# Copyright 2018 The TensorFlow Probability Authors. # # Licensed under the Apache License, Version 2.0 (the "License"); # you may not use this file except in compliance with the License. # You may obtain a copy of the License at # # http://www.apache.org/licenses/LICENSE-2.0 # # Unless required by applicable law or agreed to in writing, software # distributed under the License is distributed on an "AS IS" BASIS, # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. # See the License for the specific language governing permissions and # limitations under the License. # ============================================================================ """TransformedTransitionKernel Transition Kernel.""" from __future__ import absolute_import from __future__ import division from __future__ import print_function import collections from tensorflow_probability.python.internal.backend.numpy.compat import v2 as tf from tensorflow_probability.python.internal._numpy import prefer_static from tensorflow_probability.python.mcmc._numpy import kernel as kernel_base from tensorflow_probability.python.mcmc.internal._numpy import util as mcmc_util from tensorflow_probability.python.internal.backend.numpy import deprecation # pylint: disable=g-direct-tensorflow-import __all__ = [ 'TransformedTransitionKernel', ] class TransformedTransitionKernelResults( mcmc_util.PrettyNamedTupleMixin, collections.namedtuple('TransformedTransitionKernelResults', ['transformed_state', 'inner_results', ])): """Internal state and diagnostics for Transformed kernel.""" __slots__ = () def make_log_det_jacobian_fn(bijector, direction): """Makes a function which applies a list of Bijectors' `log_det_jacobian`s.""" if not mcmc_util.is_list_like(bijector): bijector = [bijector] attr = '{}_log_det_jacobian'.format(direction) def fn(state_parts, event_ndims): return [ getattr(b, attr)(sp, event_ndims=e) for b, e, sp in zip(bijector, event_ndims, state_parts) ] return fn def make_transform_fn(bijector, direction): """Makes a function which applies a list of Bijectors' `forward`s.""" if not mcmc_util.is_list_like(bijector): bijector = [bijector] def fn(state_parts): return [getattr(b, direction)(sp) for b, sp in zip(bijector, state_parts)] return fn def make_transformed_log_prob( log_prob_fn, bijector, direction, enable_bijector_caching=True): """Transforms a log_prob function using bijectors. Note: `direction = 'inverse'` corresponds to the transformation calculation done in `tfp.distributions.TransformedDistribution.log_prob`. Args: log_prob_fn: Python `callable` taking an argument for each state part which returns a `Tensor` representing the joint `log` probability of those state parts. bijector: `tfp.bijectors.Bijector`-like instance (or list thereof) corresponding to each state part. When `direction = 'forward'` the `Bijector`-like instance must possess members `forward` and `forward_log_det_jacobian` (and corresponding when `direction = 'inverse'`). direction: Python `str` being either `'forward'` or `'inverse'` which indicates the nature of the bijector transformation applied to each state part. enable_bijector_caching: Python `bool` indicating if `Bijector` caching should be invalidated. Default value: `True`. Returns: transformed_log_prob_fn: Python `callable` which takes an argument for each transformed state part and returns a `Tensor` representing the joint `log` probability of the transformed state parts. """ if direction not in {'forward', 'inverse'}: raise ValueError('Argument `direction` must be either `"forward"` or ' '`"inverse"`; saw "{}".'.format(direction)) fn = make_transform_fn(bijector, direction) ldj_fn = make_log_det_jacobian_fn(bijector, direction) def transformed_log_prob_fn(*state_parts): """Log prob of the transformed state.""" if not enable_bijector_caching: state_parts = [tf.identity(sp) for sp in state_parts] tlp = log_prob_fn(*fn(state_parts)) tlp_rank = prefer_static.rank(tlp) event_ndims = [(prefer_static.rank(sp) - tlp_rank) for sp in state_parts] return tlp + sum(ldj_fn(state_parts, event_ndims)) return transformed_log_prob_fn def _make_kernel_stack(kernel): kernel_stack = [kernel] while 'target_log_prob_fn' not in kernel.parameters: if 'inner_kernel' not in kernel.parameters: raise ValueError('"None