def test_mixture_1d():
neg_log_probs = [neg_log_normal(1.0, 1.0), neg_log_normal(-1.0, 1.0)]
probs = [0.2, 0.8]
neg_log_p = mixture(neg_log_probs, probs)
true_rvs = [st.norm(1.0, 1.0), st.norm(-1.0, 1)]
true_log_p = lambda x: -np.log(sum(p * rv.pdf(x) for p, rv in zip(probs, true_rvs)))
for x in np.random.randn(10):
assert_almost_equal(neg_log_p(x), true_log_p(x))
def test_hamiltonian_monte_carlo():
# This mostly tests consistency. Tolerance chosen by experiment
# Do statistical tests on your own time.
np.random.seed(1)
neg_log_p = neg_log_normal(2, 0.1)
samples, *_ = hamiltonian_monte_carlo(100, neg_log_p, np.array(0.0))
assert_allclose(2.0, np.mean(samples), atol=0.006)
assert_allclose(0.1, np.std(samples), atol=0.025)
def test_leapfrog():
neg_log_p = neg_log_normal(2, 0.1)
dlogp = grad(neg_log_p)
q, p = np.array(0.0), np.array(2.0)
path_len, step_size = 1, 0.1
# Should be reversible
q_new, p_new, *_ = leapfrog(q, p, dlogp, path_len, step_size)
q_new, p_new, *_ = leapfrog(q_new, p_new, dlogp, path_len, step_size)
assert_almost_equal(q_new, q)
assert_almost_equal(p_new, p)
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 samples.shape[0] == 100
assert_allclose(2.0, np.mean(samples), atol=0.1)
assert_allclose(0.1, np.std(samples), atol=0.1)
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)
"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 ###
def test_neg_log_normal():
neg_log_p = neg_log_normal(2, 0.1)
true_rv = st.norm(2, 0.1)
for x in np.random.randn(10):
assert_almost_equal(neg_log_p(x), -true_rv.logpdf(x))
import autograd.numpy as np
from autograd import grad
from minimc import neg_log_normal, mixture, hamiltonian_monte_carlo, neg_log_mvnormal
from minimc.minimc_slow import hamiltonian_monte_carlo as hmc_slow
import matplotlib.pyplot as plt
HERE = os.path.dirname(os.path.abspath(__file__))
FIGSIZE = (10, 7)
if __name__ == "__main__":
plt.style.use("tufte")
### Example 1 ###
samples = hamiltonian_monte_carlo(2000,
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 = hmc_slow(50,
neg_log_normal(0, 0.1),
0.0,
step_size=0.01)
