn=self.tempered_log_prob_fn,
)
# TODO(b/159636942): Clean up the helpful error msg after 2020-11-10.
try:
inner_kernel = self.make_kernel_fn( # pylint: disable=not-callable
target_log_prob_for_inner_kernel)
except TypeError as e:
if 'argument' not in str(e):
raise
raise TypeError(
'`ReplicaExchangeMC`s `make_kernel_fn` no longer receives a `seed` '
'argument. `TransitionKernel` instances now receive seeds via '
'`one_step`.')
seed = samplers.sanitize_seed(seed) # Retain for diagnostics.
inner_seed, swap_seed, logu_seed = samplers.split_seed(seed, n=3)
# Step the inner TransitionKernel.
[
pre_swap_replica_states,
pre_swap_replica_results,
] = inner_kernel.one_step(
previous_kernel_results.post_swap_replica_states,
previous_kernel_results.post_swap_replica_results,
seed=inner_seed)
pre_swap_replica_target_log_prob = _get_field(
# These are tempered log probs (have been divided by temperature).
pre_swap_replica_results,
'target_log_prob')
dtype = pre_swap_replica_target_log_prob.dtype
replica_and_batch_shape = ps.shape(
pre_swap_replica_target_log_prob)
batch_shape = replica_and_batch_shape[1:]
replica_and_batch_rank = ps.rank(pre_swap_replica_target_log_prob)
num_replica = ps.size0(inverse_temperatures)
inverse_temperatures = mcmc_util.left_justified_broadcast_to(
inverse_temperatures, replica_and_batch_shape)
# Now that each replica has done one_step, it is time to consider swaps.
# swap.shape = [n_replica], and is a "once only" permutation, meaning it
# is achievable by a sequence of pairwise permutations, where each element
# is moved at most once.
# E.g. if swaps = [1, 0, 2], we will consider swapping temperatures 0 and
# 1, keeping 2 fixed. This exact same swap is considered for *every*
# batch member. Of course some batch members may accept and some reject.
try:
swaps = tf.cast(
self.swap_proposal_fn( # pylint: disable=not-callable
num_replica,
batch_shape=batch_shape,
seed=swap_seed,
step_count=previous_kernel_results.step_count),
dtype=tf.int32)
except TypeError as e:
if 'step_count' not in str(e):
raise
warnings.warn(
'The `swap_proposal_fn` given to ReplicaExchangeMC did not accept '
'the `step_count` argument. Falling back to omitting the '
'argument. This fallback will be removed after 24-Oct-2020.'
)
swaps = tf.cast(
self.swap_proposal_fn( # pylint: disable=not-callable
num_replica,
batch_shape=batch_shape,
seed=swap_seed),
dtype=tf.int32)
null_swaps = mcmc_util.left_justified_expand_dims_like(
tf.range(num_replica, dtype=swaps.dtype), swaps)
swaps = _maybe_embed_swaps_validation(swaps, null_swaps,
self.validate_args)
# Un-temper the log probs for use in the swap acceptance ratio.
if self.tempered_log_prob_fn is None:
# Efficient way of re-evaluating target_log_prob_fn on the
# pre_swap_replica_states.
untempered_energy_ignoring_ulp = (
# Since untempered_log_prob_fn is None, we may assume
# inverse_temperatures > 0 (else the target is improper).
pre_swap_replica_target_log_prob / inverse_temperatures)
else:
# The untempered_log_prob_fn does not factor into the acceptance ratio.
# Proof: Suppose the tempered target is
# p_k(x) = f(x)^{beta_k} g(x),
# So f(x) is tempered, and g(x) is not. Then, the acceptance ratio for
# a 1 <--> 2 swap is...
# (p_1(x_2) p_2(x_1)) / (p_1(x_1) p_2(x_2))
# which depends only on f(x), since terms involving g(x) cancel.
untempered_energy_ignoring_ulp = self.tempered_log_prob_fn(
*pre_swap_replica_states)
