def main(_):
# setting up output directory
outdir = os.path.expanduser(FLAGS.outdir)
#os.makedirs(outdir, exist_ok=True)
# DATA
N, M, D, R_true, I_train, I_test = get_data()
# 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:]) * I,
# scale=tf.ones([N, M]))
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
sess = tf.InteractiveSession()
p_joint = Joint(R_true, I_train, sess, D, N, M)
# 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)
qUV = Normal(loc=mean_suv, scale=scale_suv)
inference = ed.KLqp({UV: qUV}, data={R_mask: R_true, I: I_train})
inference.run(n_iter=FLAGS.VI_iter)
# CRITICISM
cR = ed.copy(R_mask, {UV: qUV}) # reconstructed matrix
test_mse = ed.evaluate('mean_squared_error',
data={
cR: R_true,
I: I_test.astype(bool)
})
logger.info("iters %d ed test mse %.5f" % (FLAGS.VI_iter, test_mse))
train_mse = ed.evaluate('mean_squared_error',
data={
cR: R_true,
I: I_train.astype(bool)
})
logger.info("iters %d ed train mse %.5f" % (FLAGS.VI_iter, train_mse))
elbo_t = elbo(qUV, p_joint)
logger.info('iters %d elbo %.2f' % (FLAGS.VI_iter, elbo_t))
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 adaptive_pfw(weights, params, q_t, mu_s, cov_s, s_t, p, data, 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: joint distribution p(z, x)
data: training data
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
"""
d_t_norm = divergence(s_t, q_t, metric=FLAGS.distance_metric)
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)
v_t = qcomps[index_v_t]
# Pairwise gap
step_s = grad_kl_dotp(q_t, p, s_t)
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, data, 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)
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 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=False) for c in new_params
]
qt_new = coreutils.get_mixture(new_weights, new_components)
quad_bound_lhs = -elbo(qt_new, p)
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, data, k, gap)
def adaptive_afw(weights, params, q_t, mu_s, cov_s, s_t, p, data, 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: joint distribution p(z, x)
data: training data
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
"""
d_t_norm = divergence(s_t, q_t, metric=FLAGS.distance_metric)
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)
v_t = qcomps[index_v_t]
# Frank-Wolfe gap
step_s = grad_kl_dotp(q_t, p, s_t)
step_q = grad_kl_dotp(q_t, p, q_t)
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, data, 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)
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=False) for c in new_params
]
qt_new = coreutils.get_mixture(new_weights, new_components)
quad_bound_lhs = -elbo(qt_new, p)
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, data, k, gap)
def adaptive_fw(weights,
params,
q_t,
mu_s,
cov_s,
s_t,
p,
data,
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: joint distribution p(z, x)
data: training data
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
"""
# NOTE TODO try div(q_t, s_t)
d_t_norm = divergence(s_t, q_t, metric=FLAGS.distance_metric)
logger.info('\ndistance norm is %.3e' % d_t_norm)
if gap is None:
step_s = grad_kl_dotp(q_t, p, s_t)
step_q = grad_kl_dotp(q_t, p, q_t)
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, data, 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, elbo loss
def neg_elbo(q):
elbo_loss = elboModel.KLqp({pz: q}, data)
return elbo_loss.run()['loss']
f_t = -elbo(q_t, p)
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})
else:
new_weights = [1.]
new_params = [{'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)
quad_bound_lhs = -elbo(qt_new, p)
#quad_bound_lhs = neg_elbo(qt_new)
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, data, k, gap)