def top_K_loss(self, sentence, image, K=50, margin=0.5, img_input_feat=None, text_input_feat=None):
sim_matrix = tf.matmul(sentence, image, transpose_b=True)
s_square = tf.reduce_sum(tf.square(sentence), axis=1)
im_square = tf.reduce_sum(tf.square(image), axis=1)
d = tf.reshape(s_square,[-1,1]) - 2 * sim_matrix + tf.reshape(im_square, [1, -1])
positive = tf.stack([tf.matrix_diag_part(d)] * K, axis=1)
length = tf.shape(d)[-1]
d = tf.matrix_set_diag(d, 8 * tf.ones([length]))
if img_input_feat is not None:
img_input_norm1 = img_input_feat / tf.norm(img_input_feat, axis=-1, keep_dims=True)
S_input_img = tf.matmul(img_input_norm1, img_input_norm1, transpose_b=True)
img_coeff = 8 - 7 * tf.sign(tf.nn.relu(0.99 - S_input_img))
sen_loss_K ,_ = tf.nn.top_k(-1.0 * d * img_coeff, K, sorted=False) # note: this is negative value
self.endpoint['debug/S_input_img'] = S_input_img
self.endpoint['debug/img_coeff'] = img_coeff
else:
sen_loss_K ,_ = tf.nn.top_k(-1.0 * d, K, sorted=False) # note: this is negative value
if text_input_feat is not None:
text_input_norm1 = text_input_feat / (tf.norm(text_input_feat, axis=-1, keep_dims=True) + 1e-10)
S_input_text = tf.matmul(text_input_norm1, text_input_norm1, transpose_b=True)
text_coeff = 8 - 7 * tf.sign(tf.nn.relu(0.98 - S_input_text))
im_loss_K,_ = tf.nn.top_k(tf.transpose(-1.0 * d * text_coeff), K, sorted=False)
self.endpoint['debug/S_input_text'] = S_input_text
self.endpoint['debug/text_coeff'] = text_coeff
else:
im_loss_K,_ = tf.nn.top_k(tf.transpose(-1.0 * d), K, sorted=False) # note: this is negative value
sentence_center_loss = tf.nn.relu(positive + sen_loss_K + margin)
image_center_loss = tf.nn.relu(positive + im_loss_K + margin)
self.d_neg = (sen_loss_K + im_loss_K)/-2.0
self.d_pos = positive
self.endpoint['debug/im_loss_topK'] = -1.0 * im_loss_K
self.endpoint['debug/sen_loss_topK'] = -1.0 * sen_loss_K
self.endpoint['debug/d_Matrix'] = d
self.endpoint['debug/positive'] = positive
self.endpoint['debug/s_center_loss'] = sentence_center_loss
self.endpoint['debug/i_center_loss'] = image_center_loss
self.endpoint['debug/S'] = sim_matrix
self.endpoint['debug/sentence_square'] = s_square
self.endpoint['debug/image_square'] = im_square
return tf.reduce_sum(sentence_center_loss), tf.reduce_sum(image_center_loss)
python类matrix_diag_part()的实例源码
BidirectionNet_4wtfidf.py 文件源码
项目：Sohu-LuckData-Image-Text-Matching-Competition
作者: WeitaoVan
项目源码
文件源码
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def _build_likelihood(self):
"""
q_alpha, q_lambda are variational parameters, size N x R
This method computes the variational lower bound on the likelihood,
which is:
E_{q(F)} [ \log p(Y|F) ] - KL[ q(F) || p(F)]
with
q(f) = N(f | K alpha + mean, [K^-1 + diag(square(lambda))]^-1) .
