Runs one step of the RWM algorithm with symmetric proposal.
Inherits From: TransitionKernel
tfp.mcmc.RandomWalkMetropolis( target_log_prob_fn, new_state_fn=None, experimental_shard_axis_names=None, name=None )
Random Walk Metropolis is a gradient-free Markov chain Monte Carlo (MCMC) algorithm. The algorithm involves a proposal generating step proposal_state = current_state + perturb by a random perturbation, followed by Metropolis-Hastings accept/reject step. For more details see Section 2.1 of Roberts and Rosenthal (2004).
Current class implements RWM for normal and uniform proposals. Alternatively, the user can supply any custom proposal generating function.
The function one_step can update multiple chains in parallel. It assumes that all leftmost dimensions of current_state index independent chain states (and are therefore updated independently). The output of target_log_prob_fn(*current_state) should sum log-probabilities across all event dimensions. Slices along the rightmost dimensions may have different target distributions; for example, current_state[0, :] could have a different target distribution from current_state[1, :]. These semantics are governed by target_log_prob_fn(*current_state). (The number of independent chains is tf.size(target_log_prob_fn(*current_state)).)
Examples:
Sampling from the Standard Normal Distribution.
import numpy as np import tensorflow.compat.v2 as tf import tensorflow_probability as tfp tfd = tfp.distributions dtype = np.float32 target = tfd.Normal(loc=dtype(0), scale=dtype(1)) samples = tfp.mcmc.sample_chain( num_results=1000, current_state=dtype(1), kernel=tfp.mcmc.RandomWalkMetropolis(target.log_prob), num_burnin_steps=500, trace_fn=None, seed=42) sample_mean = tf.math.reduce_mean(samples, axis=0) sample_std = tf.sqrt( tf.math.reduce_mean( tf.math.squared_difference(samples, sample_mean), axis=0)) print('Estimated mean: {}'.format(sample_mean)) print('Estimated standard deviation: {}'.format(sample_std))
Sampling from a 2-D Normal Distribution.
import numpy as np import tensorflow.compat.v2 as tf import tensorflow_probability as tfp tfd = tfp.distributions dtype = np.float32 true_mean = dtype([0, 0]) true_cov = dtype([[1, 0.5], [0.5, 1]]) num_results = 500 num_chains = 100 # Target distribution is defined through the Cholesky decomposition `L`: L = tf.linalg.cholesky(true_cov) target = tfd.MultivariateNormalTriL(loc=true_mean, scale_tril=L) # Initial state of the chain init_state = np.ones([num_chains, 2], dtype=dtype) # Run Random Walk Metropolis with normal proposal for `num_results` # iterations for `num_chains` independent chains: samples = tfp.mcmc.sample_chain( num_results=num_results, current_state=init_state, kernel=tfp.mcmc.RandomWalkMetropolis(target_log_prob_fn=target.log_prob), num_burnin_steps=200, num_steps_between_results=1, # Thinning. trace_fn=None, seed=54) sample_mean = tf.math.reduce_mean(samples, axis=0) x = tf.squeeze(samples - sample_mean) sample_cov = tf.matmul(tf.transpose(x, [1, 2, 0]), tf.transpose(x, [1, 0, 2])) / num_results mean_sample_mean = tf.math.reduce_mean(sample_mean) mean_sample_cov = tf.math.reduce_mean(sample_cov, axis=0) x = tf.reshape(sample_cov - mean_sample_cov, [num_chains, 2 * 2]) cov_sample_cov = tf.reshape(tf.matmul(x, x, transpose_a=True) / num_chains, shape=[2 * 2, 2 * 2]) print('Estimated mean: {}'.format(mean_sample_mean)) print('Estimated avg covariance: {}'.format(mean_sample_cov)) print('Estimated covariance of covariance: {}'.format(cov_sample_cov))
Sampling from the Standard Normal Distribution using Cauchy proposal.
