def em(rules, hypergraphs, group_getter, iters=10):
"""
Runs the Expectation-Maximization for parse forests on the given data.
`hypergraphs` is a set of (pre-parsed) training examples where each node has
been labeled with one of the rules in `rules`. `group-getter` takes a rule
object as input and returns an object (typically the rule RHS symbol) shared
by a group of rules whose probabilities should be constrained to sum to 1.
"""
# precompute normalization groups
normalizing_groups = defaultdict(list)
for rule in rules:
normalizing_groups[group_getter(rule)].append(rule)
# compute initial weights
unnormalized_weights = {}
for rule in rules:
unnormalized_weights[rule] = 0
weights = {}
for key in unnormalized_weights:
norm = mu.logspace_sum([
unnormalized_weights[k]
for k in normalizing_groups[group_getter(key)]
])
weights[key] = mu.logspace_prod([unnormalized_weights[key], -norm])
logging.info('Running EM for %d iterations.', iters)
# run EM
for i in range(iters):
def scorer(label):
pr = weights[label]
return (pr, {label: pr})
semiring = ExpectationSemiring()
prob = 0
counts = {}
for hg in hypergraphs:
hg.inside(scorer, semiring)
prob_single, counts_single = hg.alpha
prob = mu.logspace_prod([prob, prob_single])
ncounts = du.d_logspace_scalar_prod(-prob_single, counts_single)
counts = du.d_logspace_sum([counts, ncounts])
weights = {}
for key in counts:
norm = mu.logspace_sum([
counts[k] for k in normalizing_groups[group_getter(key)]
if k in counts
])
weights[key] = mu.logspace_prod([counts[key], -norm])
logging.info('Iteration %d. NLL: %f.', i, prob)
def em(rules, hypergraphs, group_getter, iters=10):
"""
Runs the Expectation-Maximization for parse forests on the given data.
`hypergraphs` is a set of (pre-parsed) training examples where each node has
been labeled with one of the rules in `rules`. `group-getter` takes a rule
object as input and returns an object (typically the rule RHS symbol) shared
by a group of rules whose probabilities should be constrained to sum to 1.
"""
# precompute normalization groups
normalizing_groups = defaultdict(list)
for rule in rules:
normalizing_groups[group_getter(rule)].append(rule)
# compute initial weights
unnormalized_weights = {}
for rule in rules:
unnormalized_weights[rule] = 0
weights = {}
for key in unnormalized_weights:
norm = mu.logspace_sum([unnormalized_weights[k] for k in
normalizing_groups[group_getter(key)]])
weights[key] = mu.logspace_prod([unnormalized_weights[key], -norm])
logging.info('Running EM for %d iterations.', iters)
# run EM
for i in range(iters):
def scorer(label):
pr = weights[label]
return (pr, {label: pr})
semiring = ExpectationSemiring()
prob = 0
counts = {}
for hg in hypergraphs:
hg.inside(scorer, semiring)
prob_single, counts_single = hg.alpha
prob = mu.logspace_prod([prob, prob_single])
ncounts = du.d_logspace_scalar_prod(-prob_single, counts_single)
counts = du.d_logspace_sum([counts, ncounts])
weights = {}
for key in counts:
norm = mu.logspace_sum([counts[k] for k in
normalizing_groups[group_getter(key)]
if k in counts])
weights[key] = mu.logspace_prod([counts[key], -norm])
logging.info('Iteration %d. NLL: %f.', i, prob)
def prod_op(self, values):
exps = [ex for pr,ex in values]
for i in range(len(values)):
pr,ex = values[i]
for j in range(len(exps)):
if i == j:
continue
exps[j] = du.d_logspace_scalar_prod(pr, exps[j])
return (mu.logspace_prod([pr for pr,ex in values]),
du.d_logspace_sum(exps))
def prod_op(self, values):
exps = [ex for pr, ex in values]
for i in range(len(values)):
pr, ex = values[i]
for j in range(len(exps)):
if i == j:
continue
exps[j] = du.d_logspace_scalar_prod(pr, exps[j])
return (mu.logspace_prod([pr for pr, ex in values]),
du.d_logspace_sum(exps))