def adaptive_fw(weights,
params,
q_t,
mu_s,
cov_s,
s_t,
p,
k,
l_prev,
gap=None):
"""Adaptive Frank-Wolfe algorithm.
Sets step size as suggested in Algorithm 1 of
https://arxiv.org/pdf/1806.05123.pdf
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
gap: Duality-Gap (if already computed)
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)
N_samples = FLAGS.n_monte_carlo_samples
if gap is None:
# create and sample from $s_t, q_t$
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 = step_q - step_s
logger.info('duality gap %.3e' % gap)
if gap < 0:
logger.warning("Duality gap is negative returning fixed step")
return fixed(weights, params, q_t, mu_s, cov_s, s_t, p, k, gap)
gamma = 2. / (k + 2.)
tau = FLAGS.exp_adafw
eta = FLAGS.damping_adafw
# NOTE: this is from v1 of the paper, new version
# replaces multiplicative eta with divisor eta
pow_tau = 1.0
i, l_t = 0, l_prev
# Objective in this case is -ELBO
f_t = -elbo(q_t, p, N_samples, return_std=False)
debug('f(q_t) = %.3e' % (f_t))
# return intial estimate if gap is -ve
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), 1.0)
d_1 = -gamma * gap
d_2 = gamma * gamma * l_t * d_t_norm / 2.
debug('linear d1 = %.3e, quad d2 = %.3e' % (d_1, d_2))
quad_bound_rhs = f_t + d_1 + d_2
# $w_{t + 1} = [(1 - \gamma)w_t, \gamma]$
# Handling the case of gamma = 1.0
# separately, weights might not get exactly 0 because
# of precision issues. 0 wt components should be removed
if gamma != 1.0:
new_weights = copy.copy(weights)
new_weights = [(1. - gamma) * w for w in new_weights]
new_weights.append(gamma)
new_params = copy.copy(params)
new_params.append({'loc': mu_s, 'scale': cov_s})
new_components = [
coreutils.base_loc_scale(FLAGS.base_dist,
c['loc'],
c['scale'],
multivariate=is_vector)
for c in new_params
]
else:
new_weights = [1.]
new_params = [{'loc': mu_s, 'scale': cov_s}]
new_components = [s_t]
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:
# Adaptive loop succeeded
return {
'gamma': gamma,
'l_estimate': l_t,
'weights': new_weights,
'params': new_params,
'gap': gap,
'step_type': 'adaptive'
}
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(_):
ed.set_seed(FLAGS.seed)
# setting up output directory
outdir = FLAGS.outdir
if '~' in outdir: outdir = os.path.expanduser(outdir)
os.makedirs(outdir, exist_ok=True)
is_vector = FLAGS.base_dist in ['mvnormal', 'mvlaplace']
((Xtrain, ytrain), (Xtest, ytest)) = blr_utils.get_data()
N, D = Xtrain.shape
N_test, D_test = Xtest.shape
assert D_test == D, 'Test dimension %d different than train %d' % (D_test,
D)
logger.info('D = %d, Ntrain = %d, Ntest = %d' % (D, N, N_test))
# Solution components
weights, q_params = [], []
# L-continous gradient estimate
lipschitz_estimate = None
# Metrics to log
times_filename = os.path.join(outdir, 'times.csv')
open(times_filename, 'w').close()
# (mean, +- std)
elbos_filename = os.path.join(outdir, 'elbos.csv')
logger.info('saving elbos to, %s' % elbos_filename)
open(elbos_filename, 'w').close()
rocs_filename = os.path.join(outdir, 'roc.csv')
logger.info('saving rocs to, %s' % rocs_filename)
