def _compute_losses(self, model_output):
mask = self.dataset.symb_mask
# regression_outputs.shape = (batch_size, seq_length, regression_layer_size)
regression_outputs = model_output
# mixture_weights.shape : (batch_size, seq_len, n_gaussians)
# means.shape : (batch_size, seq_len, n_gaussians, 3)
# stds.shape : (batch_size, seq_len, n_gaussians, 3)
mixture_weights, means, stds = self.model.get_mixture_parameters(
regression_outputs, ndim=4)
# targets.shape : (batch_size, seq_len, 1, 3)
targets = self.dataset.symb_targets[:, :, None, :]
log_prefix = -2 * T.log(mixture_weights) + self.d * np.float32(
np.log(2 * np.pi)) + 2 * T.sum(T.log(stds), axis=-1)
square_mahalanobis_dist = T.sum(T.square((targets - means) / stds),
axis=-1)
# loss_per_timestep.shape : (batch_size, seq_len)
self.loss_per_time_step = -logsumexp(
-0.5 * (log_prefix + square_mahalanobis_dist), axis=2)
# loss_per_seq.shape : (batch_size,)
# loss_per_seq is the log probability for each sequence
self.loss_per_seq = T.sum(self.loss_per_time_step * mask, axis=1)
if not self.sum_over_timestep:
# loss_per_seq is the average log probability for each sequence
self.loss_per_seq /= T.sum(mask, axis=1)
return self.loss_per_seq
def _compute_losses(self, model_output):
# model_output.shape : (batch_size, seq_len, K, M, target_size)
# self.dataset.symb_targets.shape = (batch_size, seq_len+K-1, target_dims)
# mask.shape : (batch_size, seq_len) or None
mask = self.dataset.symb_mask
# mu.shape = (batch_size, seq_len, K, M, target_dims)
mu = model_output[:, :, :, :, 0:3]
# sigma.shape = (batch_size, seq_len, K, M, target_dims)
sigma = model_output[:, :, :, :, 3:6]
# Stack K targets for each input (sliding window style)
# targets.shape = (batch_size, seq_len, K, target_dims)
targets = T.stack(
[self.dataset.symb_targets[:, i : (-self.model.k + i + 1) or None] for i in range(self.model.k)], axis=2
)
# Add new axis for sum over M
# targets.shape = (batch_size, seq_len, K, 1, target_dims)
targets = targets[:, :, :, None, :]
# For monitoring the L2 error of using $mu$ as the predicted direction (should be comparable to MICCAI's work).
normalized_mu = mu[:, :, 0, 0] / l2distance(mu[:, :, 0, 0], keepdims=True, eps=1e-8)
normalized_targets = targets[:, :, 0, 0] / l2distance(targets[:, :, 0, 0], keepdims=True, eps=1e-8)
self.L2_error_per_item = T.sqrt(T.sum(((normalized_mu - normalized_targets) ** 2), axis=2))
if mask is not None:
self.mean_sqr_error = T.sum(self.L2_error_per_item * mask, axis=1) / T.sum(mask, axis=1)
else:
self.mean_sqr_error = T.mean(self.L2_error_per_item, axis=1)
# Likelihood of multivariate gaussian (n dimensions) is :
# ((2 \pi)^D |\Sigma|)^{-1/2} exp(-1/2 (x - \mu)^T \Sigma^-1 (x - \mu))
# We suppose a diagonal covariance matrix, so we have :
# => |\Sigma| = \prod_n \sigma_n^2
# => (x - \mu)^T \Sigma^-1 (x - \mu) = \sum_n ((x_n - \mu_n) / \sigma_n)^2
m_log_likelihoods = -np.float32((self.target_dims / 2.0) * np.log(2 * np.pi)) + T.sum(
-T.log(sigma) - 0.5 * T.sqr((targets - mu) / sigma), axis=4
)
# k_losses_per_timestep.shape : (batch_size, seq_len, K)
self.k_losses_per_timestep = T.log(self.m) - logsumexp(m_log_likelihoods, axis=3, keepdims=False)
# loss_per_timestep.shape : (batch_size, seq_len)
self.loss_per_time_step = T.mean(self.k_losses_per_timestep, axis=2)
