def main(argv):
del argv
if FLAGS.grid2d:
raise NotImplementedError('Only 1D Normal supported...')
if FLAGS.qt == "":
eprint("provide some qt to the `--qt` option if you would like to "
"plot")
if FLAGS.label:
label = FLAGS.label
else:
qt_file = os.path.splitext(FLAGS.qt)[0]
label = qt_file[qt_file.find('qt_') + len('qt_'):]
plt.figure(1)
debug("visualizing %s" % FLAGS.qt)
mixture_params = get_mixture_params_from_file(FLAGS.qt)
#plot_normal_mix(mixture_params['weights'], mixture_params['locs'],
# mixture_params['scale_diags'], plt, label)
plt.figure(2)
w = mixture_params['weights']
barlist = plt.bar(np.arange(len(w)), w, color='b', label=label)
if FLAGS.iter_labels:
label_name = os.path.basename(FLAGS.iter_labels)
if label_name.startswith('iter_types'):
# label which iterations came from adaptive which
# from fixed.
with open(FLAGS.iter_labels, 'r') as f:
iter_types = f.readlines()
for i, it in enumerate(iter_types):
it = it.strip()
if it != 'adaptive':
if it == 'fixed':
barlist[i + 1].set_color('r')
elif it == 'fixed_adaptive_MAXITER':
barlist[i + 1].set_color('g')
else:
barlist[i + 1].set_color('k')
ad = mpatches.Patch(color='b', label='Adaptive step')
fi = mpatches.Patch(color='r',
label='Fixed step (adafw loop long)')
fa = mpatches.Patch(color='g', label='Fixed step (-ve gap)')
plt.legend(handles=[ad, fi, fa], loc=2)
if FLAGS.outdir == 'stdout':
plt.show()
else:
fig.tight_layout()
outname = os.path.join(os.path.expanduser(FLAGS.outdir), FLAGS.outfile)
fig.savefig(outname,
bbox_extra_artists=(legend, ),
bbox_inches='tight')
print('saved to ', outname)
def adaptive_pfw(weights, comps, locs, diags, q_t, mu_s, cov_s, s_t, p,
k, l_prev):
"""
Adaptive pairwise variant.
Args:
same as fixed
"""
d_t_norm = divergence(s_t, q_t, metric=FLAGS.distance_metric).eval()
logger.info('distance norm is %.5f' % d_t_norm)
# Find v_t
qcomps = q_t.components
index_v_t, step_v_t = argmax_grad_dotp(p, q_t, qcomps,
FLAGS.n_monte_carlo_samples)
v_t = qcomps[index_v_t]
# Pairwise gap
sample_s = s_t.sample([FLAGS.n_monte_carlo_samples])
step_s = tf.reduce_mean(grad_kl(q_t, p, sample_s)).eval()
gap_pw = step_v_t - step_s
if gap_pw < 0: eprint("Pairwise gap is negative")
def default_fixed_step(fail_type='fixed'):
# adaptive failed, return to fixed
gamma = 2. / (k + 2.)
new_comps = copy.copy(comps)
new_comps.append({'loc': mu_s, 'scale_diag': cov_s})
new_weights = [(1. - gamma) * w for w in weights]
new_weights.append(gamma)
return {
'gamma': 2. / (k + 2.),
'l_estimate': l_prev,
'weights': new_weights,
'comps': new_comps,
'gap': gap_pw,
'step_type': fail_type
}
logger.info('Pairwise gap %.5f' % gap_pw)
# Set $q_{t+1}$'s params
new_locs = copy.copy(locs)
new_diags = copy.copy(diags)
new_locs.append(mu_s)
new_diags.append(cov_s)
gap = gap_pw
if gap <= 0:
return default_fixed_step()
gamma_max = weights[index_v_t]
step_type = 'adaptive'
tau = FLAGS.exp_adafw
eta = FLAGS.damping_adafw
pow_tau = 1.0
i, l_t = 0, l_prev
f_t = kl_divergence(q_t, p, allow_nan_stats=False).eval()
drop_step = False
debug('f(q_t) = %.5f' % (f_t))
gamma = 2. / (k + 2)
while gamma >= MIN_GAMMA and i < FLAGS.adafw_MAXITER:
# compute $L_t$ and $\gamma_t$
l_t = pow_tau * eta * l_prev
gamma = min(gap / (l_t * d_t_norm), gamma_max)
d_1 = - gamma * gap
d_2 = gamma * gamma * l_t * d_t_norm / 2.
