def adaptive_hamiltonian_monte_carlo_init(
state: 'fun_mc.TensorNest',
target_log_prob_fn: 'fun_mc.PotentialFn',
step_size: 'fun_mc.FloatTensor' = 1e-2,
initial_mean: 'fun_mc.FloatNest' = 0.,
initial_scale: 'fun_mc.FloatNest' = 1.,
scale_smoothing_steps: 'fun_mc.IntTensor' = 10,
) -> 'AdaptiveHamiltonianMonteCarloState':
"""Initializes `AdaptiveHamiltonianMonteCarloState`.
Args:
state: Initial state of the chain.
target_log_prob_fn: Target log prob fn.
step_size: Initial scalar step size.
initial_mean: Initial mean for computing the running variance estimate. Must
broadcast structurally and tensor-wise with state.
initial_scale: Initial scale for computing the running variance estimate.
Must broadcast structurally and tensor-wise with state.
scale_smoothing_steps: How much weight to assign to the `initial_mean` and
`initial_scale`. Increase this to stabilize early adaptation.
Returns:
adaptive_hmc_state: State of the `adaptive_hamiltonian_monte_carlo_step`
`TransitionOperator`.
"""
hmc_state = fun_mc.hamiltonian_monte_carlo_init(state, target_log_prob_fn)
dtype = util.flatten_tree(hmc_state.state)[0].dtype
chain_ndims = len(hmc_state.target_log_prob.shape)
running_var_state = fun_mc.running_variance_init(
shape=util.map_tree(lambda s: s.shape[chain_ndims:], hmc_state.state),
dtype=util.map_tree(lambda s: s.dtype, hmc_state.state),
)
initial_mean = fun_mc.maybe_broadcast_structure(initial_mean, state)
initial_scale = fun_mc.maybe_broadcast_structure(initial_scale, state)
# It's important to add some smoothing here, as initial updates can be very
# different than the stationary distribution.
# TODO(siege): Add a pseudo-update functionality to avoid fiddling with the
# internals here.
running_var_state = running_var_state._replace(
num_points=util.map_tree(
lambda p: ( # pylint: disable=g-long-lambda
int(np.prod(hmc_state.target_log_prob.shape)) * tf.cast(
scale_smoothing_steps, p.dtype)),
running_var_state.num_points),
mean=util.map_tree( # pylint: disable=g-long-lambda
lambda m, init_m: tf.ones_like(m) * init_m, running_var_state.mean,
initial_mean),
variance=util.map_tree( # pylint: disable=g-long-lambda
lambda v, init_s: tf.ones_like(v) * init_s**2,
running_var_state.variance, initial_scale),
)
log_step_size_opt_state = fun_mc.adam_init(
tf.math.log(tf.convert_to_tensor(step_size, dtype=dtype)))
return AdaptiveHamiltonianMonteCarloState(
hmc_state=hmc_state,
running_var_state=running_var_state,
log_step_size_opt_state=log_step_size_opt_state,
step=tf.zeros([], tf.int32))
def computation(state, seed):
bijector = tfp.bijectors.Softplus()
base_dist = tfp.distributions.MultivariateNormalFullCovariance(
loc=base_mean, covariance_matrix=base_cov)
target_dist = bijector(base_dist)
def orig_target_log_prob_fn(x):
return target_dist.log_prob(x), ()
target_log_prob_fn, state = fun_mcmc.transform_log_prob_fn(
orig_target_log_prob_fn, bijector, state)
def kernel(hmc_state, step_size_state, step, seed):
hmc_seed, seed = util.split_seed(seed, 2)
hmc_state, hmc_extra = fun_mcmc.hamiltonian_monte_carlo(
hmc_state,
step_size=tf.exp(step_size_state.state),
num_integrator_steps=num_leapfrog_steps,
target_log_prob_fn=target_log_prob_fn,
seed=hmc_seed)
rate = prefab._polynomial_decay( # pylint: disable=protected-access
step=step,
step_size=self._constant(0.01),
power=0.5,
decay_steps=num_adapt_steps,
final_step_size=0.)
mean_p_accept = tf.reduce_mean(
tf.exp(tf.minimum(self._constant(0.), hmc_extra.log_accept_ratio)))
loss_fn = fun_mcmc.make_surrogate_loss_fn(
lambda _: (0.9 - mean_p_accept, ()))
step_size_state, _ = fun_mcmc.adam_step(
step_size_state, loss_fn, learning_rate=rate)
return ((hmc_state, step_size_state, step + 1, seed),
(hmc_state.state_extra[0], hmc_extra.log_accept_ratio))
_, (chain, log_accept_ratio_trace) = fun_mcmc.trace(
state=(fun_mcmc.hamiltonian_monte_carlo_init(state,
target_log_prob_fn),
fun_mcmc.adam_init(tf.math.log(step_size)), 0, seed),
fn=kernel,
num_steps=num_adapt_steps + num_steps,
)
true_samples = target_dist.sample(
4096, seed=self._make_seed(_test_seed()))
return chain, log_accept_ratio_trace, true_samples
def testAdam(self):
def loss_fn(x, y):
return tf.square(x - 1.) + tf.square(y - 2.), []
_, [(x, y), loss] = fun_mcmc.trace(
fun_mcmc.adam_init([self._constant(0.), self._constant(0.)]),
lambda adam_state: fun_mcmc.adam_step( # pylint: disable=g-long-lambda
adam_state,
loss_fn,
learning_rate=self._constant(0.01)),
num_steps=1000,
trace_fn=lambda state, extra: [state.state, extra.loss])
self.assertAllClose(1., x[-1], atol=1e-3)
self.assertAllClose(2., y[-1], atol=1e-3)
self.assertAllClose(0., loss[-1], atol=1e-3)