# Since `swaps` is its own inverse permutation we automatically know the
# swap counterpart: range(num_replica). We use this idea to compute the
# acceptance in a vectorized manner at the cost of wasting roughly half
# our computation. Although we could use `unique` to solve this problem,
# we expect the cost of `unique` to be higher than the dozens of wasted
# arithmetic calculations. Worse, it'd mean we need dynamic sized Tensors
# (eg, using `tf.where(bool)`) and so we wouldn't be able to XLA compile.
# Note: diffs would normally be "proposed - current" however energy is
# flipped since `energy == -log_prob`.
# Note: The untempered_log_prob_fn (if provided) is not included in
# untempered_pre_swap_replica_target_log_prob, and hence does not factor
# into energy_diff. Why? Because, it cancels out in the acceptance ratio.
energy_diff = (untempered_energy_ignoring_ulp -
mcmc_util.index_remapping_gather(
untempered_energy_ignoring_ulp,
swaps,
name='gather_swap_tlp'))
swapped_inverse_temperatures = mcmc_util.index_remapping_gather(
inverse_temperatures, swaps, name='gather_swap_temps')
inverse_temp_diff = swapped_inverse_temperatures - inverse_temperatures
# If i and j are swapping, log_accept_ratio[] i and j are equal.
log_accept_ratio = (energy_diff *
mcmc_util.left_justified_expand_dims_to(
inverse_temp_diff, replica_and_batch_rank))
log_accept_ratio = tf.where(tf.math.is_finite(log_accept_ratio),
log_accept_ratio,
tf.constant(-np.inf, dtype=dtype))
# Produce log[Uniform] draws that are identical at swapped indices.
log_uniform = tf.math.log(
samplers.uniform(shape=replica_and_batch_shape,
dtype=dtype,
seed=logu_seed))
anchor_swaps = tf.minimum(swaps, null_swaps)
log_uniform = mcmc_util.index_remapping_gather(
log_uniform, anchor_swaps)
is_swap_accepted_mask = tf.less(log_uniform,
log_accept_ratio,
name='is_swap_accepted_mask')
def _swap_tensor(x):
return mcmc_util.choose(
is_swap_accepted_mask,
mcmc_util.index_remapping_gather(x, swaps), x)
post_swap_replica_states = [
_swap_tensor(s) for s in pre_swap_replica_states
]
expanded_null_swaps = mcmc_util.left_justified_broadcast_to(
null_swaps, replica_and_batch_shape)
is_swap_proposed = _compute_swap_notmatrix(
# Broadcast both so they have shape [num_replica] + batch_shape.
# This (i) makes them have same shape as is_swap_accepted, and
# (ii) keeps shape consistent if someday swaps has a batch shape.
expanded_null_swaps,
mcmc_util.left_justified_broadcast_to(swaps,
replica_and_batch_shape))
# To get is_swap_accepted in ordered position, we use
# _compute_swap_notmatrix on current and next replica positions.
post_swap_replica_position = _swap_tensor(expanded_null_swaps)
is_swap_accepted = _compute_swap_notmatrix(
post_swap_replica_position, expanded_null_swaps)
if self._state_includes_replicas:
post_swap_states = post_swap_replica_states
else:
post_swap_states = [s[0] for s in post_swap_replica_states]
post_swap_replica_results = _set_swapped_fields_to_nan(
_swap_log_prob_and_maybe_grads(pre_swap_replica_results,
post_swap_replica_states,
inner_kernel))
if mcmc_util.is_list_like(current_state):
# We *always* canonicalize the states in the kernel results.
states = post_swap_states
else:
states = post_swap_states[0]
post_swap_kernel_results = ReplicaExchangeMCKernelResults(
post_swap_replica_states=post_swap_replica_states,
pre_swap_replica_results=pre_swap_replica_results,
post_swap_replica_results=post_swap_replica_results,
is_swap_proposed=is_swap_proposed,
is_swap_accepted=is_swap_accepted,
is_swap_proposed_adjacent=_sub_diag(is_swap_proposed),
is_swap_accepted_adjacent=_sub_diag(is_swap_accepted),
# Store the original pkr.inverse_temperatures in case its a
# `tf.Variable`.
inverse_temperatures=previous_kernel_results.
inverse_temperatures,
swaps=swaps,
step_count=previous_kernel_results.step_count + 1,
seed=seed,
)
return states, post_swap_kernel_results
def bootstrap_results(self, init_state):
"""Returns an object with the same type as returned by `one_step`.
Args:
init_state: `Tensor` or Python `list` of `Tensor`s representing the
initial state(s) of the Markov chain(s).
Returns:
kernel_results: A (possibly nested) `tuple`, `namedtuple` or `list` of
`Tensor`s representing internal calculations made within this function.