debug('linear d1 = %.5f, quad d2 = %.5f' % (d_1, d_2))
quad_bound_rhs = f_t + d_1 + d_2
# construct $q_{t + 1}$
new_weights = copy.copy(weights)
new_weights.append(gamma)
if gamma == gamma_max:
# hardcoding to 0 for precision issues
new_weights[index_v_t] = 0
drop_step = True
else:
new_weights[index_v_t] -= gamma
drop_step = False
qt_new = Mixture(
cat=Categorical(probs=tf.convert_to_tensor(new_weights)),
components=[
MultivariateNormalDiag(loc=loc, scale_diag=diag)
for loc, diag in zip(new_locs, new_diags)
])
quad_bound_lhs = kl_divergence(qt_new, p, allow_nan_stats=False).eval()
logger.info('lt = %.5f, gamma = %.3f, f_(qt_new) = %.5f, '
'linear extrapolated = %.5f' % (l_t, gamma, quad_bound_lhs,
quad_bound_rhs))
if quad_bound_lhs <= quad_bound_rhs:
new_comps = copy.copy(comps)
new_comps.append({'loc': mu_s, 'scale_diag': cov_s})
if drop_step:
del new_comps[index_v_t]
del new_weights[index_v_t]
logger.info("...drop step")
step_type = 'drop'
return {
'gamma': gamma,
'l_estimate': l_t,
'weights': new_weights,
'comps': new_comps,
'gap': gap,
'step_type': step_type
}
pow_tau *= tau
i += 1
# gamma below MIN_GAMMA
logger.warning("gamma below threshold value, returning fixed step")
return default_fixed_step("fixed_adaptive_MAXITER")
def adaptive_afw(weights, comps, locs, diags, q_t, mu_s, cov_s, s_t, p,
k, l_prev):
"""
Away steps variant
Args:
same as fixed
"""
d_t_norm = divergence(s_t, q_t, metric=FLAGS.distance_metric).eval()
logger.info('distance norm is %.5f' % d_t_norm)
# Find v_t
qcomps = q_t.components
index_v_t, step_v_t = argmax_grad_dotp(p, q_t, qcomps,
FLAGS.n_monte_carlo_samples)
v_t = qcomps[index_v_t]
# Frank-Wolfe gap
sample_q = q_t.sample([FLAGS.n_monte_carlo_samples])
sample_s = s_t.sample([FLAGS.n_monte_carlo_samples])
step_s = tf.reduce_mean(grad_kl(q_t, p, sample_s)).eval()
step_q = tf.reduce_mean(grad_kl(q_t, p, sample_q)).eval()
gap_fw = step_q - step_s
if gap_fw < 0: logger.warning("Frank-Wolfe duality gap is negative")
# Away gap
gap_a = step_v_t - step_q
if gap_a < 0: eprint('Away gap < 0!!!')
logger.info('fw gap %.5f, away gap %.5f' % (gap_fw, gap_a))
# Set $q_{t+1}$'s params
new_locs = copy.copy(locs)
new_diags = copy.copy(diags)
if (gap_fw >= gap_a) or (len(comps) == 1):
# FW direction, proceeds exactly as adafw
logger.info('Proceeding in FW direction ')
adaptive_step_type = 'fw'
gap = gap_fw
new_locs.append(mu_s)
new_diags.append(cov_s)
gamma_max = 1.0
else:
# Away direction
logger.info('Proceeding in Away direction ')
adaptive_step_type = 'away'
gap = gap_a
if weights[index_v_t] < 1.0:
gamma_max = weights[index_v_t] / (1.0 - weights[index_v_t])
else:
gamma_max = 100. # Large value when t = 1
def default_fixed_step(fail_type='fixed'):
# adaptive failed, return to fixed
gamma = 2. / (k + 2.)
new_comps = copy.copy(comps)
new_comps.append({'loc': mu_s, 'scale_diag': cov_s})
new_weights = [(1. - gamma) * w for w in weights]
new_weights.append(gamma)
return {
'gamma': 2. / (k + 2.),
'l_estimate': l_prev,
'weights': new_weights,
'comps': new_comps,
'gap': gap,
'step_type': fail_type
}
if gap <= 0:
return default_fixed_step()
tau = FLAGS.exp_adafw
eta = FLAGS.damping_adafw
pow_tau = 1.0
i, l_t = 0, l_prev
f_t = kl_divergence(q_t, p, allow_nan_stats=False).eval()
debug('f(q_t) = %.5f' % (f_t))
gamma = 2. / (k + 2)
is_drop_step = False
while gamma >= MIN_GAMMA and i < FLAGS.adafw_MAXITER:
# compute $L_t$ and $\gamma_t$
l_t = pow_tau * eta * l_prev
# NOTE: Handle extreme values of gamma carefully
gamma = min(gap / (l_t * d_t_norm), gamma_max)
d_1 = - gamma * gap
d_2 = gamma * gamma * l_t * d_t_norm / 2.