open(rocs_filename, 'w').close()
gap_filename = os.path.join(outdir, 'gap.csv')
open(gap_filename, 'w').close()
step_filename = os.path.join(outdir, 'steps.csv')
open(step_filename, 'w').close()
# (mean, std)
ll_train_filename = os.path.join(outdir, 'll_train.csv')
open(ll_train_filename, 'w').close()
ll_test_filename = os.path.join(outdir, 'll_test.csv')
open(ll_test_filename, 'w').close()
# (bin_ac_train, bin_ac_test)
bin_ac_filename = os.path.join(outdir, 'bin_ac.csv')
open(bin_ac_filename, 'w').close()
# 'adafw', 'ada_afw', 'ada_pfw'
if FLAGS.fw_variant.startswith('ada'):
lipschitz_filename = os.path.join(outdir, 'lipschitz.csv')
open(lipschitz_filename, 'w').close()
iter_info_filename = os.path.join(outdir, 'iter_info.txt')
open(iter_info_filename, 'w').close()
for t in range(FLAGS.n_fw_iter):
g = tf.Graph()
with g.as_default():
sess = tf.InteractiveSession()
with sess.as_default():
tf.set_random_seed(FLAGS.seed)
# Build Model
w = Normal(loc=tf.zeros(D, tf.float32),
scale=tf.ones(D, tf.float32))
X = tf.placeholder(tf.float32, [None, D])
y = Bernoulli(logits=ed.dot(X, w))
p_joint = blr_utils.Joint(Xtrain, ytrain, sess,
FLAGS.n_monte_carlo_samples, logger)
# vectorized Model evaluations
n_test_samples = 100
W = tf.placeholder(tf.float32, [n_test_samples, D])
y_data = tf.placeholder(tf.float32, [None]) # N -> (N, n_test)
y_data_matrix = tf.tile(tf.expand_dims(y_data, 1),
(1, n_test_samples))
pred_logits = tf.matmul(X, tf.transpose(W)) # (N, n_test)
ypred = tf.sigmoid(tf.reduce_mean(pred_logits, axis=1))
pY = Bernoulli(logits=pred_logits) # (N, n_test)
log_likelihoods = pY.log_prob(y_data_matrix) # (N, n_test)
log_likelihood_expectation = tf.reduce_mean(log_likelihoods,
axis=1) # (N, )
ll_mean, ll_std = tf.nn.moments(log_likelihood_expectation,
axes=[0])
if t == 0:
fw_iterates = {}
else:
# Current solution
prev_components = [
coreutils.base_loc_scale(FLAGS.base_dist,
c['loc'],
c['scale'],
multivariate=is_vector)
for c in q_params
]
qtw_prev = coreutils.get_mixture(weights, prev_components)
fw_iterates = {w: qtw_prev}
# s is the solution to LMO, random initialization
s = coreutils.construct_base(FLAGS.base_dist, [D],
t,
's',
multivariate=is_vector)
sess.run(tf.global_variables_initializer())
total_time = 0.
inference_time_start = time.time()
# Run relbo to solve LMO problem
# If the first atom is being selected through running LMO
# it is equivalent to running vi on a uniform prior
# Since uniform is not in our variational family try
# only random element (without LMO inference) as initial iterate
if FLAGS.iter0 == 'vi' or t > 0:
inference = relbo.KLqp({w: s},
fw_iterates=fw_iterates,
data={
X: Xtrain,
y: ytrain
},
fw_iter=t)
inference.run(n_iter=FLAGS.LMO_iter)
inference_time_end = time.time()
# compute only step size selection time
#total_time += float(inference_time_end - inference_time_start)
loc_s = s.mean().eval()
scale_s = s.stddev().eval()
# Evaluate the next step
step_result = {}
if t == 0:
# Initialization, q_0
q_params.append({'loc': loc_s, 'scale': scale_s})
weights.append(1.)