"""
K = self.kern.K(self.X)
K_alpha = tf.matmul(K, self.q_alpha)
f_mean = K_alpha + self.mean_function(self.X)
# compute the variance for each of the outputs
I = tf.tile(tf.expand_dims(tf.eye(self.num_data, dtype=settings.float_type), 0),
[self.num_latent, 1, 1])
A = I + tf.expand_dims(tf.transpose(self.q_lambda), 1) * \
tf.expand_dims(tf.transpose(self.q_lambda), 2) * K
L = tf.cholesky(A)
Li = tf.matrix_triangular_solve(L, I)
tmp = Li / tf.expand_dims(tf.transpose(self.q_lambda), 1)
f_var = 1. / tf.square(self.q_lambda) - tf.transpose(tf.reduce_sum(tf.square(tmp), 1))
# some statistics about A are used in the KL
A_logdet = 2.0 * tf.reduce_sum(tf.log(tf.matrix_diag_part(L)))
trAi = tf.reduce_sum(tf.square(Li))
KL = 0.5 * (A_logdet + trAi - self.num_data * self.num_latent +
tf.reduce_sum(K_alpha * self.q_alpha))
v_exp = self.likelihood.variational_expectations(f_mean, f_var, self.Y)
return tf.reduce_sum(v_exp) - KL
def _build_likelihood(self):
"""
Construct a tensorflow function to compute the bound on the marginal
likelihood. For a derivation of the terms in here, see the associated
SGPR notebook.
"""
num_inducing = len(self.feature)
num_data = tf.cast(tf.shape(self.Y)[0], settings.float_type)
output_dim = tf.cast(tf.shape(self.Y)[1], settings.float_type)
err = self.Y - self.mean_function(self.X)
Kdiag = self.kern.Kdiag(self.X)
Kuf = self.feature.Kuf(self.kern, self.X)
Kuu = self.feature.Kuu(self.kern, jitter=settings.numerics.jitter_level)
L = tf.cholesky(Kuu)
sigma = tf.sqrt(self.likelihood.variance)
# Compute intermediate matrices
A = tf.matrix_triangular_solve(L, Kuf, lower=True) / sigma
AAT = tf.matmul(A, A, transpose_b=True)
B = AAT + tf.eye(num_inducing, dtype=settings.float_type)
LB = tf.cholesky(B)
Aerr = tf.matmul(A, err)
c = tf.matrix_triangular_solve(LB, Aerr, lower=True) / sigma
# compute log marginal bound
bound = -0.5 * num_data * output_dim * np.log(2 * np.pi)
bound += tf.negative(output_dim) * tf.reduce_sum(tf.log(tf.matrix_diag_part(LB)))
bound -= 0.5 * num_data * output_dim * tf.log(self.likelihood.variance)
bound += -0.5 * tf.reduce_sum(tf.square(err)) / self.likelihood.variance
bound += 0.5 * tf.reduce_sum(tf.square(c))
bound += -0.5 * output_dim * tf.reduce_sum(Kdiag) / self.likelihood.variance
bound += 0.5 * output_dim * tf.reduce_sum(tf.matrix_diag_part(AAT))
return bound
def eKxz(self, Z, Xmu, Xcov):
"""
Also known as phi_1: <K_{x, Z}>_{q(x)}.
:param Z: MxD inducing inputs
:param Xmu: X mean (NxD)
:param Xcov: NxDxD
:return: NxM
"""
# use only active dimensions
Xcov = self._slice_cov(Xcov)
Z, Xmu = self._slice(Z, Xmu)
D = tf.shape(Xmu)[1]
if self.ARD:
lengthscales = self.lengthscales
else:
lengthscales = tf.zeros((D,), dtype=settings.float_type) + self.lengthscales
vec = tf.expand_dims(Xmu, 2) - tf.expand_dims(tf.transpose(Z), 0) # NxDxM
chols = tf.cholesky(tf.expand_dims(tf.matrix_diag(lengthscales ** 2), 0) + Xcov)
Lvec = tf.matrix_triangular_solve(chols, vec)
q = tf.reduce_sum(Lvec ** 2, [1])
chol_diags = tf.matrix_diag_part(chols) # N x D
half_log_dets = tf.reduce_sum(tf.log(chol_diags), 1) - tf.reduce_sum(tf.log(lengthscales)) # N,
return self.variance * tf.exp(-0.5 * q - tf.expand_dims(half_log_dets, 1))
def test_MatrixDiagPart(self):
if td._tf_version[:2] >= (0, 12):
t = tf.matrix_diag_part(self.random(3, 4, 4, 5))
self.check(t)
def _build_likelihood(self):
"""
Construct a tensorflow function to compute the bound on the marginal
likelihood.