This inculdes replica states.
"""
with tf.name_scope(
mcmc_util.make_name(self.name, 'remc', 'bootstrap_results')):
init_state, unused_is_multipart_state = mcmc_util.prepare_state_parts(
init_state)
inverse_temperatures = tf.convert_to_tensor(
self.inverse_temperatures, name='inverse_temperatures')
if self._state_includes_replicas:
it_n_replica = inverse_temperatures.shape[0]
state_n_replica = init_state[0].shape[0]
if ((it_n_replica is not None)
and (state_n_replica is not None)
and (it_n_replica != state_n_replica)):
raise ValueError(
'Number of replicas implied by initial state ({}) must equal '
'number of replicas implied by inverse_temperatures ({}), but '
'did not'.format(it_n_replica, state_n_replica))
# We will now replicate each of a possible batch of initial stats, one for
# each inverse_temperature. So if init_state=[x, y] of shapes [Sx, Sy]
# then the new shape is [(T, Sx), (T, Sy)] where (a, b) means
# concatenation and T=shape(inverse_temperature).
num_replica = ps.size0(inverse_temperatures)
replica_shape = tf.convert_to_tensor([num_replica])
if self._state_includes_replicas:
replica_states = init_state
else:
replica_states = [
tf.broadcast_to( # pylint: disable=g-complex-comprehension
x,
ps.concat([replica_shape, ps.shape(x)], axis=0),
name='replica_states') for x in init_state
]
target_log_prob_for_inner_kernel = _make_replica_target_log_prob_fn(
self.target_log_prob_fn, inverse_temperatures)
# Seed handling complexity is due to users possibly expecting an old-style
# stateful seed to be passed to `self.make_kernel_fn`.
# In other words:
# - We try `make_kernel_fn` without a seed first; this is the future. The
# kernel will receive a seed later, as part of `one_step`.
# - If the user code doesn't like that (Python complains about a missing
# required argument), we fall back to the previous behavior and warn.
try:
inner_kernel = self.make_kernel_fn( # pylint: disable=not-callable
target_log_prob_for_inner_kernel)
except TypeError as e:
if 'argument' not in str(e):
raise
warnings.warn(
'The second (`seed`) argument to `ReplicaExchangeMC`s '
'`make_kernel_fn` is deprecated. `TransitionKernel` instances now '
'receive seeds via `bootstrap_results` and `one_step`. This '
'fallback may become an error 2020-09-20.')
inner_kernel = self.make_kernel_fn( # pylint: disable=not-callable
target_log_prob_for_inner_kernel, self._seed_stream())
replica_results = inner_kernel.bootstrap_results(replica_states)
pre_swap_replica_target_log_prob = _get_field(
replica_results, 'target_log_prob')
replica_and_batch_shape = ps.shape(
pre_swap_replica_target_log_prob)
batch_shape = replica_and_batch_shape[1:]
inverse_temperatures = mcmc_util.left_justified_broadcast_to(
inverse_temperatures, replica_and_batch_shape)
# Pretend we did a "null swap", which will always be accepted.
swaps = mcmc_util.left_justified_broadcast_to(
tf.range(num_replica), replica_and_batch_shape)
# is_swap_accepted.shape = [n_replica, n_replica] + batch_shape.
is_swap_accepted = distribution_util.rotate_transpose(tf.eye(
num_replica, batch_shape=batch_shape, dtype=tf.bool),
shift=2)
post_swap_replica_results = _make_post_swap_replica_results(
replica_results,
inverse_temperatures,
inverse_temperatures,
is_swap_accepted[0],
lambda x: x,
)
return ReplicaExchangeMCKernelResults(
post_swap_replica_states=replica_states,
pre_swap_replica_results=replica_results,
post_swap_replica_results=post_swap_replica_results,
is_swap_proposed=is_swap_accepted,
is_swap_accepted=is_swap_accepted,
is_swap_proposed_adjacent=_sub_diag(is_swap_accepted),
is_swap_accepted_adjacent=_sub_diag(is_swap_accepted),
inverse_temperatures=self.inverse_temperatures,
swaps=swaps,
step_count=tf.zeros(shape=(), dtype=tf.int32),
seed=samplers.zeros_seed(),
)
def one_step(self, current_state, previous_kernel_results, seed=None):
"""Takes one step of the TransitionKernel.
