def sample_kernel(hmc_state, model_args=(), model_kwargs=None):
"""
Given an existing :data:`~numpyro.infer.mcmc.HMCState`, run HMC with fixed (possibly adapted)
step size and return a new :data:`~numpyro.infer.mcmc.HMCState`.
:param hmc_state: Current sample (and associated state).
:param tuple model_args: Model arguments if `potential_fn_gen` is specified.
:param dict model_kwargs: Model keyword arguments if `potential_fn_gen` is specified.
:return: new proposed :data:`~numpyro.infer.mcmc.HMCState` from simulating
Hamiltonian dynamics given existing state.
"""
model_kwargs = {} if model_kwargs is None else model_kwargs
rng_key, rng_key_momentum, rng_key_transition = random.split(hmc_state.rng_key, 3)
r = momentum_generator(hmc_state.z, hmc_state.adapt_state.mass_matrix_sqrt, rng_key_momentum)
vv_state = IntegratorState(hmc_state.z, r, hmc_state.potential_energy, hmc_state.z_grad)
vv_state, energy, num_steps, accept_prob, diverging = _next(hmc_state.adapt_state.step_size,
hmc_state.adapt_state.inverse_mass_matrix,
vv_state,
model_args,
model_kwargs,
rng_key_transition)
# not update adapt_state after warmup phase
adapt_state = cond(hmc_state.i < wa_steps,
(hmc_state.i, accept_prob, vv_state, hmc_state.adapt_state),
lambda args: wa_update(*args),
hmc_state.adapt_state,
identity)
itr = hmc_state.i + 1
n = jnp.where(hmc_state.i < wa_steps, itr, itr - wa_steps)
mean_accept_prob = hmc_state.mean_accept_prob + (accept_prob - hmc_state.mean_accept_prob) / n
return HMCState(itr, vv_state.z, vv_state.z_grad, vv_state.potential_energy, energy, num_steps,
accept_prob, mean_accept_prob, diverging, adapt_state, rng_key)
def _nuts_next(step_size, inverse_mass_matrix, vv_state, rng_key):
binary_tree = build_tree(vv_update,
kinetic_fn,
vv_state,
inverse_mass_matrix,
step_size,
rng_key,
max_delta_energy=max_delta_energy,
max_tree_depth=max_treedepth)
accept_prob = binary_tree.sum_accept_probs / binary_tree.num_proposals
num_steps = binary_tree.num_proposals
vv_state = IntegratorState(z=binary_tree.z_proposal,
r=vv_state.r,
potential_energy=binary_tree.z_proposal_pe,
z_grad=binary_tree.z_proposal_grad)
return vv_state, binary_tree.z_proposal_energy, num_steps, accept_prob, binary_tree.diverging
def _nuts_next(step_size, inverse_mass_matrix, vv_state,
model_args, model_kwargs, rng_key):
if potential_fn_gen:
nonlocal vv_update
pe_fn = potential_fn_gen(*model_args, **model_kwargs)
_, vv_update = velocity_verlet(pe_fn, kinetic_fn)
binary_tree = build_tree(vv_update, kinetic_fn, vv_state,
inverse_mass_matrix, step_size, rng_key,
max_delta_energy=max_delta_energy,
max_tree_depth=max_treedepth)
accept_prob = binary_tree.sum_accept_probs / binary_tree.num_proposals
num_steps = binary_tree.num_proposals
vv_state = IntegratorState(z=binary_tree.z_proposal,
r=vv_state.r,
potential_energy=binary_tree.z_proposal_pe,
z_grad=binary_tree.z_proposal_grad)
return vv_state, binary_tree.z_proposal_energy, num_steps, accept_prob, binary_tree.diverging
def init_kernel(init_params,
num_warmup,
step_size=1.0,
inverse_mass_matrix=None,
adapt_step_size=True,
adapt_mass_matrix=True,
dense_mass=False,
target_accept_prob=0.8,
trajectory_length=2 * math.pi,
max_tree_depth=10,
find_heuristic_step_size=False,
model_args=(),
model_kwargs=None,
rng_key=random.PRNGKey(0)):
"""
Initializes the HMC sampler.
:param init_params: Initial parameters to begin sampling. The type must
be consistent with the input type to `potential_fn`.
:param int num_warmup: Number of warmup steps; samples generated
during warmup are discarded.
:param float step_size: Determines the size of a single step taken by the
verlet integrator while computing the trajectory using Hamiltonian
dynamics. If not specified, it will be set to 1.
:param numpy.ndarray inverse_mass_matrix: Initial value for inverse mass matrix.
This may be adapted during warmup if adapt_mass_matrix = True.
If no value is specified, then it is initialized to the identity matrix.
:param bool adapt_step_size: A flag to decide if we want to adapt step_size
during warm-up phase using Dual Averaging scheme.
:param bool adapt_mass_matrix: A flag to decide if we want to adapt mass
matrix during warm-up phase using Welford scheme.
