def expectation(model, instance):
'''
Perform forward-backward algorithm to calculate the second component
of the detrieve.
'''
# get the cached score
L = len(instance)
T = model.nr_tags
A = model.nr_attrs
g0, g = build_score_cache(model.w, L, T, A, instance)
a = forward(g0, g, L, T)
b = backward(g, L, T)
logZ = logsumexp(a[L-1,:])
E = defaultdict(float)
f = instance.features_table
c = exp(g0 + b[0,:] - logZ).clip(0., 1.)
for j in xrange(T):
for k in f[0,None,j]:
E[k] += c[j]
for i in xrange(1, L):
c = exp(add.outer(a[i-1,:], b[i,:]) + g[i,:,:] - logZ).clip(0.,1.)
for j in range(T):
for k in range(T):
for e in f[i,j,k]:
E[e] += c[j,k]
return E
def expectation(model, instance):
'''
Perform forward-backward algorithm to calculate the second component
of the detrieve.
'''
# get the cached score
L = len(instance)
T = model.nr_tags
A = model.nr_attrs
g0, g = build_score_cache(model.w, L, T, A, instance)
a = forward(g0, g, L, T)
b = backward(g, L, T)
logZ = logsumexp(a[L - 1, :])
E = defaultdict(float)
f = instance.features_table
c = exp(g0 + b[0, :] - logZ).clip(0., 1.)
for j in xrange(T):
for k in f[0, None, j]:
E[k] += c[j]
for i in xrange(1, L):
c = exp(add.outer(a[i - 1, :], b[i, :]) + g[i, :, :] - logZ).clip(
0., 1.)
for j in range(T):
for k in range(T):
for e in f[i, j, k]:
E[e] += c[j, k]
return E
def _dlikelihood(w, instance, model):
'''
Calculate gradient of a instance
- param[in] w The weight vector
- param[in] instance The instance
- param[in] model The model
'''
grad = zeros(w.shape[0], dtype=float)
L = len(instance)
T = model.nr_tags
A = model.nr_attrs
build_instance(model.attrs, model.tags, instance, True)
g0, g = build_score_cache(w, L, T, A, instance)
F = instance.correct_features
for k, v in F.iteritems():
grad[k] += v
a = forward(g0, g, L, T) # forward
b = backward(g, L, T) # backward
logZ = logsumexp(a[L - 1, :])
U = instance.unigram_features_table
B = instance.bigram_features_table
c = exp(g0 + b[0, :] - logZ).clip(0., 1.)
for j in xrange(T):
grad[U[0, j]] -= c[j]
for i in xrange(1, L):
c = exp(add.outer(a[i - 1, :], b[i, :]) + g[i, :, :] - logZ).clip(
0., 1.)
# The following code is an equilism of this
#for j in range(T):
# for k in range(T):
# grad[U[i,k]] -= c[j,k]
# grad[B[j,k]] -= c[j,k]
for k in range(T):
grad[U[i, k]] -= c[:, k].sum()
grad[range(A * T, (A + T) * T)] -= c.flatten()
return grad
def _dlikelihood(w, instance, model):
'''
Calculate gradient of a instance
- param[in] w The weight vector
- param[in] instance The instance
- param[in] model The model
'''
grad = zeros(w.shape[0], dtype=float)
L = len(instance)
T = model.nr_tags
A = model.nr_attrs
build_instance(model.attrs, model.tags, instance, True)
g0, g = build_score_cache(w, L, T, A, instance)
F = instance.correct_features
for k, v in F.iteritems():
grad[k] += v
a = forward(g0, g, L, T) # forward
b = backward(g, L, T) # backward
logZ = logsumexp(a[L-1,:])
U = instance.unigram_features_table
B = instance.bigram_features_table
c = exp(g0 + b[0,:] - logZ).clip(0., 1.)
for j in xrange(T):
grad[U[0,j]] -= c[j]
for i in xrange(1, L):
c = exp(add.outer(a[i-1,:], b[i,:]) + g[i,:,:] - logZ).clip(0.,1.)
# The following code is an equilism of this
#for j in range(T):
# for k in range(T):
# grad[U[i,k]] -= c[j,k]
# grad[B[j,k]] -= c[j,k]
for k in range(T):
grad[U[i,k]] -= c[:,k].sum()
grad[range(A*T, (A+T)*T)] -= c.flatten()
return grad
def _likelihood(w, instance, model):
'''
Calculate the likelihood of one instance
- param[in] w
- param[in] Instance
- param[in] model
'''
L = len(instance)
T = model.nr_tags
A = model.nr_attrs
# Filling the correct_features and features_table
build_instance(model.attrs, model.tags, instance, True)
g0, g = build_score_cache(w, L, T, A, instance)
# calcualte the correct likelihood
F = instance.correct_features
ret = array([w[k] * v for k, v in F.iteritems()]).sum()
# calcualte the marginal
a = forward(g0, g, L, T)
return ret - logsumexp(a[L - 1, :])
def _likelihood(w, instance, model):
'''
Calculate the likelihood of one instance
- param[in] w
- param[in] Instance
- param[in] model
'''
L = len(instance)
T = model.nr_tags
A = model.nr_attrs
# Filling the correct_features and features_table
build_instance(model.attrs, model.tags, instance, True)
g0, g = build_score_cache(w, L, T, A, instance)
# calcualte the correct likelihood
F = instance.correct_features
ret = array([w[k] * v for k, v in F.iteritems()]).sum()
# calcualte the marginal
a = forward(g0, g, L, T)
return ret - logsumexp(a[L-1,:])