debug('linear d1 = %.5f, quad d2 = %.5f' % (d_1, d_2))
quad_bound_rhs = f_t + d_1 + d_2
# construct $q_{t + 1}$
if adaptive_step_type == 'fw':
if gamma == gamma_max:
# gamma = 1.0, q_{t + 1} = s_t
new_comps = [{'loc': mu_s, 'scale_diag': cov_s}]
new_weights = [1.]
qt_new = MultivariateNormalDiag(loc=mu_s, scale_diag=cov_s)
else:
new_comps = copy.copy(comps)
new_comps.append({'loc': mu_s, 'scale_diag': cov_s})
new_weights = copy.copy(weights)
new_weights = [(1. - gamma) * w for w in new_weights]
new_weights.append(gamma)
qt_new = Mixture(
cat=Categorical(probs=tf.convert_to_tensor(new_weights)),
components=[
MultivariateNormalDiag(loc=loc, scale_diag=diag)
for loc, diag in zip(new_locs, new_diags)
])
elif adaptive_step_type == 'away':
new_weights = copy.copy(weights)
new_comps = copy.copy(comps)
if gamma == gamma_max:
# drop v_t
is_drop_step = True
logger.info('...drop step')
del new_weights[index_v_t]
new_weights = [(1. + gamma) * w for w in new_weights]
del new_comps[index_v_t]
# NOTE: recompute locs and diags after dropping v_t
drop_locs = [c['loc'] for c in new_comps]
drop_diags = [c['scale_diag'] for c in new_comps]
qt_new = Mixture(
cat=Categorical(probs=tf.convert_to_tensor(new_weights)),
components=[
MultivariateNormalDiag(loc=loc, scale_diag=diag)
for loc, diag in zip(drop_locs, drop_diags)
])
else:
is_drop_step = False
new_weights = [(1. + gamma) * w for w in new_weights]
new_weights[index_v_t] -= gamma
qt_new = Mixture(
cat=Categorical(probs=tf.convert_to_tensor(new_weights)),
components=[
MultivariateNormalDiag(loc=loc, scale_diag=diag)
for loc, diag in zip(new_locs, new_diags)
])
quad_bound_lhs = kl_divergence(qt_new, p, allow_nan_stats=False).eval()
logger.info('lt = %.5f, gamma = %.3f, f_(qt_new) = %.5f, '
'linear extrapolated = %.5f' % (l_t, gamma, quad_bound_lhs,
quad_bound_rhs))
if quad_bound_lhs <= quad_bound_rhs:
step_type = "adaptive"
if adaptive_step_type == "away": step_type = "away"
if is_drop_step: step_type = "drop"
return {
'gamma': gamma,
'l_estimate': l_t,
'weights': new_weights,
'comps': new_comps,
'gap': gap,
'step_type': step_type
}
pow_tau *= tau
i += 1
# adaptive loop failed, return fixed step size
logger.warning("gamma below threshold value, returning fixed step")
return default_fixed_step()
def run_gap(pi, mus, stds):
weights, comps = [], []
elbos = []
relbo_vals = []
for t in range(FLAGS.n_fw_iter):
logger.info('Frank Wolfe Iteration %d' % t)
g = tf.Graph()
with g.as_default():
tf.set_random_seed(FLAGS.seed)
sess = tf.InteractiveSession()
with sess.as_default():
# target distribution components
pcomps = [
MultivariateNormalDiag(
loc=tf.convert_to_tensor(mus[i], dtype=tf.float32),
scale_diag=tf.convert_to_tensor(stds[i],
dtype=tf.float32))
for i in range(len(mus))
]
# target distribution
p = Mixture(cat=Categorical(probs=tf.convert_to_tensor(pi)),
components=pcomps)
# LMO appoximation
s = construct_normal([1], t, 's')
fw_iterates = {}
if t > 0:
qtx = Mixture(
cat=Categorical(probs=tf.convert_to_tensor(weights)),
components=[
MultivariateNormalDiag(**c) for c in comps
])
fw_iterates = {p: qtx}
sess.run(tf.global_variables_initializer())
# Run inference on relbo to solve LMO problem
# NOTE: KLqp has a side effect, it is modifying s
inference = relbo.KLqp({p: s},
fw_iterates=fw_iterates,
fw_iter=t)
inference.run(n_iter=FLAGS.LMO_iter)
# s now contains solution to LMO
if t > 0:
sample_s = s.sample([FLAGS.n_monte_carlo_samples])
sample_q = qtx.sample([FLAGS.n_monte_carlo_samples])
step_s = tf.reduce_mean(grad_kl(qtx, p, sample_s)).eval()
step_q = tf.reduce_mean(grad_kl(qtx, p, sample_q)).eval()
gap = step_q - step_s
logger.info('Frank-Wolfe gap at iter %d is %.5f' %
(t, gap))
if gap < 0:
eprint('Frank-Wolfe gab becoming negative!')