Args:
current_state: `Tensor` or Python `list` of `Tensor`s representing the
current state(s) of the Markov chain(s).
previous_kernel_results: A (possibly nested) `tuple`, `namedtuple` or
`list` of `Tensor`s representing internal calculations made within the
previous call to this function (or as returned by `bootstrap_results`).
seed: Optional, a seed for reproducible sampling.
Returns:
next_state: `Tensor` or Python `list` of `Tensor`s representing the
next state(s) of the Markov chain(s).
kernel_results: A (possibly nested) `tuple`, `namedtuple` or `list` of
`Tensor`s representing internal calculations made within this function.
This inculdes replica states.
"""
# The code below propagates one step states of shape
# [n_replica] + batch_shape + event_shape.
#
# The step is done in three parts:
# 1) Call one_step to transition states via a tempered version of
# self.target_log_prob_fn (see _replica_target_log_prob).
# 2) Permute values in states
# 3) Update state-dependent values, such as log_probs.
#
# We chose to swap states, rather than temperatures, because...
# (i) If swapping temperatures, you *still* have to swap log_probs to
# determine acceptance, as well as states (for kernel results).
# So it's just as difficult to swap temperatures.
# (ii) If swapping temperatures, you have to take care to swap any user-
# supplied temperature related things (like step size).
# A-priori, we don't know what else will need to be swapped!
# (iii)In both cases, the kernel results need to be updated in a non-trivial
# manner....so we either special-case, or use bootstrap.
with tf.name_scope(mcmc_util.make_name(self.name, 'remc', 'one_step')):
# Force a read in case the `inverse_temperatures` is a `tf.Variable`.
inverse_temperatures = tf.convert_to_tensor(
previous_kernel_results.inverse_temperatures,
name='inverse_temperatures')
target_log_prob_for_inner_kernel = _make_replica_target_log_prob_fn(
self.target_log_prob_fn, inverse_temperatures)
# Seed handling complexity is due to users possibly expecting an old-style
# stateful seed to be passed to `self.make_kernel_fn`, and no seed
# expected by `kernel.one_step`.
# In other words:
# - We try `make_kernel_fn` without a seed first; this is the future. The
# kernel will receive a seed later, as part of `one_step`.
# - If the user code doesn't like that (Python complains about a missing
# required argument), we warn and fall back to the previous behavior.
try:
inner_kernel = self.make_kernel_fn( # pylint: disable=not-callable
target_log_prob_for_inner_kernel)
except TypeError as e:
if 'argument' not in str(e):
raise
warnings.warn(
'The `seed` argument to `ReplicaExchangeMC`s `make_kernel_fn` is '
'deprecated. `TransitionKernel` instances now receive seeds via '
'`one_step`.')
inner_kernel = self.make_kernel_fn( # pylint: disable=not-callable
target_log_prob_for_inner_kernel, self._seed_stream())
# Now that we've constructed the TransitionKernel instance:
# - If we were given a seed, we sanitize it to stateless and pass along
# to `kernel.one_step`. If it doesn't like that, we crash and propagate
# the error. Rationale: The contract is stateless sampling given
# seed, and doing otherwise would not meet it.
# - If not given a seed, we don't pass one along. This avoids breaking
# underlying kernels lacking a `seed` arg on `one_step`.
# TODO(b/159636942): Clean up after 2020-09-20.
if seed is not None:
seed = samplers.sanitize_seed(seed)
inner_seed, swap_seed, logu_seed = samplers.split_seed(
seed, n=3, salt='remc_one_step')
inner_kwargs = dict(seed=inner_seed)
else:
if self._seed_stream.original_seed is not None:
warnings.warn(mcmc_util.SEED_CTOR_ARG_DEPRECATION_MSG)
inner_kwargs = {}
swap_seed, logu_seed = samplers.split_seed(self._seed_stream())
[
pre_swap_replica_states,
pre_swap_replica_results,
] = inner_kernel.one_step(
previous_kernel_results.post_swap_replica_states,
previous_kernel_results.post_swap_replica_results,
**inner_kwargs)
pre_swap_replica_target_log_prob = _get_field(
# These are tempered log probs (have been divided by temperature).
pre_swap_replica_results,
'target_log_prob')
dtype = pre_swap_replica_target_log_prob.dtype
replica_and_batch_shape = ps.shape(
pre_swap_replica_target_log_prob)
batch_shape = replica_and_batch_shape[1:]
replica_and_batch_rank = ps.rank(pre_swap_replica_target_log_prob)
num_replica = ps.size0(inverse_temperatures)
inverse_temperatures = mcmc_util.left_justified_broadcast_to(
inverse_temperatures, replica_and_batch_shape)