of the nested `inner_kernel`s contains a ' '`target_log_prob_fn`."') kernel = kernel.inner_kernel kernel_stack.append(kernel) return kernel_stack def _find_nested_target_log_prob_recursively(kernel): kernel_stack = _make_kernel_stack(kernel) target_log_prob_fn = kernel_stack[-1].parameters['target_log_prob_fn'] return target_log_prob_fn def _update_target_log_prob(kernel, new_target_log_prob): """Replaces `target_log_prob_fn` of outermost `inner_kernel` of `kernel`.""" kernel_stack = _make_kernel_stack(kernel) # Update to target_log_prob to `new_target_log_prob`. prev_kernel = kernel_stack.pop().copy(target_log_prob_fn=new_target_log_prob) # Propagate the change upwards by reconstructing wrapper kernels. while kernel_stack: curr_kernel = kernel_stack.pop() with deprecation.silence(): updated_kernel = type(prev_kernel)(**prev_kernel.parameters) curr_kernel = curr_kernel.copy(inner_kernel=updated_kernel) prev_kernel = curr_kernel return prev_kernel class TransformedTransitionKernel(kernel_base.TransitionKernel): """TransformedTransitionKernel applies a bijector to the MCMC's state space. The `TransformedTransitionKernel` `TransitionKernel` enables fitting a `tfp.bijectors.Bijector` which serves to decorrelate the Markov chain Monte Carlo (MCMC) event dimensions thus making the chain mix faster. This is particularly useful when the geometry of the target distribution is unfavorable. In such cases it may take many evaluations of the `target_log_prob_fn` for the chain to mix between faraway states. The idea of training an affine function to decorrelate chain event dims was presented in [Parno and Marzouk (2014)][1]. Used in conjunction with the `HamiltonianMonteCarlo` `TransitionKernel`, the [Parno and Marzouk (2014)][1] idea is an instance of Riemannian manifold HMC [(Girolami and Calderhead, 2011)][2]. The `TransformedTransitionKernel` enables arbitrary bijective transformations of arbitrary `TransitionKernel`s, e.g., one could use bijectors `tfp.bijectors.Affine`, `tfp.bijectors.RealNVP`, etc. with transition kernels `tfp.mcmc.HamiltonianMonteCarlo`, `tfp.mcmc.RandomWalkMetropolis`, etc. ### Transforming nested kernels `TransformedTransitionKernel` can operate on multiply nested kernels, as in the following example: ```python tfp.mcmc.TransformedTransitionKernel( inner_kernel=tfp.mcmc.SimpleStepSizeAdaptation( inner_kernel=tfp.mcmc.HamiltonianMonteCarlo( ... # doesn't matter ), num_adaptation_steps=9) bijector=tfb.Identity())) ``` Upon construction, `TransformedTransitionKernel` searches the given `inner_kernel` and the "stack" of nested kernels in any `inner_kernel` fields thereof until it finds one with a field called `target_log_prob_fn`, and replaces this with the transformed function. If no `inner_kernel` has such a target log prob a `ValueError` is raised. #### Mathematical Details `TransformedTransitionKernel` enables Markov chains which operate in "unconstrained space." Since we interpret the bijector as mapping "unconstrained space" to "user space", this means that the MCMC transformed `target_log_prob` is: ```python target_log_prob(bij.forward(x)) + bij.forward_log_det_jacobian(x) ``` Recall that `tfp.distributions.TransformedDistribution` uses the `inverse` to compute its `log_prob`. Despite this difference, the use of `forward` in `TransformedTransitionKernel` is perfectly consistent with `TransformedDistribution` following the TFP convention of "sampling" being what defines semantics. The apparent difference is because `TransformedDistribution.log_prob` is derived from a user provided distribution while in `TransformedTransitionKernel` samples are derived from `target_log_prob_fn`. That is, in `TransformedDistribution` we do: ```python x ~ NoiseDistribution() y = bij.forward(x) log_prob_y = NoiseDistribution().log_prob(bij.inverse(y)) + bij.inverse_log_det_jacobian(y) ``` yet in `TransformedTransitionKernel` we do: ```python x ~ MCMC() y = bij.forward(x) log_prob_y = log_prob(y) + bij.forward_log_det_jacobian(x) ``` In other words (and in general), `tfp.mcmc` is derived from a `log_prob` which what induces a *seeming* direction convention change. Aside from TFP convention, that Bijectors should adhere to "sample first" semantics is important because it mitigates pervasive necessity