# f(q*) = f(p) = 0
logger.info('Objective value (actual gap) is %.5f' %
kl_divergence(qtx, p).eval())
gamma = 2. / (t + 2.)
comps.append({
'loc': s.mean().eval(),
'scale_diag': s.stddev().eval()
})
weights = coreutils.update_weights(weights, gamma, t)
tf.reset_default_graph()
def adaptive_afw(weights, params, q_t, mu_s, cov_s, s_t, p, k, l_prev):
"""Adaptive Away Steps algorithm.
Args:
weights: [k], weights of the mixture components of q_t
params: list containing dictionary of mixture params ('mu', 'scale')
q_t: current mixture iterate q_t
mu_s: [dim], mean for LMO solution s
cov_s: [dim], cov matrix for LMO solution s
s_t: Current atom & LMO Solution s
p: edward.model, target distribution p
k: iteration number of Frank-Wolfe
l_prev: previous lipschitz estimate
Returns:
a dictionary containing gamma, new weights, new parameters
lipschitz estimate, duality gap of current iterate
and step information
"""
# FIXME
is_vector = FLAGS.base_dist in ['mvnormal', 'mvlaplace']
d_t_norm = divergence(s_t, q_t, metric=FLAGS.distance_metric).eval()
logger.info('\ndistance norm is %.3e' % d_t_norm)
# Find v_t
qcomps = q_t.components
index_v_t, step_v_t = argmax_grad_dotp(p, q_t, qcomps,
FLAGS.n_monte_carlo_samples)
v_t = qcomps[index_v_t]
# Frank-Wolfe gap
N_samples = FLAGS.n_monte_carlo_samples
sample_q = q_t.sample([N_samples])
sample_s = s_t.sample([N_samples])
step_s = tf.reduce_mean(grad_elbo(q_t, p, sample_s)).eval()
step_q = tf.reduce_mean(grad_elbo(q_t, p, sample_q)).eval()
gap_fw = step_q - step_s
if gap_fw < 0: logger.warning("Frank-Wolfe duality gap is negative")
# Away gap
gap_a = step_v_t - step_q
if gap_a < 0: eprint('Away gap < 0!!!')
logger.info('fw gap %.3e, away gap %.3e' % (gap_fw, gap_a))
if (gap_fw >= gap_a) or (len(params) == 1):
# FW direction, proceeds exactly as adafw
logger.info('Proceeding in FW direction ')
return adaptive_fw(weights, params, q_t, mu_s, cov_s, s_t, p, k,
l_prev, gap_fw)
# Away direction
logger.info('Proceeding in Away direction ')
adaptive_step_type = 'away'
gap = gap_a
if weights[index_v_t] < 1.0:
MAX_GAMMA = weights[index_v_t] / (1.0 - weights[index_v_t])
else:
MAX_GAMMA = 100. # Large value when t = 1
gamma = 2. / (k + 2.)
tau = FLAGS.exp_adafw
eta = FLAGS.damping_adafw
pow_tau = 1.0
i, l_t = 0, l_prev
f_t = -elbo(q_t, p, N_samples, return_std=False)
debug('f(q_t) = %.5f' % (f_t))
is_drop_step = False
while gamma >= MIN_GAMMA and i < FLAGS.adafw_MAXITER:
# compute $L_t$ and $\gamma_t$
l_t = pow_tau * eta * l_prev
# NOTE: Handle extreme values of gamma carefully
gamma = min(gap / (l_t * d_t_norm), MAX_GAMMA)
d_1 = -gamma * gap
d_2 = gamma * gamma * l_t * d_t_norm / 2.