# Now that each replica has done one_step, it is time to consider swaps.
# swap.shape = [n_replica], and is a "once only" permutation, meaning it
# is achievable by a sequence of pairwise permutations, where each element
# is moved at most once.
# E.g. if swaps = [1, 0, 2], we will consider swapping temperatures 0 and
# 1, keeping 2 fixed. This exact same swap is considered for *every*
# batch member. Of course some batch members may accept and some reject.
try:
swaps = tf.cast(
self.swap_proposal_fn( # pylint: disable=not-callable
num_replica,
batch_shape=batch_shape,
seed=swap_seed,
step_count=previous_kernel_results.step_count),
dtype=tf.int32)
except TypeError as e:
if 'step_count' not in str(e):
raise
warnings.warn(
'The `swap_proposal_fn` given to ReplicaExchangeMC did not accept '
'the `step_count` argument. Falling back to omitting the '
'argument. This fallback will be removed after 24-Oct-2020.'
)
swaps = tf.cast(
self.swap_proposal_fn( # pylint: disable=not-callable
num_replica,
batch_shape=batch_shape,
seed=swap_seed),
dtype=tf.int32)
null_swaps = mcmc_util.left_justified_expand_dims_like(
tf.range(num_replica, dtype=swaps.dtype), swaps)
swaps = _maybe_embed_swaps_validation(swaps, null_swaps,
self.validate_args)
# Un-temper the log probs. E.g., for replica k, at point x_k, this is
# Log[p(x_k)], and *not* Log[p_x(x_k)] = Log[p(x_k)] * beta_k.
untempered_pre_swap_replica_target_log_prob = (
pre_swap_replica_target_log_prob / inverse_temperatures)
# Since `swaps` is its own inverse permutation we automatically know the
# swap counterpart: range(num_replica). We use this idea to compute the
# acceptance in a vectorized manner at the cost of wasting roughly half
# our computation. Although we could use `unique` to solve this problem,
# we expect the cost of `unique` to be higher than the dozens of wasted
# arithmetic calculations. Worse, it'd mean we need dynamic sized Tensors
# (eg, using `tf.where(bool)`) and so we wouldn't be able to XLA compile.
# Note: diffs would normally be "proposed - current" however energy is
# flipped since `energy == -log_prob`.
energy_diff = (untempered_pre_swap_replica_target_log_prob -
mcmc_util.index_remapping_gather(
untempered_pre_swap_replica_target_log_prob,
swaps,
name='gather_swap_tlp'))
swapped_inverse_temperatures = mcmc_util.index_remapping_gather(
inverse_temperatures, swaps, name='gather_swap_temps')
inverse_temp_diff = swapped_inverse_temperatures - inverse_temperatures
# If i and j are swapping, log_accept_ratio[] i and j are equal.
log_accept_ratio = (energy_diff *
mcmc_util.left_justified_expand_dims_to(
inverse_temp_diff, replica_and_batch_rank))
log_accept_ratio = tf.where(tf.math.is_finite(log_accept_ratio),
log_accept_ratio,
tf.constant(-np.inf, dtype=dtype))
# Produce Log[Uniform] draws that are identical at swapped indices.
log_uniform = tf.math.log(
samplers.uniform(shape=replica_and_batch_shape,
dtype=dtype,
seed=logu_seed))
anchor_swaps = tf.minimum(swaps, null_swaps)
log_uniform = mcmc_util.index_remapping_gather(
log_uniform, anchor_swaps)
is_swap_accepted_mask = tf.less(log_uniform,
log_accept_ratio,
name='is_swap_accepted_mask')
def _swap_tensor(x):
return mcmc_util.choose(
is_swap_accepted_mask,
mcmc_util.index_remapping_gather(x, swaps), x)
post_swap_replica_states = [
_swap_tensor(s) for s in pre_swap_replica_states
]
expanded_null_swaps = mcmc_util.left_justified_broadcast_to(
null_swaps, replica_and_batch_shape)
