def main_simu(d, nb_exps=10000, nb_iters=40000, sigma_max=2.0, seed=1):
np.random.seed(123456 + seed)
error_ula_all = np.zeros((nb_iters, 1))
error_ula_02_all = np.zeros((nb_iters, 1))
error_mala_all = np.zeros((nb_iters, 1))
error_rwmh_all = np.zeros((nb_iters, 1))
mean = np.zeros(d)
sigma = np.array([1.0 + (sigma_max - 1.0) / (d - 1) * i for i in range(d)])
L = 1. / sigma[0]**2
m = 1. / sigma[-1]**2
kappa = L / m
print("d = %d, m = %0.2f, L = %0.2f, kappa = %0.2f" % (d, m, L, kappa))
def error_quantile(x_curr):
q3 = sigma[-1] * scipy.stats.norm.ppf(0.75)
e1 = np.abs(np.percentile(x_curr[:, -1], 75) - q3) / q3
return np.array([e1])
init_distr = 1. / np.sqrt(L) * np.random.randn(nb_exps, d)
def grad_f_local(x):
return grad_f(x, mean=mean, sigma=sigma)
def f_local(x):
return density_f(x, mean=mean, sigma=sigma)
error_ula_all, x_ula = mcmc.ula(init_distr,
grad_f_local,
error_quantile,
epsilon=1.0,
kappa=kappa,
L=L,
nb_iters=nb_iters,
nb_exps=nb_exps)
error_ula_02_all, x_ula_02 = mcmc.ula(init_distr,
grad_f_local,
error_quantile,
epsilon=0.2,
kappa=kappa,
L=L,
nb_iters=nb_iters,
nb_exps=nb_exps)
error_mala_all, x_mala = mcmc.mala(init_distr,
grad_f_local,
f_local,
error_quantile,
kappa=kappa,
L=L,
nb_iters=nb_iters,
nb_exps=nb_exps)
error_rwmh_all, x_rwmh = mcmc.rwmh(init_distr,
f_local,
error_quantile,
kappa=kappa,
L=L,
nb_iters=nb_iters,
nb_exps=nb_exps)
result = {}
result['d'] = d
result['nb_iters'] = nb_iters
result['nb_exps'] = nb_exps
result['sigma_max'] = sigma_max
result['ula'] = error_ula_all
result['ula_02'] = error_ula_02_all
result['mala'] = error_mala_all
result['rwmh'] = error_rwmh_all
save_path = "PLEASE UPDATE BEFORE USE"
np.save(
'%s/gaussian_nonisotropic_d%d_iters%d_exps%d_seed%d.npy' %
(save_path, d, nb_iters, nb_exps, seed), result)
def main_simu(nb_exps=10000, nb_iters=40000, sigma_max=2.0, seed=1):
d = 3
epsilons = np.arange(10)*0.1+0.1
np.random.seed(123456+seed)
error_ula_all = np.zeros((epsilons.shape[0], nb_iters, 1))
error_ula_02_all = np.zeros((epsilons.shape[0], nb_iters, 1))
error_mala_all = np.zeros((epsilons.shape[0], nb_iters, 1))
error_rwmh_all = np.zeros((epsilons.shape[0], nb_iters, 1))
mean = np.zeros(d)
sigma = np.array([1.0 + (sigma_max - 1.0)/(d-1)*i for i in range(d)])
# make the last sigma large, so that it is close to nonstrongly convex
sigma[-1] = 1000.
L = 1./sigma[0]**2
m = 1./sigma[-1]**2
kappa = L/m
print("d = %d, m = %0.2f, L = %0.2f, kappa = %0.2f" %(d, m, L, kappa))
for j, eps in enumerate(epsilons):
# modify the objective function to make it gamma/2 strongly convex
# fourth moment bound
nu = 1.0
gamma = 2. * eps/d/nu
L_mod = L + gamma/2.
m_mod = m + gamma/2.