if FLAGS.fw_variant.startswith('ada'):
lipschitz_estimate = opt.adafw_linit(s, p_joint)
step_type = 'init'
elif FLAGS.fw_variant == 'fixed':
start_step_time = time.time()
step_result = opt.fixed(weights, q_params, qtw_prev, loc_s,
scale_s, s, p_joint, t)
end_step_time = time.time()
total_time += float(end_step_time - start_step_time)
elif FLAGS.fw_variant == 'adafw':
start_step_time = time.time()
step_result = opt.adaptive_fw(weights, q_params, qtw_prev,
loc_s, scale_s, s, p_joint,
t, lipschitz_estimate)
end_step_time = time.time()
total_time += float(end_step_time - start_step_time)
step_type = step_result['step_type']
if step_type == 'adaptive':
lipschitz_estimate = step_result['l_estimate']
elif FLAGS.fw_variant == 'ada_pfw':
start_step_time = time.time()
step_result = opt.adaptive_pfw(weights, q_params, qtw_prev,
loc_s, scale_s, s, p_joint,
t, lipschitz_estimate)
end_step_time = time.time()
total_time += float(end_step_time - start_step_time)
step_type = step_result['step_type']
if step_type in ['adaptive', 'drop']:
lipschitz_estimate = step_result['l_estimate']
elif FLAGS.fw_variant == 'ada_afw':
start_step_time = time.time()
step_result = opt.adaptive_afw(weights, q_params, qtw_prev,
loc_s, scale_s, s, p_joint,
t, lipschitz_estimate)
end_step_time = time.time()
total_time += float(end_step_time - start_step_time)
step_type = step_result['step_type']
if step_type in ['adaptive', 'away', 'drop']:
lipschitz_estimate = step_result['l_estimate']
elif FLAGS.fw_variant == 'line_search':
start_step_time = time.time()
step_result = opt.line_search_dkl(weights, q_params,
qtw_prev, loc_s, scale_s,
s, p_joint, t)
end_step_time = time.time()
total_time += float(end_step_time - start_step_time)
step_type = step_result['step_type']
else:
raise NotImplementedError(
'Step size variant %s not implemented' %
FLAGS.fw_variant)
if t == 0:
gamma = 1.
new_components = [s]
else:
q_params = step_result['params']
weights = step_result['weights']
gamma = step_result['gamma']
new_components = [
coreutils.base_loc_scale(FLAGS.base_dist,
c['loc'],
c['scale'],
multivariate=is_vector)
for c in q_params
]
qtw_new = coreutils.get_mixture(weights, new_components)
# Log metrics for current iteration
logger.info('total time %f' % total_time)
append_to_file(times_filename, total_time)
elbo_t = elbo(qtw_new, p_joint, return_std=False)
# testing elbo directory from KLqp
elbo_loss = elboModel.KLqp({w: qtw_new},
data={
X: Xtrain,
y: ytrain
})
res_update = elbo_loss.run()
logger.info("iter, %d, elbo, %.2f loss %.2f" %
(t, elbo_t, res_update['loss']))
append_to_file(elbos_filename,
"%f,%f" % (elbo_t, res_update['loss']))
logger.info('iter %d, gamma %.4f' % (t, gamma))
append_to_file(step_filename, gamma)
if t > 0:
gap_t = step_result['gap']
logger.info('iter %d, gap %.4f' % (t, gap_t))
append_to_file(gap_filename, gap_t)
if FLAGS.fw_variant.startswith('ada'):
append_to_file(lipschitz_filename, lipschitz_estimate)
append_to_file(iter_info_filename, step_type)
logger.info('lt = %.5f, iter_type = %s' %
(lipschitz_estimate, step_type))
# get weight samples to evaluate expectations
w_samples = qtw_new.sample([n_test_samples]).eval()
ll_train_mean, ll_train_std = sess.run([ll_mean, ll_std],
feed_dict={
W: w_samples,
X: Xtrain,
y_data: ytrain
})
logger.info("iter, %d, train ll, %.2f +/- %.2f" %
(t, ll_train_mean, ll_train_std))
append_to_file(ll_train_filename,
"%f,%f" % (ll_train_mean, ll_train_std))
ll_test_mean, ll_test_std, y_test_pred = sess.run(
[ll_mean, ll_std, ypred],
feed_dict={
W: w_samples,
X: Xtest,
y_data: ytest
})
logger.info("iter, %d, test ll, %.2f +/- %.2f" %
(t, ll_test_mean, ll_test_std))
append_to_file(ll_test_filename,
"%f,%f" % (ll_test_mean, ll_test_std))
roc_score = roc_auc_score(ytest, y_test_pred)
logger.info("iter %d, roc %.4f" % (t, roc_score))
append_to_file(rocs_filename, roc_score)
y_post = ed.copy(y, {w: qtw_new})
# eq. to y = Bernoulli(logits=ed.dot(X, qtw_new))
ed_train_ll = ed.evaluate('log_likelihood',
data={
X: Xtrain,
y_post: ytrain,
})
ed_test_ll = ed.evaluate('log_likelihood',
data={
X: Xtest,
y_post: ytest,
})
logger.info("edward train ll %.2f test ll %.2f" %
(ed_train_ll, ed_test_ll))
bin_ac_train = ed.evaluate('binary_accuracy',
data={
X: Xtrain,
y_post: ytrain,
})
bin_ac_test = ed.evaluate('binary_accuracy',
data={
X: Xtest,
y_post: ytest,
})
append_to_file(bin_ac_filename,
"%f,%f" % (bin_ac_train, bin_ac_test))
logger.info(
"edward binary accuracy train ll %.2f test ll %.2f" %
(bin_ac_train, bin_ac_test))
mse_test = ed.evaluate('mean_squared_error',
data={
X: Xtest,
y_post: ytest,
})
logger.info("edward mse test ll %.2f" % (mse_test))
sess.close()
tf.reset_default_graph()
def line_search_dkl(weights, params, q_t, mu_s, cov_s, s_t, p, k, gap=None):
"""Performs line search for the best step size gamma.