is_swap_proposed = _compute_swap_notmatrix(
# Broadcast both so they have shape [num_replica] + batch_shape.
# This (i) makes them have same shape as is_swap_accepted, and
# (ii) keeps shape consistent if someday swaps has a batch shape.
expanded_null_swaps,
mcmc_util.left_justified_broadcast_to(swaps,
replica_and_batch_shape))
# To get is_swap_accepted in ordered position, we use
# _compute_swap_notmatrix on current and next replica positions.
post_swap_replica_position = _swap_tensor(expanded_null_swaps)
is_swap_accepted = _compute_swap_notmatrix(
post_swap_replica_position, expanded_null_swaps)
if self._state_includes_replicas:
post_swap_states = post_swap_replica_states
else:
post_swap_states = [s[0] for s in post_swap_replica_states]
post_swap_replica_results = _make_post_swap_replica_results(
pre_swap_replica_results, inverse_temperatures,
swapped_inverse_temperatures, is_swap_accepted_mask,
_swap_tensor)
if mcmc_util.is_list_like(current_state):
# We *always* canonicalize the states in the kernel results.
states = post_swap_states
else:
states = post_swap_states[0]
post_swap_kernel_results = ReplicaExchangeMCKernelResults(
post_swap_replica_states=post_swap_replica_states,
pre_swap_replica_results=pre_swap_replica_results,
post_swap_replica_results=post_swap_replica_results,
is_swap_proposed=is_swap_proposed,
is_swap_accepted=is_swap_accepted,
is_swap_proposed_adjacent=_sub_diag(is_swap_proposed),
is_swap_accepted_adjacent=_sub_diag(is_swap_accepted),
# Store the original pkr.inverse_temperatures in case its a
# `tf.Variable`.
inverse_temperatures=previous_kernel_results.
inverse_temperatures,
swaps=swaps,
step_count=previous_kernel_results.step_count + 1,
seed=samplers.zeros_seed() if seed is None else seed,
)
return states, post_swap_kernel_results
def bootstrap_results(self, init_state):
"""Returns an object with the same type as returned by `one_step`.
Args:
init_state: `Tensor` or Python `list` of `Tensor`s representing the
initial state(s) of the Markov chain(s).
Returns:
kernel_results: A (possibly nested) `tuple`, `namedtuple` or `list` of
`Tensor`s representing internal calculations made within this function.
This inculdes replica states.
"""
with tf.name_scope(
mcmc_util.make_name(self.name, 'remc', 'bootstrap_results')):
init_state, unused_is_multipart_state = mcmc_util.prepare_state_parts(
init_state)
inverse_temperatures = tf.convert_to_tensor(
self.inverse_temperatures, name='inverse_temperatures')
# We will now replicate each of a possible batch of initial stats, one for
# each inverse_temperature. So if init_state=[x, y] of shapes [Sx, Sy]
# then the new shape is [(T, Sx), (T, Sy)] where (a, b) means
# concatenation and T=shape(inverse_temperature).
num_replica = prefer_static.size0(inverse_temperatures)
replica_shape = tf.convert_to_tensor([num_replica])
replica_states = [
tf.broadcast_to( # pylint: disable=g-complex-comprehension
x,
prefer_static.concat(
[replica_shape, prefer_static.shape(x)], axis=0),
name='replica_states') for x in init_state
]
inner_kernel = self.make_kernel_fn( # pylint: disable=not-callable
_make_replica_target_log_prob_fn(self.target_log_prob_fn,
inverse_temperatures),
self._seed_stream())
replica_results = inner_kernel.bootstrap_results(replica_states)
pre_swap_replica_target_log_prob = _get_field(
replica_results, 'target_log_prob')
replica_and_batch_shape = prefer_static.shape(
pre_swap_replica_target_log_prob)
batch_shape = replica_and_batch_shape[1:]
inverse_temperatures = mcmc_util.left_justified_broadcast_to(
inverse_temperatures, replica_and_batch_shape)
# Pretend we did a "null swap", which will always be accepted.
swaps = mcmc_util.left_justified_broadcast_to(
tf.range(num_replica), replica_and_batch_shape)