"""
# FITC approximation to the log marginal likelihood is
# log ( normal( y | mean, K_fitc ) )
# where K_fitc = Qff + diag( \nu )
# where Qff = Kfu Kuu^{-1} Kuf
# with \nu_i = Kff_{i,i} - Qff_{i,i} + \sigma^2
# We need to compute the Mahalanobis term -0.5* err^T K_fitc^{-1} err
# (summed over functions).
# We need to deal with the matrix inverse term.
# K_fitc^{-1} = ( Qff + \diag( \nu ) )^{-1}
# = ( V^T V + \diag( \nu ) )^{-1}
# Applying the Woodbury identity we obtain
# = \diag( \nu^{-1} ) - \diag( \nu^{-1} ) V^T ( I + V \diag( \nu^{-1} ) V^T )^{-1) V \diag(\nu^{-1} )
# Let \beta = \diag( \nu^{-1} ) err
# and let \alpha = V \beta
# then Mahalanobis term = -0.5* ( \beta^T err - \alpha^T Solve( I + V \diag( \nu^{-1} ) V^T, alpha ) )
err, nu, Luu, L, alpha, beta, gamma = self._build_common_terms()
mahalanobisTerm = -0.5 * tf.reduce_sum(tf.square(err) / tf.expand_dims(nu, 1)) \
+ 0.5 * tf.reduce_sum(tf.square(gamma))
# We need to compute the log normalizing term -N/2 \log 2 pi - 0.5 \log \det( K_fitc )
# We need to deal with the log determinant term.
# \log \det( K_fitc ) = \log \det( Qff + \diag( \nu ) )
# = \log \det( V^T V + \diag( \nu ) )
# Applying the determinant lemma we obtain
# = \log [ \det \diag( \nu ) \det( I + V \diag( \nu^{-1} ) V^T ) ]
# = \log [ \det \diag( \nu ) ] + \log [ \det( I + V \diag( \nu^{-1} ) V^T ) ]
constantTerm = -0.5 * self.num_data * tf.log(tf.constant(2. * np.pi, settings.float_type))
logDeterminantTerm = -0.5 * tf.reduce_sum(tf.log(nu)) - tf.reduce_sum(tf.log(tf.matrix_diag_part(L)))
logNormalizingTerm = constantTerm + logDeterminantTerm
return mahalanobisTerm + logNormalizingTerm * self.num_latent
def _build_likelihood(self):
"""
Construct a tensorflow function to compute the bound on the marginal
likelihood.
