def test_hamiltonian_monte_carlo(integrator):
# This mostly tests consistency. Tolerance chosen by experiment
# Do statistical tests on your own time.
np.random.seed(1)
neg_log_p = AutogradPotential(neg_log_normal(2, 0.1))
samples, *_ = hamiltonian_monte_carlo(100,
neg_log_p,
np.array(0.0),
integrator=integrator)
assert_allclose(2.0, np.mean(samples), atol=0.007)
assert_allclose(0.1, np.std(samples), atol=0.16)
def test_hamiltonian_monte_carlo_mv():
np.random.seed(1)
mu = np.arange(2)
cov = 0.8 * np.ones((2, 2)) + 0.2 * np.eye(2)
neg_log_p = AutogradPotential(neg_log_mvnormal(mu, cov))
samples, *_ = hamiltonian_monte_carlo(100,
neg_log_p,
np.zeros(mu.shape),
path_len=2.0)
assert_allclose(mu, np.mean(samples, axis=0), atol=0.21)
assert_allclose(cov, np.cov(samples.T), atol=0.31)
def test_leapfrog():
neg_log_p = AutogradPotential(neg_log_normal(2, 0.1))
q, p = np.array(0.0), np.array(2.0)
path_len, step_size = 1, 0.1
V, dVdq = neg_log_p(q)
# Should be reversible
q_new, p_new, _, dVdq = leapfrog(q, p, dVdq, neg_log_p, path_len,
step_size)
q_new, p_new, _, _ = leapfrog(q_new, p_new, dVdq, neg_log_p, path_len,
step_size)
assert_almost_equal(q_new, q)
assert_almost_equal(p_new, p)
def test_leapfrog_mv():
mu = np.arange(10)
cov = 0.8 * np.ones((10, 10)) + 0.2 * np.eye(10)
neg_log_p = AutogradPotential(neg_log_mvnormal(mu, cov))
q, p = np.zeros(mu.shape), np.ones(mu.shape)
path_len, step_size = 1, 0.1
V, dVdq = neg_log_p(q)
# Should be reversible
q_new, p_new, _, dVdq = leapfrog(q, p, dVdq, neg_log_p, path_len,
step_size)
q_new, p_new, _, _ = leapfrog(q_new, p_new, dVdq, neg_log_p, path_len,
step_size)
assert_almost_equal(q_new, q)
assert_almost_equal(p_new, p)
"font.family": "serif",
"figure.facecolor": "#fffff8",
"axes.facecolor": "#fffff8",
"figure.constrained_layout.use": True,
"font.size": 14.0,
"hist.bins": "auto",
"lines.linewidth": 3.0,
"lines.markeredgewidth": 2.0,
"lines.markerfacecolor": "none",
"lines.markersize": 8.0,
}
)
### Example 1 ###
samples = hamiltonian_monte_carlo(
2000, AutogradPotential(neg_log_normal(0, 0.1)), initial_position=0.0
)
### Plot 1 ###
fig, ax = plt.subplots(figsize=FIGSIZE)
ax.hist(samples, bins="auto")
ax.axvline(0, color="C1", linestyle="--")
ax.set_title("1D Gaussians!")
plt.savefig(os.path.join(HERE, "plot1.png"))
### Example 2 ###
samples, positions, momentums, accepted, p_accepts = hmc_slow(
50, AutogradPotential(neg_log_normal(0, 0.1)), 0.0, step_size=0.01
)
### Plot 2 ###