# is_swap_accepted.shape = [n_replica, n_replica] + batch_shape.
is_swap_accepted = distribution_util.rotate_transpose(tf.eye(
num_replica, batch_shape=batch_shape, dtype=tf.bool),
shift=2)
post_swap_replica_results = _make_post_swap_replica_results(
replica_results,
inverse_temperatures,
inverse_temperatures,
is_swap_accepted[0],
lambda x: x,
)
return ReplicaExchangeMCKernelResults(
post_swap_replica_states=replica_states,
pre_swap_replica_results=replica_results,
post_swap_replica_results=post_swap_replica_results,
is_swap_proposed=is_swap_accepted,
is_swap_accepted=is_swap_accepted,
is_swap_proposed_adjacent=_sub_diag(is_swap_accepted),
is_swap_accepted_adjacent=_sub_diag(is_swap_accepted),
inverse_temperatures=self.inverse_temperatures,
swaps=swaps,
)
def one_step(self, current_state, previous_kernel_results):
"""Takes one step of the TransitionKernel.
Args:
current_state: `Tensor` or Python `list` of `Tensor`s representing the
current state(s) of the Markov chain(s).
previous_kernel_results: A (possibly nested) `tuple`, `namedtuple` or
`list` of `Tensor`s representing internal calculations made within the
previous call to this function (or as returned by `bootstrap_results`).
Returns:
next_state: `Tensor` or Python `list` of `Tensor`s representing the
next state(s) of the Markov chain(s).
kernel_results: A (possibly nested) `tuple`, `namedtuple` or `list` of
`Tensor`s representing internal calculations made within this function.
This inculdes replica states.
"""
# The code below propagates one step states of shape
# [n_replica] + batch_shape + event_shape.
#
# The step is done in three parts:
# 1) Call one_step to transition states via a tempered version of
# self.target_log_prob_fn (see _replica_target_log_prob).
# 2) Permute values in states
# 3) Update state-dependent values, such as log_probs.
#
# We chose to swap states, rather than temperatures, because...
# (i) If swapping temperatures, you *still* have to swap log_probs to
# determine acceptance, as well as states (for kernel results).
# So it's just as difficult to swap temperatures.
# (ii) If swapping temperatures, you have to take care to swap any user-
# supplied temperature related things (like step size).
# A-priori, we don't know what else will need to be swapped!
# (iii)In both cases, the kernel results need to be updated in a non-trivial
# manner....so we either special-case, or use bootstrap.
with tf.name_scope(mcmc_util.make_name(self.name, 'remc', 'one_step')):
# Force a read in case the `inverse_temperatures` is a `tf.Variable`.
inverse_temperatures = tf.convert_to_tensor(
previous_kernel_results.inverse_temperatures,
name='inverse_temperatures')
inner_kernel = self.make_kernel_fn( # pylint: disable=not-callable
_make_replica_target_log_prob_fn(self.target_log_prob_fn,
inverse_temperatures),
self._seed_stream())
[
pre_swap_replica_states,
pre_swap_replica_results,
] = inner_kernel.one_step(
previous_kernel_results.post_swap_replica_states,
previous_kernel_results.post_swap_replica_results)
pre_swap_replica_target_log_prob = _get_field(
# These are tempered log probs (have been divided by temperature).
pre_swap_replica_results,
'target_log_prob')
dtype = pre_swap_replica_target_log_prob.dtype
replica_and_batch_shape = prefer_static.shape(
pre_swap_replica_target_log_prob)
batch_shape = replica_and_batch_shape[1:]
replica_and_batch_rank = prefer_static.rank(
pre_swap_replica_target_log_prob)
num_replica = prefer_static.size0(inverse_temperatures)
inverse_temperatures = mcmc_util.left_justified_broadcast_to(
inverse_temperatures, replica_and_batch_shape)
# Now that each replica has done one_step, it is time to consider swaps.
# swap.shape = [n_replica], and is a "once only" permutation, meaning it
# is achievable by a sequence of pairwise permutations, where each element
# is moved at most once.
# E.g. if swaps = [1, 0, 2], we will consider swapping temperatures 0 and
# 1, keeping 2 fixed. This exact same swap is considered for *every*
# batch member. Of course some batch members may accept and some reject.
swaps = tf.cast(
self.swap_proposal_fn( # pylint: disable=not-callable
num_replica,
batch_shape=batch_shape,
seed=self._seed_stream()),
dtype=tf.int32)
null_swaps = mcmc_util.left_justified_expand_dims_like(
tf.range(num_replica, dtype=swaps.dtype), swaps)
swaps = _maybe_embed_swaps_validation(swaps, null_swaps,
self.validate_args)
