def _test(cat, components, n):
x = Mixture(cat=cat, components=components)
val_est = get_dims(x.sample(n))
val_true = n + get_dims(components[0].mu)
assert val_est == val_true
def _test(cat, components, n):
x = Mixture(cat=cat, components=components)
val_est = get_dims(x.sample(n))
val_true = n + get_dims(components[0].mu)
assert val_est == val_true
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()