Uses gradient ascent to find gamma that minimizes
ELBO(q_t + gamma (s - q_t) || p)
Args:
weights: [k], weights of 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
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']
N_samples = FLAGS.n_monte_carlo_samples
# sample from $q_t$ and s
sample_q = q_t.sample([N_samples])
sample_s = s_t.sample([N_samples])
if gap is None:
# create and sample from $s_t, q_t$
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 = step_q - step_s
logger.info('duality gap %.3e' % gap)
if gap < 0:
logger.warning("Duality gap is negative.")
# initialize $\gamma$
gamma = 2. / (k + 2.)
for it in range(FLAGS.n_line_search_iter):
print("line_search iter %d, %.5f" % (it, gamma))
new_weights = copy.copy(weights)
new_weights = [(1. - gamma) * w for w in new_weights]
new_weights.append(gamma)
new_params = copy.copy(params)
new_params.append({'loc': mu_s, 'scale': cov_s})
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)
step_s = tf.reduce_mean(grad_elbo(qt_new, p, sample_s)).eval()
step_q = tf.reduce_mean(grad_elbo(qt_new, p, sample_q)).eval()
gap = step_q - step_s
# Gradient descent step size decreasing as $\frac{1}{it + 1}$
gamma_prime = gamma - FLAGS.linit_fixed * (step_s - step_q) / (it + 1.)
# Projecting it back to [0, 1]
if gamma_prime >= 1 or gamma_prime <= 0:
gamma_prime = max(min(gamma_prime, 1.), 0.)
if np.abs(gamma - gamma_prime) < 1e-6:
gamma = gamma_prime
break
gamma = gamma_prime
return {
'gamma': gamma,
'n_samples': N_samples,
'weights': new_weights,
'params': new_params,
'step_type': 'line_search',
'gap': gap
}
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 adaptive_pfw(weights, params, q_t, mu_s, cov_s, s_t, p, k, l_prev):
"""Adaptive pairwise variant.