debug('linear d1 = %.5f, quad d2 = %.5f' % (d_1, d_2))
quad_bound_rhs = f_t + d_1 + d_2
# construct $q_{t + 1}$
new_weights = copy.copy(weights)
new_params = copy.copy(params)
if gamma == MAX_GAMMA:
# drop v_t
is_drop_step = True
del new_weights[index_v_t]
new_weights = [(1. + gamma) * w for w in new_weights]
del new_params[index_v_t]
else:
is_drop_step = False
new_weights = [(1. + gamma) * w for w in new_weights]
new_weights[index_v_t] -= gamma
new_components = [
coreutils.base_loc_scale(FLAGS.base_dist,
c['loc'],
c['scale'],
multivariate=is_vector)
for c in new_params
]
qt_new = coreutils.get_mixture(new_weights, new_components)
quad_bound_lhs = -elbo(qt_new, p, N_samples, return_std=False)
logger.info('lt = %.3e, gamma = %.3f, f_(qt_new) = %.3e, '
'linear extrapolated = %.3e' %
(l_t, gamma, quad_bound_lhs, quad_bound_rhs))
if quad_bound_lhs <= quad_bound_rhs:
return {
'gamma': gamma,
'l_estimate': l_t,
'weights': new_weights,
'params': new_params,
'gap': gap,
'step_type': "drop" if is_drop_step else "away"
}
pow_tau *= tau
i += 1
# gamma below MIN_GAMMA
logger.warning("gamma below threshold value, returning fixed step")
return fixed(weights, params, q_t, mu_s, cov_s, s_t, p, k, gap)
def main(argv):
del argv
x = deserialize_target_from_file(FLAGS.target)
if FLAGS.widegrid:
grid = np.arange(-25, 25, 0.1).astype(np.float32)
else:
grid = np.arange(-4, 4, 0.1).astype(np.float32)
if FLAGS.grid2d:
# 2D grid
grid = np.arange(-2, 2, 0.1).astype(np.float32)
gridx, gridy = np.meshgrid(grid, grid)
grid = np.vstack((gridx.flatten(), gridy.flatten())).T
if FLAGS.labels:
labels = FLAGS.labels
else:
labels = ['approximation'] * len(FLAGS.qt)
if FLAGS.styles:
styles = FLAGS.styles
else:
styles = ['+', 'x', '.', '-']
colors = ['Greens', 'Reds']
sess = tf.Session()
if FLAGS.grid2d:
fig = plt.figure()
ax = fig.add_subplot(211)
else:
fig, ax = plt.subplots()
grid = np.expand_dims(grid, 1) # package dims for tf
with sess.as_default():
xprobs = x.log_prob(grid)
xprobs = tf.exp(xprobs).eval()
if FLAGS.grid2d:
ax.pcolormesh(gridx,
gridy,
xprobs.reshape(gridx.shape),
cmap='Blues')
else:
ax.plot(grid, xprobs, label='target', linewidth=2.0)
if len(FLAGS.qt) == 0:
eprint(
"provide some qts to the `--qt` option if you would like to "
"plot them")
for i, (qt_filename, label) in enumerate(zip(FLAGS.qt, labels)):
debug("visualizing %s" % qt_filename)
qt = deserialize_mixture_from_file(qt_filename)
qtprobs = tf.exp(qt.log_prob(grid))
qtprobs = qtprobs.eval()
if FLAGS.grid2d:
ax2 = fig.add_subplot(212)
ax2.pcolormesh(gridx,
gridy,
qtprobs.reshape(gridx.shape),
cmap='Greens')
else:
ax.plot(grid,
qtprobs,
styles[i % len(styles)],
label=label,
linewidth=2.0)
if len(FLAGS.qt) == 1 and FLAGS.bars:
locs = [comp.loc.eval() for comp in qt.components]
ax.plot(locs, [0] * len(locs), '+')
weights = qt.cat.probs.eval()
for i in range(len(locs)):
ax.bar(locs[i], weights[i], .05)
ax.set_xticks([])
ax.set_xticklabels([])
ax.set_xlabel(FLAGS.xlabel)
ax.set_ylabel(FLAGS.ylabel)
fig.suptitle(FLAGS.title)
if not FLAGS.grid2d:
legend = plt.legend(loc='upper right',
prop={'size': 15},
bbox_to_anchor=(1.08, 1))
if FLAGS.outdir == 'stdout':
plt.show()
else:
fig.tight_layout()
outname = os.path.join(os.path.expanduser(FLAGS.outdir), FLAGS.outfile)
fig.savefig(outname,
bbox_extra_artists=(legend, ),
bbox_inches='tight')
print('saved to ', outname)