"""
num_inducing = tf.shape(self.Z)[0]
psi0 = tf.reduce_sum(self.kern.eKdiag(self.X_mean, self.X_var), 0)
psi1 = self.kern.eKxz(self.Z, self.X_mean, self.X_var)
psi2 = tf.reduce_sum(self.kern.eKzxKxz(self.Z, self.X_mean, self.X_var), 0)
Kuu = self.kern.K(self.Z) + tf.eye(num_inducing, dtype=settings.float_type) * settings.numerics.jitter_level
L = tf.cholesky(Kuu)
sigma2 = self.likelihood.variance
sigma = tf.sqrt(sigma2)
# Compute intermediate matrices
A = tf.matrix_triangular_solve(L, tf.transpose(psi1), lower=True) / sigma
tmp = tf.matrix_triangular_solve(L, psi2, lower=True)
AAT = tf.matrix_triangular_solve(L, tf.transpose(tmp), lower=True) / sigma2
B = AAT + tf.eye(num_inducing, dtype=settings.float_type)
LB = tf.cholesky(B)
log_det_B = 2. * tf.reduce_sum(tf.log(tf.matrix_diag_part(LB)))
c = tf.matrix_triangular_solve(LB, tf.matmul(A, self.Y), lower=True) / sigma
# KL[q(x) || p(x)]
dX_var = self.X_var if len(self.X_var.get_shape()) == 2 else tf.matrix_diag_part(self.X_var)
NQ = tf.cast(tf.size(self.X_mean), settings.float_type)
D = tf.cast(tf.shape(self.Y)[1], settings.float_type)
KL = -0.5 * tf.reduce_sum(tf.log(dX_var)) \
+ 0.5 * tf.reduce_sum(tf.log(self.X_prior_var)) \
- 0.5 * NQ \
+ 0.5 * tf.reduce_sum((tf.square(self.X_mean - self.X_prior_mean) + dX_var) / self.X_prior_var)
# compute log marginal bound
ND = tf.cast(tf.size(self.Y), settings.float_type)
bound = -0.5 * ND * tf.log(2 * np.pi * sigma2)
bound += -0.5 * D * log_det_B
bound += -0.5 * tf.reduce_sum(tf.square(self.Y)) / sigma2
bound += 0.5 * tf.reduce_sum(tf.square(c))
bound += -0.5 * D * (tf.reduce_sum(psi0) / sigma2 -
tf.reduce_sum(tf.matrix_diag_part(AAT)))
bound -= KL
return bound
def _build_graph(self, raw_weights, raw_means, raw_covars, raw_inducing_inputs,
train_inputs, train_outputs, num_train, test_inputs):
# First transform all raw variables into their internal form.
# Use softmax(raw_weights) to keep all weights normalized.
weights = tf.exp(raw_weights) / tf.reduce_sum(tf.exp(raw_weights))
if self.diag_post:
# Use exp(raw_covars) so as to guarantee the diagonal matrix remains positive definite.
covars = tf.exp(raw_covars)
else:
# Use vec_to_tri(raw_covars) so as to only optimize over the lower triangular portion.
# We note that we will always operate over the cholesky space internally.
covars_list = [None] * self.num_components
for i in xrange(self.num_components):
mat = util.vec_to_tri(raw_covars[i, :, :])
diag_mat = tf.matrix_diag(tf.matrix_diag_part(mat))
exp_diag_mat = tf.matrix_diag(tf.exp(tf.matrix_diag_part(mat)))
covars_list[i] = mat - diag_mat + exp_diag_mat
covars = tf.stack(covars_list, 0)
# Both inducing inputs and the posterior means can vary freely so don't change them.
means = raw_means
inducing_inputs = raw_inducing_inputs
# Build the matrices of covariances between inducing inputs.
kernel_mat = [self.kernels[i].kernel(inducing_inputs[i, :, :])
for i in xrange(self.num_latent)]
kernel_chol = tf.stack([tf.cholesky(k) for k in kernel_mat], 0)
# Now build the objective function.
entropy = self._build_entropy(weights, means, covars)
cross_ent = self._build_cross_ent(weights, means, covars, kernel_chol)
ell = self._build_ell(weights, means, covars, inducing_inputs,
kernel_chol, train_inputs, train_outputs)
batch_size = tf.to_float(tf.shape(train_inputs)[0])
nelbo = -((batch_size / num_train) * (entropy + cross_ent) + ell)
# Build the leave one out loss function.
loo_loss = self._build_loo_loss(weights, means, covars, inducing_inputs,
kernel_chol, train_inputs, train_outputs)
# Finally, build the prediction function.
predictions = self._build_predict(weights, means, covars, inducing_inputs,
kernel_chol, test_inputs)
return nelbo, loo_loss, predictions