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]
# Pairwise gap
N_samples = FLAGS.n_monte_carlo_samples
sample_s = s_t.sample([N_samples])
step_s = tf.reduce_mean(grad_elbo(q_t, p, sample_s)).eval()
gap_pw = step_v_t - step_s
logger.info('Pairwise gap %.3e' % gap_pw)
if gap_pw <= 0:
logger.warning('Pairwise gap <= 0, returning fixed step')
return fixed(weights, params, q_t, mu_s, cov_s, s_t, p, k, gap_pw)
gap = gap_pw
MAX_GAMMA = weights[index_v_t]
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) = %.3e' % 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
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}
# handle the case of gamma = MAX_GAMMA separately
new_weights = copy.copy(weights)
new_weights.append(gamma)
new_params = copy.copy(params)
new_params.append({'loc': mu_s, 'scale': cov_s})
if gamma != MAX_GAMMA:
new_weights[index_v_t] -= gamma
is_drop_step = False
else:
# hardcoding to 0
del new_weights[index_v_t]
del new_params[index_v_t]
is_drop_step = True
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:
# Adaptive loop succeeded
return {
'gamma': gamma,
'l_estimate': l_t,
'weights': new_weights,
'params': new_params,
'gap': gap,
'step_type': 'drop' if is_drop_step else 'adaptive'
}
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(_):
# setting up output directory
outdir = os.path.expanduser(FLAGS.outdir)
os.makedirs(outdir, exist_ok=True)
N, M, D, R_true, I_train, I_test = get_data()
debug('N, M, D', N, M, D)
# Solution components
weights, qUVt_components = [], []
# Files to log metrics
times_filename = os.path.join(outdir, 'times.csv')
mse_train_filename = os.path.join(outdir, 'mse_train.csv')
mse_test_filename = os.path.join(outdir, 'mse_test.csv')
ll_test_filename = os.path.join(outdir, 'll_test.csv')
ll_train_filename = os.path.join(outdir, 'll_train.csv')
elbos_filename = os.path.join(outdir, 'elbos.csv')
gap_filename = os.path.join(outdir, 'gap.csv')
step_filename = os.path.join(outdir, 'steps.csv')
# 'adafw', 'ada_afw', 'ada_pfw'
if FLAGS.fw_variant.startswith('ada'):
lipschitz_filename = os.path.join(outdir, 'lipschitz.csv')
iter_info_filename = os.path.join(outdir, 'iter_info.txt')
start = 0
if FLAGS.restore:
#start = 50
#qUVt_components = get_random_components(D, N, M, start)
#weights = np.random.dirichlet([1.] * start).astype(np.float32)
#lipschitz_estimate = opt.adafw_linit()
parameters = np.load(os.path.join(outdir, 'qt_latest.npz'))
weights = list(parameters['weights'])
start = parameters['fw_iter']
qUVt_components = list(parameters['comps'])
assert len(weights) == len(qUVt_components), "Inconsistent storage"
# get lipschitz estimate from the file, could've stored it
# in params but that would mean different saved file for
# adaptive variants
if FLAGS.fw_variant.startswith('ada'):
lipschitz_filename = os.path.join(outdir, 'lipschitz.csv')
if not os.path.isfile(lipschitz_filename):
raise ValueError("Inconsistent storage")
with open(lipschitz_filename, 'r') as f:
l = f.readlines()
lipschitz_estimate = float(l[-1].strip())
else:
# empty the files present in the folder already
open(times_filename, 'w').close()
open(mse_train_filename, 'w').close()
open(mse_test_filename, 'w').close()
open(ll_test_filename, 'w').close()
open(ll_train_filename, 'w').close()
open(elbos_filename, 'w').close()
open(gap_filename, 'w').close()
open(step_filename, 'w').close()
# 'adafw', 'ada_afw', 'ada_pfw'
if FLAGS.fw_variant.startswith('ada'):
open(lipschitz_filename, 'w').close()
open(iter_info_filename, 'w').close()
for t in range(start, start + FLAGS.n_fw_iter):
g = tf.Graph()
with g.as_default():
tf.set_random_seed(FLAGS.seed)
sess = tf.InteractiveSession()
with sess.as_default():
# MODEL
I = tf.placeholder(tf.float32, [N, M])
scale_uv = tf.concat(
[tf.ones([D, N]), tf.ones([D, M])], axis=1)
mean_uv = tf.concat(
[tf.zeros([D, N]), tf.zeros([D, M])], axis=1)
UV = Normal(loc=mean_uv, scale=scale_uv)
R = Normal(loc=tf.matmul(tf.transpose(UV[:, :N]), UV[:, N:]),
scale=tf.ones([N, M])) # generator dist. for matrix
R_mask = R * I # generated masked matrix
p_joint = Joint(R_true, I_train, sess, D, N, M)
if t == 0:
fw_iterates = {}
else:
# Current solution
prev_components = [
coreutils.base_loc_scale('mvn0',
c['loc'],
c['scale'],
multivariate=False)
for c in qUVt_components
]
qUV_prev = coreutils.get_mixture(weights, prev_components)
fw_iterates = {UV: qUV_prev}
# LMO (via relbo INFERENCE)
mean_suv = tf.concat([
tf.get_variable("qU/loc", [D, N]),
tf.get_variable("qV/loc", [D, M])
],
axis=1)
scale_suv = tf.concat([
tf.nn.softplus(tf.get_variable("qU/scale", [D, N])),
tf.nn.softplus(tf.get_variable("qV/scale", [D, M]))
],
axis=1)
sUV = Normal(loc=mean_suv, scale=scale_suv)
#inference = relbo.KLqp({UV: sUV}, data={R: R_true, I: I_train},
inference = relbo.KLqp({UV: sUV},
data={
R_mask: R_true,
I: I_train
},
fw_iterates=fw_iterates,
fw_iter=t)
inference.run(n_iter=FLAGS.LMO_iter)
loc_s = sUV.mean().eval()
scale_s = sUV.stddev().eval()
# sUV is batched distrbution, there are issues making
# Mixture with batch distributions. mvn0
# with event size (D, N + M) and batch size ()
# NOTE log_prob(sample) still returns tensor
# mvn and multivariatenormaldiag work for 1-D not 2-D shapes
sUV_mv = coreutils.base_loc_scale('mvn0',
loc_s,
scale_s,
multivariate=False)
# TODO send sUV or sUV_mv as argument to step size? sample
# works the same way. same with log_prob
total_time = 0.