:param bool dense_mass: A flag to decide if mass matrix is dense or
diagonal (default when ``dense_mass=False``)
:param float target_accept_prob: Target acceptance probability for step size
adaptation using Dual Averaging. Increasing this value will lead to a smaller
step size, hence the sampling will be slower but more robust. Default to 0.8.
:param float trajectory_length: Length of a MCMC trajectory for HMC. Default
value is :math:`2\\pi`.
:param int max_tree_depth: Max depth of the binary tree created during the doubling
scheme of NUTS sampler. Defaults to 10.
:param bool find_heuristic_step_size: whether to a heuristic function to adjust the
step size at the beginning of each adaptation window. Defaults to False.
:param tuple model_args: Model arguments if `potential_fn_gen` is specified.
:param dict model_kwargs: Model keyword arguments if `potential_fn_gen` is specified.
:param jax.random.PRNGKey rng_key: random key to be used as the source of
randomness.
"""
step_size = lax.convert_element_type(step_size,
canonicalize_dtype(jnp.float64))
nonlocal wa_update, trajectory_len, max_treedepth, vv_update, wa_steps
wa_steps = num_warmup
trajectory_len = trajectory_length
max_treedepth = max_tree_depth
if isinstance(init_params, ParamInfo):
z, pe, z_grad = init_params
else:
z, pe, z_grad = init_params, None, None
pe_fn = potential_fn
if potential_fn_gen:
if pe_fn is not None:
raise ValueError(
'Only one of `potential_fn` or `potential_fn_gen` must be provided.'
)
else:
kwargs = {} if model_kwargs is None else model_kwargs
pe_fn = potential_fn_gen(*model_args, **kwargs)
find_reasonable_ss = None
if find_heuristic_step_size:
find_reasonable_ss = partial(find_reasonable_step_size, pe_fn,
kinetic_fn, momentum_generator)
wa_init, wa_update = warmup_adapter(
num_warmup,
adapt_step_size=adapt_step_size,
adapt_mass_matrix=adapt_mass_matrix,
dense_mass=dense_mass,
target_accept_prob=target_accept_prob,
find_reasonable_step_size=find_reasonable_ss)
rng_key_hmc, rng_key_wa, rng_key_momentum = random.split(rng_key, 3)
z_info = IntegratorState(z=z, potential_energy=pe, z_grad=z_grad)
wa_state = wa_init(z_info,
rng_key_wa,
step_size,
inverse_mass_matrix=inverse_mass_matrix,
mass_matrix_size=jnp.size(ravel_pytree(z)[0]))
r = momentum_generator(z, wa_state.mass_matrix_sqrt, rng_key_momentum)
vv_init, vv_update = velocity_verlet(pe_fn, kinetic_fn)
vv_state = vv_init(z, r, potential_energy=pe, z_grad=z_grad)
energy = kinetic_fn(wa_state.inverse_mass_matrix, vv_state.r)
hmc_state = HMCState(0, vv_state.z, vv_state.z_grad,
vv_state.potential_energy, energy, 0, 0., 0.,
False, wa_state, rng_key_hmc)
return device_put(hmc_state)
def init_kernel(
init_params,
num_warmup,
*,
step_size=1.0,
inverse_mass_matrix=None,
adapt_step_size=True,
adapt_mass_matrix=True,
dense_mass=False,
target_accept_prob=0.8,
trajectory_length=2 * math.pi,
max_tree_depth=10,
find_heuristic_step_size=False,
forward_mode_differentiation=False,
regularize_mass_matrix=True,
model_args=(),
model_kwargs=None,
rng_key=random.PRNGKey(0),
):
"""
Initializes the HMC sampler.
:param init_params: Initial parameters to begin sampling. The type must
be consistent with the input type to `potential_fn`.
:param int num_warmup: Number of warmup steps; samples generated
during warmup are discarded.
:param float step_size: Determines the size of a single step taken by the
verlet integrator while computing the trajectory using Hamiltonian
dynamics. If not specified, it will be set to 1.
:param inverse_mass_matrix: Initial value for inverse mass matrix.
This may be adapted during warmup if adapt_mass_matrix = True.
If no value is specified, then it is initialized to the identity matrix.
For a potential_fn with general JAX pytree parameters, the order of entries
of the mass matrix is the order of the flattened version of pytree parameters
obtained with `jax.tree_flatten`, which is a bit ambiguous (see more at
https://jax.readthedocs.io/en/latest/pytrees.html). If `model` is not None,
here we can specify a structured block mass matrix as a dictionary, where
keys are tuple of site names and values are the corresponding block of the
mass matrix.
For more information about structured mass matrix, see `dense_mass` argument.
:type inverse_mass_matrix: numpy.ndarray or dict
:param bool adapt_step_size: A flag to decide if we want to adapt step_size
during warm-up phase using Dual Averaging scheme.