of `tfp.bijectors.Invert` in user code. #### Examples ##### RealNVP + HamiltonianMonteCarlo Note: this example is only meant to illustrate how to wire up a `TransformedTransitionKernel`. As it is this won't work well because: * a 1-layer RealNVP is a pretty weak density model, since it can't change the density of the masked dimensions * we're not actually training the bijector to do anything useful. ```python from tensorflow_probability.python.internal.backend import numpy as tf import tensorflow_probability as tfp; tfp = tfp.experimental.substrates.numpy tfd = tfp.distributions tfb = tfp.bijectors def make_likelihood(true_variances): return tfd.MultivariateNormalDiag( scale_diag=tf.sqrt(true_variances)) dims = 10 dtype = np.float32 true_variances = tf.linspace(dtype(1), dtype(3), dims) likelihood = make_likelihood(true_variances) realnvp_hmc = tfp.mcmc.TransformedTransitionKernel( inner_kernel=tfp.mcmc.HamiltonianMonteCarlo( target_log_prob_fn=likelihood.log_prob, step_size=0.5, num_leapfrog_steps=2), bijector=tfb.RealNVP( num_masked=2, shift_and_log_scale_fn=tfb.real_nvp_default_template( hidden_layers=[512, 512]))) states, kernel_results = tfp.mcmc.sample_chain( num_results=1000, current_state=tf.zeros(dims), kernel=realnvp_hmc, num_burnin_steps=500) # Compute sample stats. sample_mean = tf.reduce_mean(states, axis=0) sample_var = tf.reduce_mean( tf.squared_difference(states, sample_mean), axis=0) ``` #### References [1]: Matthew Parno and Youssef Marzouk. Transport map accelerated Markov chain Monte Carlo. _arXiv preprint arXiv:1412.5492_, 2014. https://arxiv.org/abs/1412.5492 [2]: Mark Girolami and Ben Calderhead. Riemann manifold langevin and hamiltonian monte carlo methods. In _Journal of the Royal Statistical Society_, 2011. https://doi.org/10.1111/j.1467-9868.2010.00765.x """ def __init__(self, inner_kernel, bijector, name=None): """Instantiates this object. Args: inner_kernel: `TransitionKernel`-like object that either has a `target_log_prob_fn` argument, or wraps around another `inner_kernel` with said argument. bijector: `tfp.distributions.Bijector` or list of `tfp.distributions.Bijector`s. These bijectors use `forward` to map the `inner_kernel` state space to the state expected by `inner_kernel.target_log_prob_fn`. name: Python `str` name prefixed to Ops created by this function. Default value: `None` (i.e., "transformed_kernel"). Returns: transformed_kernel: Instance of `TransitionKernel` which copies the input transition kernel then modifies its `target_log_prob_fn` by applying the provided bijector(s). """ self._parameters = dict( inner_kernel=inner_kernel, bijector=bijector, name=name or 'transformed_kernel') target_log_prob_fn = _find_nested_target_log_prob_recursively(inner_kernel) new_target_log_prob = make_transformed_log_prob( target_log_prob_fn, bijector, direction='forward', # TODO(b/72831017): Disable caching until gradient linkage # generally works. enable_bijector_caching=False) self._inner_kernel = _update_target_log_prob(inner_kernel, new_target_log_prob) # Prebuild `_forward_transform` which is used by `one_step`. self._transform_unconstrained_to_target_support = make_transform_fn( bijector, direction='forward') # Prebuild `_inverse_transform` which is used by `bootstrap_kernel_results`. self._transform_target_support_to_unconstrained = make_transform_fn( bijector, direction='inverse') @property def inner_kernel(self): return self._parameters['inner_kernel'] @property def bijector(self): return self._parameters['bijector'] @property def name(self): return self._parameters['name'] @property def parameters(self): """Return `dict` of ``__init__`` arguments and their values.""" return self._parameters @property def is_calibrated(self): return self._inner_kernel.is_calibrated def one_step(self, current_state, previous_kernel_results, seed=None): """Runs one iteration of the Transformed Kernel. Args: current_state: `Tensor` or Python `list` of `Tensor`s representing the current state(s) of the Markov chain(s), _after_ application of `bijector.forward`. The first `r` dimensions index independent chains, `r = tf.rank(target_log_prob_fn(*current_state))`. The `inner_kernel.one_step` does not actually use `current_state`, rather it takes as input `previous_kernel_results.transformed_state` (because `TransformedTransitionKernel` creates a copy of the input inner_kernel with a modified `target_log_prob_fn` which internally applies the `bijector.forward`). previous_kernel_results: `collections.namedtuple` containing `Tensor`s representing values from previous calls to this function (or from the `bootstrap_results` function.) seed: Optional, a seed for reproducible sampling. Returns: next_state: Tensor or Python list of `Tensor`s representing the state(s) of the Markov chain(s) after taking exactly one step. Has same type and shape as `current_state`. kernel_results: `collections.namedtuple` of internal calculations used to advance the chain. """ with tf.name_scope(mcmc_util.make_name( self.name, 'transformed_kernel', 'one_step')): inner_kwargs = {} if seed is None else dict(seed=seed) transformed_next_state, kernel_results = self._inner_kernel.one_step( previous_kernel_results.transformed_state, previous_kernel_results.inner_results, **inner_kwargs) transformed_next_state_parts = ( transformed_next_state if mcmc_util.is_list_like(transformed_next_state) else [transformed_next_state]) next_state_parts = self._transform_unconstrained_to_target_support( transformed_next_state_parts) next_state = ( next_state_parts if mcmc_util.is_list_like(transformed_next_state) else next_state_parts[0]) kernel_results = TransformedTransitionKernelResults( transformed_state=transformed_next_state, inner_results=kernel_results) return next_state, kernel_results def bootstrap_results(self, init_state=None, transformed_init_state=None): """Returns an object with the same type as returned by `one_step`. Unlike other `TransitionKernel`s, `TransformedTransitionKernel.bootstrap_results` has the option of initializing the `TransformedTransitionKernelResults` from either an initial state, eg, requiring computing `bijector.inverse(init_state)`, or directly from `transformed_init_state`, i.e., a `Tensor` or list of `Tensor`s which is interpretted as the `bijector.inverse` transformed state. Args: init_state: `Tensor` or Python `list` of `Tensor`s representing the a state(s) of the Markov chain(s). Must specify `init_state` or `transformed_init_state` but not both. transformed_init_state: `Tensor` or Python `list` of `Tensor`s representing the a state(s) of the Markov chain(s). Must specify `init_state` or `transformed_init_state` but not both. Returns: kernel_results: A (possibly nested) `tuple`, `namedtuple` or `list` of `Tensor`s representing internal calculations made within this function. Raises: ValueError: if none of the nested `inner_kernel` results contain the member "target_log_prob". #### Examples To use `transformed_init_state` in context of `tfp.mcmc.sample_chain`, you need to explicitly pass the `previous_kernel_results`, e.g., ```python transformed_kernel = tfp.mcmc.TransformedTransitionKernel(...) init_state = ... # Doesnt matter. transformed_init_state = ... # Does matter. results = tfp.mcmc.sample_chain( num_results=..., current_state=init_state, previous_kernel_results=transformed_kernel.bootstrap_results( transformed_init_state=transformed_init_state), trace_fn=None, kernel=transformed_kernel) ``` """ if (init_state is None) == (transformed_init_state is None): raise ValueError('Must specify exactly one of `init_state` ' 'or `transformed_init_state`.') with tf.name_scope(mcmc_util.make_name( self.name, 'transformed_kernel', 'bootstrap_results')): if transformed_init_state is None: init_state_parts = (init_state if mcmc_util.is_list_like(init_state) else [init_state]) transformed_init_state_parts = ( self._transform_target_support_to_unconstrained(init_state_parts)) transformed_init_state = ( transformed_init_state_parts if mcmc_util.is_list_like(init_state) else transformed_init_state_parts[0]) else: if mcmc_util.is_list_like(transformed_init_state): transformed_init_state = [ tf.convert_to_tensor(s, name='transformed_init_state') for s in transformed_init_state ] else: transformed_init_state = tf.convert_to_tensor( value=transformed_init_state, name='transformed_init_state') kernel_results = TransformedTransitionKernelResults( transformed_state=transformed_init_state, inner_results=self._inner_kernel.bootstrap_results( transformed_init_state)) return kernel_results