data = {R: R_true, I: I_train}
if t == 0:
gamma = 1.
lipschitz_estimate = opt.adafw_linit()
step_type = 'init'
elif FLAGS.fw_variant == 'fixed':
start_step_time = time.time()
step_result = opt.fixed(weights, qUVt_components, qUV_prev,
loc_s, scale_s, sUV, p_joint, data,
t)
end_step_time = time.time()
total_time += float(end_step_time - start_step_time)
elif FLAGS.fw_variant == 'line_search':
start_step_time = time.time()
step_result = opt.line_search_dkl(weights, qUVt_components,
qUV_prev, loc_s, scale_s,
sUV, p_joint, data, t)
end_step_time = time.time()
total_time += float(end_step_time - start_step_time)
elif FLAGS.fw_variant == 'adafw':
start_step_time = time.time()
step_result = opt.adaptive_fw(weights, qUVt_components,
qUV_prev, loc_s, scale_s,
sUV, p_joint, data, t,
lipschitz_estimate)
end_step_time = time.time()
total_time += float(end_step_time - start_step_time)
step_type = step_result['step_type']
if step_type == 'adaptive':
lipschitz_estimate = step_result['l_estimate']
elif FLAGS.fw_variant == 'ada_pfw':
start_step_time = time.time()
step_result = opt.adaptive_pfw(weights, qUVt_components,
qUV_prev, loc_s, scale_s,
sUV, p_joint, data, t,
lipschitz_estimate)
end_step_time = time.time()
total_time += float(end_step_time - start_step_time)
step_type = step_result['step_type']
if step_type in ['adaptive', 'drop']:
lipschitz_estimate = step_result['l_estimate']
elif FLAGS.fw_variant == 'ada_afw':
start_step_time = time.time()
step_result = opt.adaptive_pfw(weights, qUVt_components,
qUV_prev, loc_s, scale_s,
sUV, p_joint, data, t,
lipschitz_estimate)
end_step_time = time.time()
total_time += float(end_step_time - start_step_time)
step_type = step_result['step_type']
if step_type in ['adaptive', 'away', 'drop']:
lipschitz_estimate = step_result['l_estimate']
if t == 0:
gamma = 1.
