def generate_main_prop(level, type, distribution='normal'):
prop_type = random.choice(MAIN_PROP[type])
if type == 'accessory':
low = MAIN_PROP_VAL[type][0] * level + MAIN_PROP_VAL[type][1]
high = MAIN_PROP_VAL[type][2] * level + MAIN_PROP_VAL[type][3]
else:
low = MAIN_PROP_VAL[type][0] * level
high = MAIN_PROP_VAL[type][1] * level
prop_val = dist(low, high, distribution)
return prop_type, prop_val
def generate_addition_val(level, add_type, distribution='normal'):
if add_type in ADDITION_CATE[0]:
low = ADDITION_PROP_VAL[0][0] * level + ADDITION_PROP_VAL[0][1]
if level in [60, 80]:
high = low + 3
elif level in [100, 120]:
high = low + 4
else:
high = low + 5
else:
for i in range(1, 4):
if add_type in ADDITION_CATE[i]:
low = ADDITION_PROP_VAL[i][0] * level
high = ADDITION_PROP_VAL[i][1] * level
add_val = dist(low, high, distribution)
return add_val
def mh_uni(init, ys, ts, iters, wid=0.1, fi=None):
"""
Component-wise MH with uniform proposals
"""
print("Running Metropolis Algorithm with Uniform proposals.")
D = len(init)
samples = np.zeros((iters, D))
my_dist = dist(init)
# initialize state and log-likelihood
state = init.copy()
Lp_state = my_dist.log_likelihood(ys, ts)
accepts = 0.
for i in np.arange(0, iters):
print '***Curr acct: %s' % (float(accepts) / ((i + 1) * 4))
for j, comp in enumerate(state):
if fi is not None:
write_samp(fi, state)
# propose a new state
prop = (np.random.uniform(comp - wid, comp + wid))
move_p = np.log(
scipy.stats.uniform(comp - wid, comp + wid).pdf(prop))
rev_p = np.log(
scipy.stats.uniform(prop - wid, prop + wid).pdf(comp))
prop_state = state.copy()
prop_state[j] = prop
my_dist.set_params(prop_state)
print "\t", prop_state
Lp_prop = my_dist.log_likelihood(ys, ts)
rand = np.random.rand()
if np.log(rand) < min(1,
((Lp_prop + rev_p) - (Lp_state + move_p))):
print ("\tacct bc %s < %s (iter %s)"%(np.log(rand),\
(Lp_prop-Lp_state),i))
accepts += 1
state = prop_state.copy()
Lp_state = Lp_prop
else:
my_dist.set_params(state)
samples[i] = state.copy()
print 'Acceptance ratio', accepts / (iters * len(init))
return samples
def mh_lognormal(init, ys, ts, iters, fi=None):
"""
MH with lognormal proposals
"""
print("Running Metropolis Algorithm with Log-Normal proposals.")
D = len(init)
my_dist = dist(init)
# initialize state and log-likelihood
state = init.copy()
Lp_state = my_dist.log_likelihood(ys, ts)
accepts = 0.
cov = (0.1**2) * np.eye(D) * 1. / D
for i in np.arange(0, iters):
if fi is not None:
write_samp(fi, state)
# log(Rv) follow a normal distribution
mu = np.log(state)
# propose a new state
prop = np.exp(np.random.multivariate_normal(mu, cov))
move_p = np.log(scipy.stats.multivariate_normal(np.log(state),cov).\
pdf(np.log(prop)))
rev_p = np.log(scipy.stats.multivariate_normal(np.log(prop),cov).\
pdf(np.log(state)))
my_dist.set_params(prop)
Lp_prop = my_dist.log_likelihood(ys, ts)
#print Lp_prop+rev_p
#print Lp_state+move_p
rand = np.random.rand()
prob = min(1, ((Lp_prop + rev_p) - (Lp_state + move_p)))
if np.log(rand) < prob:
accepts += 1
state = prop.copy()
Lp_state = Lp_prop
print("acct bc %s < %s (iter %s)" % (np.log(rand), prob, i))
print state
else:
my_dist.set_params(state)
print 'Acceptance ratio', accepts / iters
def mh_gaussian(init, ys, ts, iters, fi=None):
"""
MH with gaussian proposals
"""
print("Running Metropolis Algorithm with Gaussian proposals.")
D = len(init)
samples = np.zeros((iters, D))
my_dist = dist(init)
# initialize state and log-likelihood
state = init.copy()
Lp_state = my_dist.log_likelihood(ys, ts)
accepts = 0.
cov = (0.1)**2 * np.eye(D) * 1. / D
for i in np.arange(0, iters):
if fi is not None:
write_samp(fi, state)
# propose a new state
prop = (np.random.multivariate_normal(state.ravel(), cov))
move_p = np.log(scipy.stats.multivariate_normal(state, cov).pdf(prop))
rev_p = np.log(scipy.stats.multivariate_normal(prop, cov).pdf(state))
my_dist.set_params(prop)
Lp_prop = my_dist.log_likelihood(ys, ts)
rand = np.random.rand()
if np.log(rand) < min(1, ((Lp_prop + rev_p) - (Lp_state + move_p))):
print("acct bc %s < %s (iter %s)" % (np.log(rand),
(Lp_prop - Lp_state), i))
accepts += 1
state = prop.copy()
print state
Lp_state = Lp_prop
else:
my_dist.set_params(state)
samples[i] = state.copy()
print 'Acceptance ratio', accepts / iters
return samples