import numpy as np import tensorflow.compat.v2 as tf import tensorflow_probability as tfp tfd = tfp.distributions dtype = np.float32 num_burnin_steps = 500 num_chain_results = 1000 def cauchy_new_state_fn(scale, dtype): cauchy = tfd.Cauchy(loc=dtype(0), scale=dtype(scale)) def _fn(state_parts, seed): next_state_parts = [] part_seeds = tfp.random.split_seed( seed, n=len(state_parts), salt='rwmcauchy') for sp, ps in zip(state_parts, part_seeds): next_state_parts.append(sp + cauchy.sample( sample_shape=sp.shape, seed=ps)) return next_state_parts return _fn target = tfd.Normal(loc=dtype(0), scale=dtype(1)) samples = tfp.mcmc.sample_chain( num_results=num_chain_results, num_burnin_steps=num_burnin_steps, current_state=dtype(1), kernel=tfp.mcmc.RandomWalkMetropolis( target.log_prob, new_state_fn=cauchy_new_state_fn(scale=0.5, dtype=dtype)), trace_fn=None, seed=42) sample_mean = tf.math.reduce_mean(samples, axis=0) sample_std = tf.sqrt( tf.math.reduce_mean( tf.math.squared_difference(samples, sample_mean), axis=0)) print('Estimated mean: {}'.format(sample_mean)) print('Estimated standard deviation: {}'.format(sample_std))
Args |
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target_log_prob_fn | Python callable which takes an argument like current_state (or *current_state if it's a list) and returns its (possibly unnormalized) log-density under the target distribution. |
new_state_fn | Python callable which takes a list of state parts and a seed; returns a same-type list of Tensors, each being a perturbation of the input state parts. The perturbation distribution is assumed to be a symmetric distribution centered at the input state part. Default value: None which is mapped to tfp.mcmc.random_walk_normal_fn(). |
experimental_shard_axis_names | A structure of string names indicating how members of the state are sharded. |
name | Python str name prefixed to Ops created by this function. Default value: None (i.e., 'rwm_kernel'). |
Raises |
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ValueError | if there isn't one scale or a list with same length as current_state. |
Attributes |
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experimental_shard_axis_names | The shard axis names for members of the state. |
is_calibrated | Returns True if Markov chain converges to specified distribution. TransitionKernels which are "uncalibrated" are often calibrated by composing them with the tfp.mcmc.MetropolisHastings TransitionKernel.
|
name | |
new_state_fn | |
parameters | Return dict of __init__ arguments and their values. |
target_log_prob_fn | |
Methods
bootstrap_results
View source
bootstrap_results( init_state )
Creates initial previous_kernel_results using a supplied state.
copy
View source
copy( **override_parameter_kwargs )
Non-destructively creates a deep copy of the kernel.
| Args |
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**override_parameter_kwargs | Python String/value dictionary of initialization arguments to override with new values. |
| Returns |
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new_kernel | TransitionKernel object of same type as self, initialized with the union of self.parameters and override_parameter_kwargs, with any shared keys overridden by the value of override_parameter_kwargs, i.e., dict(self.parameters, **override_parameters_kwargs). |
experimental_with_shard_axes
View source
experimental_with_shard_axes( shard_axes )
Returns a copy of the kernel with the provided shard axis names.
| Args |
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shard_axis_names | a structure of strings indicating the shard axis names for each component of this kernel's state. |
| Returns |
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| A copy of the current kernel with the shard axis information. |
one_step
View source
one_step( current_state, previous_kernel_results, seed=None )
Runs one iteration of Random Walk Metropolis with normal proposal.
| Args |
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current_state | Tensor or Python list of Tensors representing the current state(s) of the Markov chain(s). The first r dimensions index independent chains, r = tf.rank(target_log_prob_fn(*current_state)). |
previous_kernel_results | collections.namedtuple containing Tensors representing values from previous calls to this function (or from the bootstrap_results function.) |
seed | PRNG seed; see tfp.random.sanitize_seed for details. |
| Returns |
|---|
next_state | Tensor or Python list of Tensors 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. |
| Raises |
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ValueError | if there isn't one scale or a list with same length as current_state. |
View source on GitHub