# Un-temper the log probs. E.g., for replica k, at point x_k, this is
# Log[p(x_k)], and *not* Log[p_x(x_k)] = Log[p(x_k)] * beta_k.
untempered_pre_swap_replica_target_log_prob = (
pre_swap_replica_target_log_prob / inverse_temperatures)
# Since `swaps` is its own inverse permutation we automatically know the
# swap counterpart: range(num_replica). We use this idea to compute the
# acceptance in a vectorized manner at the cost of wasting roughly half
# our computation. Although we could use `unique` to solve this problem,
# we expect the cost of `unique` to be higher than the dozens of wasted
# arithmetic calculations. Worse, it'd mean we need dynamic sized Tensors
# (eg, using `tf.where(bool)`) and so we wouldn't be able to XLA compile.
# Note: diffs would normally be "proposed - current" however energy is
# flipped since `energy == -log_prob`.
energy_diff = (untempered_pre_swap_replica_target_log_prob -
mcmc_util.index_remapping_gather(
untempered_pre_swap_replica_target_log_prob,
swaps,
name='gather_swap_tlp'))
swapped_inverse_temperatures = mcmc_util.index_remapping_gather(
inverse_temperatures, swaps, name='gather_swap_temps')
inverse_temp_diff = swapped_inverse_temperatures - inverse_temperatures
# If i and j are swapping, log_accept_ratio[] i and j are equal.
log_accept_ratio = (energy_diff *
mcmc_util.left_justified_expand_dims_to(
inverse_temp_diff, replica_and_batch_rank))
log_accept_ratio = tf.where(tf.math.is_finite(log_accept_ratio),
log_accept_ratio,
tf.constant(-np.inf, dtype=dtype))
# Produce Log[Uniform] draws that are identical at swapped indices.
log_uniform = tf.math.log(
tf.random.uniform(shape=replica_and_batch_shape,
dtype=dtype,
seed=self._seed_stream()))
anchor_swaps = tf.minimum(swaps, null_swaps)
log_uniform = mcmc_util.index_remapping_gather(
log_uniform, anchor_swaps)
is_swap_accepted_mask = tf.less(log_uniform,
log_accept_ratio,
name='is_swap_accepted_mask')
def _swap_tensor(x):
return mcmc_util.choose(
is_swap_accepted_mask,
mcmc_util.index_remapping_gather(x, swaps), x)
post_swap_replica_states = [
_swap_tensor(s) for s in pre_swap_replica_states
]
expanded_null_swaps = mcmc_util.left_justified_broadcast_to(
null_swaps, replica_and_batch_shape)
is_swap_proposed = _compute_swap_notmatrix(
# Broadcast both so they have shape [num_replica] + batch_shape.
# This (i) makes them have same shape as is_swap_accepted, and
# (ii) keeps shape consistent if someday swaps has a batch shape.
expanded_null_swaps,
mcmc_util.left_justified_broadcast_to(swaps,
replica_and_batch_shape))
# To get is_swap_accepted in ordered position, we use
# _compute_swap_notmatrix on current and next replica positions.
post_swap_replica_position = _swap_tensor(expanded_null_swaps)
is_swap_accepted = _compute_swap_notmatrix(
post_swap_replica_position, expanded_null_swaps)
post_swap_states = [s[0] for s in post_swap_replica_states]
post_swap_replica_results = _make_post_swap_replica_results(
pre_swap_replica_results, inverse_temperatures,
swapped_inverse_temperatures, is_swap_accepted_mask,
_swap_tensor)
if mcmc_util.is_list_like(current_state):
# We *always* canonicalize the states in the kernel results.
states = post_swap_states
else:
states = post_swap_states[0]
post_swap_kernel_results = ReplicaExchangeMCKernelResults(
post_swap_replica_states=post_swap_replica_states,
pre_swap_replica_results=pre_swap_replica_results,
post_swap_replica_results=post_swap_replica_results,
is_swap_proposed=is_swap_proposed,
is_swap_accepted=is_swap_accepted,
is_swap_proposed_adjacent=_sub_diag(is_swap_proposed),
is_swap_accepted_adjacent=_sub_diag(is_swap_accepted),
# Store the original pkr.inverse_temperatures in case its a
# `tf.Variable`.
inverse_temperatures=previous_kernel_results.
inverse_temperatures,
swaps=swaps,
)
return states, post_swap_kernel_results
