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Original file line number | Diff line number | Diff line change |
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@@ -1,61 +1,67 @@ | ||
from typing import Callable | ||
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import aesara | ||
import aesara.tensor as aet | ||
import aesara_hmc.hmc as hmc | ||
import numpy as np | ||
import pytest | ||
from aesara.tensor.random.utils import RandomStream | ||
from aesara.tensor.var import TensorVariable | ||
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def test_hmc(): | ||
def potential_fn(q: TensorVariable) -> TensorVariable: | ||
return -1.0 / aet.power(aet.square(q[0]) + aet.square(q[1]), 0.5) | ||
def normal_logp(q: TensorVariable): | ||
return aet.sum(aet.square(q - 3.0)) | ||
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srng = RandomStream(seed=59) | ||
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step_size = aet.scalar("step_size") | ||
inverse_mass_matrix = aet.vector("inverse_mass_matrix") | ||
num_integration_steps = aet.scalar("num_integration_steps", dtype="int32") | ||
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def build_trajectory_generator( | ||
srng: RandomStream, | ||
kernel_generator: Callable, | ||
potential_fn: Callable, | ||
num_states: int, | ||
) -> Callable: | ||
q = aet.vector("q") | ||
potential_energy = potential_fn(q) | ||
potential_energy_grad = aesara.grad(potential_energy, wrt=q) | ||
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kernel = hmc.kernel( | ||
srng, potential_fn, step_size, inverse_mass_matrix, num_integration_steps | ||
) | ||
next_step = kernel(q, potential_energy, potential_energy_grad) | ||
step_size = aet.scalar("step_size") | ||
inverse_mass_matrix = aet.vector("inverse_mass_matrix") | ||
num_integration_steps = aet.scalar("num_integration_steps", dtype="int32") | ||
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# Compile a function that returns the next state | ||
step_fn = aesara.function( | ||
(q, step_size, inverse_mass_matrix, num_integration_steps), next_step | ||
kernel = kernel_generator( | ||
srng, potential_fn, step_size, inverse_mass_matrix, num_integration_steps | ||
) | ||
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# Compile a function that integrates the trajectory integrating several times | ||
trajectory, _ = aesara.scan( | ||
trajectory, updates = aesara.scan( | ||
fn=kernel, | ||
outputs_info=[ | ||
{"initial": q}, | ||
{"initial": potential_energy}, | ||
{"initial": potential_energy_grad}, | ||
], | ||
n_steps=1000, | ||
n_steps=num_states, | ||
) | ||
trajectory_generator = aesara.function( | ||
(q, step_size, inverse_mass_matrix, num_integration_steps), | ||
trajectory, | ||
updates=updates, | ||
) | ||
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return trajectory_generator | ||
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def test_hmc(): | ||
"""Test the HMC kernel on a simple potential.""" | ||
srng = RandomStream(seed=59) | ||
step_size = 0.003 | ||
num_integration_steps = 10 | ||
initial_position = np.array([1.0]) | ||
inverse_mass_matrix = np.array([1.0]) | ||
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trajectory_generator = build_trajectory_generator( | ||
srng, hmc.kernel, normal_logp, 10_000 | ||
) | ||
traj = aesara.function( | ||
(q, step_size, inverse_mass_matrix, num_integration_steps), trajectory | ||
positions, *_ = trajectory_generator( | ||
initial_position, step_size, inverse_mass_matrix, num_integration_steps | ||
) | ||
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# Run | ||
step_size = 0.01 | ||
num_integration_steps = 3 | ||
q = np.array([1.0, 1.0]) | ||
inverse_mass_matrix = np.array([1.0, 1.0]) | ||
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# This works | ||
samples = [] | ||
for _ in range(1_000): | ||
q, *_ = step_fn(q, step_size, inverse_mass_matrix, num_integration_steps) | ||
samples.append(q) | ||
print(np.mean(np.array(samples))) | ||
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# This doesn't | ||
print(traj(q, step_size, inverse_mass_matrix, num_integration_steps)) | ||
assert np.mean(positions[9000:], axis=0) == pytest.approx(3, 1e-1) |