:param bool adapt_mass_matrix: A flag to decide if we want to adapt mass
matrix during warm-up phase using Welford scheme.
:param dense_mass: This flag controls whether mass matrix is dense (i.e. full-rank) or
diagonal (defaults to ``dense_mass=False``). To specify a structured mass matrix,
users can provide a list of tuples of site names. Each tuple represents
a block in the joint mass matrix. For example, assuming that the model
has latent variables "x", "y", "z" (where each variable can be multi-dimensional),
possible specifications and corresponding mass matrix structures are as follows:
+ dense_mass=[("x", "y")]: use a dense mass matrix for the joint
(x, y) and a diagonal mass matrix for z
+ dense_mass=[] (equivalent to dense_mass=False): use a diagonal mass
matrix for the joint (x, y, z)
+ dense_mass=[("x", "y", "z")] (equivalent to full_mass=True):
use a dense mass matrix for the joint (x, y, z)
+ dense_mass=[("x",), ("y",), ("z")]: use dense mass matrices for
each of x, y, and z (i.e. block-diagonal with 3 blocks)
:type dense_mass: bool or list
:param float target_accept_prob: Target acceptance probability for step size
adaptation using Dual Averaging. Increasing this value will lead to a smaller
step size, hence the sampling will be slower but more robust. Defaults to 0.8.
:param float trajectory_length: Length of a MCMC trajectory for HMC. Default
value is :math:`2\\pi`.
:param int max_tree_depth: Max depth of the binary tree created during the doubling
scheme of NUTS sampler. Defaults to 10. This argument also accepts a tuple of
integers `(d1, d2)`, where `d1` is the max tree depth during warmup phase and
`d2` is the max tree depth during post warmup phase.
:param bool find_heuristic_step_size: whether to a heuristic function to adjust the
step size at the beginning of each adaptation window. Defaults to False.
:param bool regularize_mass_matrix: whether or not to regularize the estimated mass
matrix for numerical stability during warmup phase. Defaults to True. This flag
does not take effect if ``adapt_mass_matrix == False``.
:param tuple model_args: Model arguments if `potential_fn_gen` is specified.
:param dict model_kwargs: Model keyword arguments if `potential_fn_gen` is specified.
:param jax.random.PRNGKey rng_key: random key to be used as the source of
randomness.
"""
step_size = lax.convert_element_type(step_size, jnp.result_type(float))
if trajectory_length is not None:
trajectory_length = lax.convert_element_type(
trajectory_length, jnp.result_type(float))
nonlocal wa_update, max_treedepth, vv_update, wa_steps, forward_mode_ad
forward_mode_ad = forward_mode_differentiation
wa_steps = num_warmup
max_treedepth = (max_tree_depth if isinstance(max_tree_depth, tuple)
else (max_tree_depth, max_tree_depth))
if isinstance(init_params, ParamInfo):
z, pe, z_grad = init_params
else:
z, pe, z_grad = init_params, None, None
pe_fn = potential_fn
if potential_fn_gen:
if pe_fn is not None:
raise ValueError(
"Only one of `potential_fn` or `potential_fn_gen` must be provided."
)
else:
kwargs = {} if model_kwargs is None else model_kwargs
pe_fn = potential_fn_gen(*model_args, **kwargs)
find_reasonable_ss = None
if find_heuristic_step_size:
find_reasonable_ss = partial(find_reasonable_step_size, pe_fn,
kinetic_fn, momentum_generator)
wa_init, wa_update = warmup_adapter(
num_warmup,
adapt_step_size=adapt_step_size,
adapt_mass_matrix=adapt_mass_matrix,
dense_mass=dense_mass,
target_accept_prob=target_accept_prob,
find_reasonable_step_size=find_reasonable_ss,
regularize_mass_matrix=regularize_mass_matrix,
)
rng_key_hmc, rng_key_wa, rng_key_momentum = random.split(rng_key, 3)
z_info = IntegratorState(z=z, potential_energy=pe, z_grad=z_grad)
wa_state = wa_init(z_info,
rng_key_wa,
step_size,
inverse_mass_matrix=inverse_mass_matrix)
r = momentum_generator(z, wa_state.mass_matrix_sqrt, rng_key_momentum)
vv_init, vv_update = velocity_verlet(pe_fn, kinetic_fn,
forward_mode_ad)
vv_state = vv_init(z, r, potential_energy=pe, z_grad=z_grad)
energy = vv_state.potential_energy + kinetic_fn(
wa_state.inverse_mass_matrix, vv_state.r)
zero_int = jnp.array(0, dtype=jnp.result_type(int))
hmc_state = HMCState(
zero_int,
vv_state.z,
vv_state.z_grad,
vv_state.potential_energy,
energy,
None,
trajectory_length,
zero_int,
jnp.zeros(()),
jnp.zeros(()),
jnp.array(False),
wa_state,
rng_key_hmc,
)
return device_put(hmc_state)