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mcmc_test.py
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mcmc_test.py
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import torch
import matplotlib.pyplot as plt
import seaborn as sns
import numpy as np
from mcmc import ULA, MALA
from function import MODEL
########################################
# ANNULUS #
########################################
def annulus_torch(radius, sigma):
def pdf(x):
r = torch.norm(x)
numerator = torch.exp(- 0.5 * ((r - radius) / sigma)**2) + \
torch.exp(- 0.5 * ((r + radius) / sigma)**2)
denominator = sigma * r
return numerator / denominator
return pdf
########################################
# GAUSSIAN #
########################################
def log_gradient_gaussian(mu, cov):
def gradient(x): return - cov @ (x - mu)
return gradient
def gaussian_torch(mu, sigma):
def pdf(x):
return torch.exp(- (x-mu) @ sigma @ (x - mu))
return pdf
########################################
# AUTO-CORRELATION #
########################################
def auto_correlation(M, kappa=100):
kappa = len(M) // kappa
auto_corr = np.zeros((kappa-1, 2))
mu = np.mean(M, axis=0)
for s in range(1, kappa-1):
auto_corr[s] = np.mean((M[:-s]-mu) * (M[s:]-mu),
axis=0) / np.var(M, axis=0)
return auto_corr
########################################
# PLOT #
########################################
def plot(points, x_axis=0, y_axis=1, kind="scatter",
n_points=400, burnin=150):
"""
{ “scatter” | “kde” | “hex” }
"""
sns.set()
x = points[burnin:(burnin+n_points), x_axis]
y = points[burnin:(burnin+n_points), y_axis]
sns.jointplot(x, y, kind=kind)
plt.show()
plt.figure(figsize=(9, 9), linewidth=1)
plt.plot(x[:n_points], y[:n_points])
plt.show()
def plot_autocorrelation(points, axis_list, kappa=100, legend=False):
auto_corr = auto_correlation(points, kappa)
for i in axis_list:
plt.plot(auto_corr[1:, i], label=f"Axis : {i}")
plt.title("Autocorrelation of the time serie (MCMC generated samples)")
plt.show()
if __name__ == '__main__':
"""
# - GAUSSIAN DISTRIBUTION EXAMPLE
MEAN = torch.zeros(2)
COV = torch.tensor([[1, .9], [.9, 1]])
GAUSSIAN_DENSITY = gaussian_torch(MEAN, COV)
GAUSSIAN_LOG_GRADIENT = log_gradient_gaussian(MEAN, COV)
GAUSSIAN = MODEL(density=GAUSSIAN_DENSITY,
log_density_gradient=GAUSSIAN_LOG_GRADIENT)
INIT_POINT = 2 * torch.randn_like(MEAN) + 3
# -- ULA - GAUSSIAN
nbr_samples = 50000
ULA_GAUSSIAN = ULA(GAUSSIAN, torch.eye(2), 5e-3, 4e-1, INIT_POINT)
points = ULA_GAUSSIAN.fit(nbr_samples)
points = np.array(points)
# plot(points, burnin=0, n_points=nbr_samples-1)
# plot(points, burnin=200, n_points=nbr_samples-201)
plot_autocorrelation(points, [0, 1])
# -- MALA - GAUSSIAN
nbr_samples = 50000
MALA_GAUSSIAN = MALA(GAUSSIAN, torch.eye(2), 2e-2, 4e-1, INIT_POINT)
points = MALA_GAUSSIAN.fit(nbr_samples)
points = np.array(points)
# plot(points, burnin=0, n_points=nbr_samples-1)
auto_corr = auto_correlation(points, 100)
plot(points, burnin=200, n_points=nbr_samples-201, kind='kde')
plot_autocorrelation(points, [0, 1])
"""
# -- MALA with adjusted acceptation ratio - GAUSSIAN
# nbr_samples = 10000
# MALA_GAUSSIAN = MALA(GAUSSIAN, torch.eye(2), 2e-2, 1e-2, INIT_POINT)
# points = MALA_GAUSSIAN.adjusted_fit(nbr_samples)
# points = np.array(points)
# plot(points, burnin=0, n_points=nbr_samples-1)
# plot(points, burnin=200, n_points=nbr_samples-201)
# - GAUSSIAN DISTRIBUTION EXAMPLE
MEAN = torch.zeros(2)
COV = torch.tensor([[1, .9], [.9, 1]])
GAUSSIAN_DENSITY = gaussian_torch(MEAN, COV)
GAUSSIAN = MODEL(density=GAUSSIAN_DENSITY)
INIT_POINT = 2 * torch.randn_like(MEAN) + 3
# -- MALA - GAUSSIAN
nbr_samples = 50000
MALA_GAUSSIAN = MALA(GAUSSIAN, torch.eye(2), 2e-2, 4e-1, INIT_POINT)
points = MALA_GAUSSIAN.fit(nbr_samples)
points = np.array(points)
# plot(points, burnin=0, n_points=nbr_samples-1)
auto_corr = auto_correlation(points, 100)
plot(points, burnin=200, n_points=nbr_samples-201, kind='kde')
plot_autocorrelation(points, [0, 1])