weights.append(gamma)
qUVt_components.append({'loc': loc_s, 'scale': scale_s})
new_components = [sUV_mv]
else:
qUVt_components = step_result['params']
weights = step_result['weights']
gamma = step_result['gamma']
new_components = [
coreutils.base_loc_scale('mvn0',
c['loc'],
c['scale'],
multivariate=False)
for c in qUVt_components
]
qUV_new = coreutils.get_mixture(weights, new_components)
#qR = Normal(
# loc=tf.matmul(
# tf.transpose(qUV_new[:, :N]), qUV_new[:, N:]),
# scale=tf.ones([N, M]))
qR = ed.copy(R, {UV: qUV_new})
cR = ed.copy(R_mask, {UV: qUV_new}) # reconstructed matrix
# Log metrics for current iteration
logger.info('total time %f' % total_time)
append_to_file(times_filename, total_time)
logger.info('iter %d, gamma %.4f' % (t, gamma))
append_to_file(step_filename, gamma)
if t > 0:
gap_t = step_result['gap']
logger.info('iter %d, gap %.4f' % (t, gap_t))
append_to_file(gap_filename, gap_t)
# CRITICISM
if FLAGS.fw_variant.startswith('ada'):
append_to_file(lipschitz_filename, lipschitz_estimate)
append_to_file(iter_info_filename, step_type)
logger.info('lt = %.5f, iter_type = %s' %
(lipschitz_estimate, step_type))
test_mse = ed.evaluate('mean_squared_error',
data={
cR: R_true,
I: I_test
})
logger.info("iter %d ed test mse %.5f" % (t, test_mse))
append_to_file(mse_test_filename, test_mse)
train_mse = ed.evaluate('mean_squared_error',
data={
cR: R_true,
I: I_train
})
logger.info("iter %d ed train mse %.5f" % (t, train_mse))
append_to_file(mse_train_filename, train_mse)
# very slow
#train_ll = log_likelihood(qUV_new, R_true, I_train, sess, D, N,
# M)
train_ll = ed.evaluate('log_lik',
data={
qR: R_true.astype(np.float32),
I: I_train
})
logger.info("iter %d train log lik %.5f" % (t, train_ll))
append_to_file(ll_train_filename, train_ll)
#test_ll = log_likelihood(qUV_new, R_true, I_test, sess, D, N, M)
test_ll = ed.evaluate('log_lik',
data={
qR: R_true.astype(np.float32),
I: I_test
})
logger.info("iter %d test log lik %.5f" % (t, test_ll))
append_to_file(ll_test_filename, test_ll)
# elbo_loss might be meaningless
elbo_loss = elboModel.KLqp({UV: qUV_new},
data={
R: R_true,
I: I_train
})
elbo_t = elbo(qUV_new, p_joint)
res_update = elbo_loss.run()
logger.info('iter %d -elbo loss %.2f or %.2f' %
(t, res_update['loss'], elbo_t))
append_to_file(elbos_filename,
"%f,%f" % (elbo_t, res_update['loss']))
# serialize the current iterate
np.savez(os.path.join(outdir, 'qt_latest.npz'),
weights=weights,
comps=qUVt_components,
fw_iter=t + 1)
sess.close()
tf.reset_default_graph()
def line_search_dkl(weights,
params,
q_t,
mu_s,
cov_s,
s_t,
p,
data,
k,
gap=None):
"""Performs line search for the best step size gamma.
Uses gradient ascent to find gamma that minimizes
ELBO(q_t + gamma (s - q_t) || p)
Args:
weights: [k], weights of 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
Returns:
a dictionary containing gamma, new weights, new parameters
lipschitz estimate, duality gap of current iterate
and step information
"""
# initialize $\gamma$
gamma = 2. / (k + 2.)
for it in range(FLAGS.n_line_search_iter):
print("line_search iter %d, %.5f" % (it, gamma))
new_weights = copy.copy(weights)
new_weights = [(1. - gamma) * w for w in new_weights]
new_weights.append(gamma)
new_params = copy.copy(params)
new_params.append({'loc': mu_s, 'scale': cov_s})
new_components = [
coreutils.base_loc_scale(FLAGS.base_dist,
c['loc'],
c['scale'],
multivariate=False) for c in new_params
]
qt_new = coreutils.get_mixture(new_weights, new_components)
step_s = grad_kl_dotp(qt_new, p, s_t)
step_q = grad_kl_dotp(qt_new, p, q_t)
gap = step_q - step_s
# Gradient descent step size decreasing as $\frac{1}{it + 1}$
gamma_prime = gamma - FLAGS.linit_fixed * (step_s - step_q) / (it + 1.)
debug('line search gap %.3e gamma_p %f' % (gap, gamma_prime))
# Projecting it back to [0, 1]
if gamma_prime >= 1 or gamma_prime <= 0:
gamma_prime = max(min(gamma_prime, 1.), 0.)
if np.abs(gamma - gamma_prime) < 1e-6:
gamma = gamma_prime
break
gamma = gamma_prime
return {
'gamma': gamma,
'weights': new_weights,
'params': new_params,
'step_type': 'line_search',
'gap': gap
}