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216 | class HMC(ProposalBase):
"""
Hamiltonian Monte Carlo sampler class builiding the hmc_sampler method
from target logpdf.
Args:
logpdf: target logpdf function
jit: whether to jit the sampler
params: dictionary of parameters for the sampler
"""
condition_matrix: Float[Array, " n_dim n_dim"]
step_size: Float
n_leapfrog: Int
def __init__(
self,
logpdf: Callable[[Float[Array, " n_dim"], PyTree], Float],
jit: bool,
condition_matrix: Float[Array, " n_dim n_dim"] | Float = 1,
step_size: Float = 0.1,
n_leapfrog: Int = 10,
):
super().__init__(logpdf, jit, condition_matrix=condition_matrix, step_size=step_size, n_leapfrog=n_leapfrog)
self.potential: Callable[
[Float[Array, " n_dim"], PyTree], Float
] = lambda x, data: -logpdf(x, data)
self.grad_potential: Callable[
[Float[Array, " n_dim"], PyTree], Float[Array, " n_dim"]
] = jax.grad(self.potential)
self.condition_matrix = condition_matrix
self.step_size = step_size
self.n_leapfrog = n_leapfrog
coefs = jnp.ones((self.n_leapfrog + 2, 2))
coefs = coefs.at[0].set(jnp.array([0, 0.5]))
coefs = coefs.at[-1].set(jnp.array([1, 0.5]))
self.leapfrog_coefs = coefs
self.kinetic: Callable[
[Float[Array, " n_dim"], Float[Array, " n_dim n_dim"]], Float
] = (lambda p, metric: 0.5 * (p**2 * metric).sum())
self.grad_kinetic = jax.grad(self.kinetic)
def get_initial_hamiltonian(
self,
rng_key: PRNGKeyArray,
position: Float[Array, " n_dim"],
data: PyTree,
):
"""
Compute the value of the Hamiltonian from positions with initial momentum draw
at random from the standard normal distribution.
"""
momentum = (
jax.random.normal(rng_key, shape=position.shape)
* self.condition_matrix ** -0.5
)
return self.potential(position, data) + self.kinetic(
momentum, self.condition_matrix
)
def leapfrog_kernel(self, carry, extras):
position, momentum, data, metric, index = carry
position = position + self.step_size * self.leapfrog_coefs[index][
0
] * self.grad_kinetic(momentum, metric)
momentum = momentum - self.step_size * self.leapfrog_coefs[index][
1
] * self.grad_potential(position, data)
index = index + 1
return (position, momentum, data, metric, index), extras
def leapfrog_step(
self,
position: Float[Array, " n_dim"],
momentum: Float[Array, " n_dim"],
data: PyTree,
metric: Float[Array, " n_dim n_dim"],
) -> tuple[Float[Array, " n_dim"], Float[Array, " n_dim"]]:
(position, momentum, data, metric, index), _ = jax.lax.scan(
self.leapfrog_kernel,
(position, momentum, data, metric, 0),
jnp.arange(self.n_leapfrog + 2),
)
return position, momentum
def kernel(
self,
rng_key: PRNGKeyArray,
position: Float[Array, " n_dim"],
log_prob: Float[Array, "1"],
data: PyTree,
) -> tuple[Float[Array, " n_dim"], Float[Array, "1"], Int[Array, "1"]]:
"""
Note that since the potential function is the negative log likelihood,
hamiltonian is going down, but the likelihood value should go up.
Args:
rng_key (n_chains, 2): random key
position (n_chains, n_dim): current position
PE (n_chains, ): Potential energy of the current position
"""
key1, key2 = jax.random.split(rng_key)
momentum: Float[Array, " n_dim"] = (
jax.random.normal(key1, shape=position.shape)
* self.condition_matrix ** -0.5
)
momentum = jnp.dot(
jax.random.normal(key1, shape=position.shape),
jnp.linalg.cholesky(jnp.linalg.inv(self.condition_matrix)).T,
)
H = -log_prob + self.kinetic(momentum, self.condition_matrix)
proposed_position, proposed_momentum = self.leapfrog_step(
position, momentum, data, self.condition_matrix
)
proposed_PE = self.potential(proposed_position, data)
proposed_ham = proposed_PE + self.kinetic(
proposed_momentum, self.condition_matrix
)
log_acc = H - proposed_ham
log_uniform = jnp.log(jax.random.uniform(key2))
do_accept = log_uniform < log_acc
position = jnp.where(do_accept, proposed_position, position)
log_prob = jnp.where(do_accept, -proposed_PE, log_prob) # type: ignore
return position, log_prob, do_accept
def update(
self, i, state
) -> tuple[
PRNGKeyArray,
Float[Array, "nstep n_dim"],
Float[Array, "nstep 1"],
Int[Array, "n_step 1"],
PyTree,
]:
key, positions, PE, acceptance, data = state
_, key = jax.random.split(key)
new_position, new_PE, do_accept = self.kernel(
key, positions[i - 1], PE[i - 1], data
)
positions = positions.at[i].set(new_position)
PE = PE.at[i].set(new_PE)
acceptance = acceptance.at[i].set(do_accept)
return (key, positions, PE, acceptance, data)
def sample(
self,
rng_key: PRNGKeyArray,
n_steps: int,
initial_position: Float[Array, "n_chains n_dim"],
data: PyTree,
verbose: bool = False,
) -> tuple[
PRNGKeyArray,
Float[Array, "n_chains n_steps n_dim"],
Float[Array, "n_chains n_steps 1"],
Int[Array, "n_chains n_steps 1"],
]:
keys = jax.vmap(jax.random.split)(rng_key)
rng_key = keys[:, 0]
logp = self.logpdf_vmap(initial_position, data)
n_chains = rng_key.shape[0]
acceptance = jnp.zeros((n_chains, n_steps))
all_positions = (
jnp.zeros(
(
n_chains,
n_steps,
)
+ initial_position.shape[-1:]
)
+ initial_position[:, None]
)
all_logp = (
jnp.zeros(
(
n_chains,
n_steps,
)
)
+ logp[:, None]
)
state = (rng_key, all_positions, all_logp, acceptance, data)
if verbose:
iterator_loop = tqdm(
range(1, n_steps),
desc="Sampling Locally",
miniters=int(n_steps / 10),
)
else:
iterator_loop = range(1, n_steps)
for i in iterator_loop:
state = self.update_vmap(i, state)
state = (state[0], state[1], state[2], state[3])
return state
|