def compute_JSD(mu_P, Sigma_P, mu_Q, Sigma_Q, N_MC_samples):
# Jensen-Shannon distance (JSD)
out_JSD = np.empty_like(mu_P)
for index in range(mu_P.size):
RV_p = MVN(mean=mu_P[index], cov=Sigma_P[index, index])
RV_q = MVN(mean=mu_Q[index], cov=Sigma_Q[index, index])
x = RV_p.rvs(N_MC_samples)
p_x = RV_p.pdf(x)
q_x = RV_q.pdf(x)
m_x = (p_x + q_x) / 2.
y = RV_q.rvs(N_MC_samples)
p_y = RV_p.pdf(y)
q_y = RV_q.pdf(y)
m_y = (p_y + q_y) / 2.
dKL_pm = np.log(p_x / m_x).mean()
dKL_qm = np.log(q_y / m_y).mean()
out_JSD[index] = 0.5 * (dKL_pm + dKL_qm)
return out_JSD
def hastings_sampler(MN_OBJ, iter=10000):
from scipy.stats import multivariate_normal as MN
samples = np.zeros((iter, 2))
d_old = np.random.rand(2)
mus = [10, 10]
sig = [[1, 0.5], [0.5, 1]]
for i in range(iter):
delta = np.random.multivariate_normal(mus, sig)
MN_PRO = MN(mus, sig)
d_new = d_old + delta
u = np.random.rand()
samples[i, :] = d_old
if u <= (MN_OBJ.pdf(d_new) * MN_PRO.pdf(-1 * delta)) / (
MN_OBJ.pdf(d_old) * MN_PRO.pdf(delta)):
samples[i, :] = d_new
d_old = d_new
"""
x = p_x_given_y(y, mus, sigmas)
y = p_y_given_x(x, mus, sigmas)
samples[i, :] = [x, y]
"""
return samples