kappa_mod = L_mod/m_mod
print("d = %d, m_mod = %0.2f, L_mod = %0.2f, kappa_mod = %0.2f, eps = %0.2f" %(d, m_mod, L_mod, kappa_mod, eps))
# compare error on the before-last dimension
def error_quantile(x_curr):
q3 = sigma[-2]*scipy.stats.norm.ppf(0.75)
e1 = np.abs(np.percentile(x_curr[:, -2], 75) - q3)/q3
return np.array([e1])
init_distr = 1./np.sqrt(L_mod)*np.random.randn(nb_exps, d)
def grad_f_local(x):
return grad_f_mod(x, mean=mean, sigma=sigma, gamma=gamma)
def f_local(x):
return density_f_mod(x, mean=mean, sigma=sigma, gamma=gamma)
error_mala_all[j], x_mala = mcmc.mala(init_distr, grad_f_local, f_local, error_quantile,
kappa=kappa_mod, L=L_mod, nb_iters=nb_iters, nb_exps=nb_exps)
error_rwmh_all[j], x_rwmh = mcmc.rwmh(init_distr, f_local, error_quantile,
kappa=kappa_mod, L=L_mod, nb_iters=nb_iters, nb_exps=nb_exps)
error_ula_all[j], x_ula = mcmc.ula(init_distr, grad_f_local, error_quantile,
epsilon=10.*eps, kappa=kappa_mod, L=L_mod, nb_iters=nb_iters, nb_exps=nb_exps)
error_ula_02_all[j], x_ula = mcmc.ula(init_distr, grad_f_local, error_quantile,
epsilon=eps, kappa=kappa_mod, L=L_mod, nb_iters=nb_iters, nb_exps=nb_exps)
result = {}
result['epsilons'] = epsilons
result['d'] = d
result['nb_iters'] = nb_iters
result['nb_exps'] = nb_exps
result['sigma_max'] = sigma_max
result['ula'] = error_ula_all
result['ula_02'] = error_ula_02_all
result['mala'] = error_mala_all
result['rwmh'] = error_rwmh_all
save_path = "PLEASE UPDATE BEFORE USE"
np.save('%s/gaussian_nonstrongly_nonisotropic_eps_iters%d_exps%d_seed%d.npy' %(save_path, nb_iters, nb_exps, seed), result)
def main_simu(d, nb_exps=100, nb_iters=40000, seed=1):
np.random.seed(123456 + seed)
error_hmc_all = np.zeros((nb_iters, 1))
error_hmcagg_all = np.zeros((nb_iters, 1))
error_mala_all = np.zeros((nb_iters, 1))
error_rwmh_all = np.zeros((nb_iters, 1))
mean = np.zeros(d)
#sigma_max = d**(5.0/12)
sigma_max = d**(1.0 / 3)
sigma = np.array([1.0 + (sigma_max - 1.0) / (d - 1) * i for i in range(d)])
L = 1. / sigma[0]**2
m = 1. / sigma[-1]**2
kappa = L / m
print("d = %d, m = %0.2f, L = %0.2f, kappa = %0.2f" % (d, m, L, kappa))
def error_quantile(x_curr):
q3 = sigma[-1] * scipy.stats.norm.ppf(0.75)
e1 = np.abs(np.percentile(x_curr[:, -1], 75) - q3) / q3
return np.array([e1])
init_distr = 1. / np.sqrt(L) * np.random.randn(nb_exps, d)
def grad_f_local(x):
return grad_f(x, mean=mean, sigma=sigma)
def f_local(x):
return f(x, mean=mean, sigma=sigma)
# cK is a multiplier on K
cK = 1
# number of leapfrog updates
K_hmc = np.int(np.ceil(d**0.75 / kappa**0.75 * cK))
nb_hmc_iters = np.int(nb_iters / K_hmc) + 1
error_hmc_all[:nb_hmc_iters, :], x_hmc, ac_hmc, _ = mcmc.hmc(
init_distr,
grad_f_local,
f_local,
error_quantile,
stepchoice=3,
kappa=kappa,
L=L,
L3=L,
cK=cK,
nb_iters=nb_hmc_iters,
nb_exps=nb_exps)
# aggressive HMC step-size choice by assuming L3 small
K_hmcagg = np.int(np.ceil(d**0.125 * kappa**0.25 * cK))
nb_hmcagg_iters = np.int(nb_iters / K_hmcagg) + 1
error_hmcagg_all[:nb_hmcagg_iters, :], x_hmcagg, ac_hmcagg, _ = mcmc.hmc(
init_distr,
grad_f_local,
f_local,
error_quantile,
stepchoice=5,
kappa=kappa,
L=L,
L3=L,
cK=cK,
nb_iters=nb_hmcagg_iters,
nb_exps=nb_exps)
error_mala_all, x_mala, ac_mala = mcmc.mala(init_distr,
grad_f_local,
f_local,
error_quantile,
kappa=kappa,
L=L,
nb_iters=nb_iters,
nb_exps=nb_exps)
error_rwmh_all, x_rwmh, ac_rwmh = mcmc.rwmh(init_distr,
f_local,
error_quantile,
kappa=kappa,
L=L,
nb_iters=nb_iters,
nb_exps=nb_exps)
result = {}
result['d'] = d
result['nb_iters'] = nb_iters
result['nb_exps'] = nb_exps
result['sigma_max'] = sigma_max
result['cK'] = cK
result['K_hmc'] = K_hmc
result['nb_hmc_iters'] = nb_hmc_iters
result['K_hmcagg'] = K_hmcagg
result['nb_hmcagg_iters'] = nb_hmcagg_iters
result['hmc'] = error_hmc_all
result['hmcagg'] = error_hmcagg_all
result['mala'] = error_mala_all
result['rwmh'] = error_rwmh_all
result['ac_hmc'] = ac_hmc
result['ac_hmcagg'] = ac_hmcagg
result['ac_mala'] = ac_mala
result['ac_rwmh'] = ac_rwmh
save_path = "/cluster/scratch/chenyua/HMC/results"
np.save(
'%s/warm_gaussian_nonisotropic_d%d_kappa23_cK%d_iters%d_exps%d_seed%d.npy'
% (save_path, d, int(cK), nb_iters, nb_exps, seed), result)