# Average over sequence steps.
# k_nlls_per_seq.shape :(batch_size, K)
if mask is not None:
self.k_losses_per_seq = T.sum(self.k_losses_per_timestep * mask[:, :, None], axis=1) / T.sum(
mask, axis=1, keepdims=True
)
else:
self.k_losses_per_seq = T.mean(self.k_losses_per_timestep, axis=1)
# Average over K
# loss_per_seq.shape :(batch_size,)
self.loss_per_seq = T.mean(self.k_losses_per_seq, axis=1)
return self.loss_per_seq
def _compute_losses(self, model_output):
mask = self.dataset.symb_mask
# regression_outputs.shape = (batch_size, seq_length, regression_layer_size)
regression_outputs = model_output
mixture_weights, means, stds = self.model.get_mixture_parameters(regression_outputs, ndim=4)
# means.shape : (batch_size, seq_len, n_gaussians, 3)
# mean_*.shape : (batch_size, seq_len, n_gaussians)
mean_x = means[:, :, :, 0]
mean_y = means[:, :, :, 1]
mean_z = means[:, :, :, 2]
# std_*.shape : (batch_size, seq_len, n_gaussians)
std_x = stds[:, :, :, 0]
std_y = stds[:, :, :, 1]
std_z = stds[:, :, :, 2]
# target_*.shape : (batch_size, seq_len, 1)
target_x = self.dataset.symb_targets[:, :, 0, None]
target_y = self.dataset.symb_targets[:, :, 1, None]
target_z = self.dataset.symb_targets[:, :, 2, None]
tg_x_c = (target_x - mean_x) / std_x
tg_y_c = (target_y - mean_y) / std_y
tg_z_c = (target_z - mean_z) / std_z
log_prefix = T.log(mixture_weights) - np.float32((self.d / 2.) * np.log(2 * np.pi)) - T.log(std_x) - T.log(std_y) - T.log(std_z)
square_mahalanobis_dist = -0.5 * (tg_x_c ** 2 + tg_y_c ** 2 + tg_z_c ** 2)
# loss_per_timestep.shape : (batch_size, seq_len)
self.loss_per_time_step = - logsumexp(log_prefix + square_mahalanobis_dist, axis=2)
# loss_per_seq.shape : (batch_size,)
self.loss_per_seq = T.sum(self.loss_per_time_step * mask, axis=1) / T.sum(mask, axis=1)
return self.loss_per_seq
def _compute_losses(self, model_output):
mask = self.dataset.symb_mask
# stopping_criteria_outputs.shape : (batch_size, seq_len)
stopping_criteria_outputs = model_output[0][:, :, 0]
# regression_outputs.shape : (batch_size, seq_len, regression_layer_size)
regression_outputs = model_output[1]
# mixture_weights.shape : (batch_size, seq_len, n_gaussians)
# means.shape : (batch_size, seq_len, n_gaussians, 3)
# stds.shape : (batch_size, seq_len, n_gaussians, 3)
mixture_weights, means, stds = self.model.get_mixture_parameters(regression_outputs, ndim=4)
# targets.shape : (batch_size, seq_len, 1, 3)
targets = self.dataset.symb_targets[:, :, None, :3]
# stopping_criteria_targets.shape : (batch_size, seq_len)
stopping_criteria_targets = self.dataset.symb_targets[:, :, 3]
log_prefix = -2 * T.log(mixture_weights) + self.d * np.float32(np.log(2*np.pi)) + 2 * T.sum(T.log(stds), axis=-1)
square_mahalanobis_dist = T.sum(T.square((targets - means) / stds), axis=-1)
gaussian_mixture_nll_per_time_step = -logsumexp(-0.5 * (log_prefix + square_mahalanobis_dist), axis=2)
stopping_cross_entropy_per_time_step = T.nnet.binary_crossentropy(stopping_criteria_outputs, stopping_criteria_targets)
# loss_per_timestep.shape : (batch_size, seq_len)
# self.gamma should be used to balance the two loss terms. Consider tweaking this hyperparameter if training goes wrong.
self.loss_per_time_step = gaussian_mixture_nll_per_time_step + self.gamma * stopping_cross_entropy_per_time_step
# loss_per_seq.shape : (batch_size,)
# loss_per_seq is the log probability for each sequence
self.loss_per_seq = T.sum(self.loss_per_time_step * mask, axis=1)
if not self.sum_over_timestep:
# loss_per_seq is the average log probability for each sequence
self.loss_per_seq /= T.sum(mask, axis=1)
return self.loss_per_seq
def _compute_losses(self, model_output):
# model_output.shape : (batch_size, seq_len, K, M, target_size)
# self.dataset.symb_targets.shape = (batch_size, seq_len+K-1, target_dims)
# mask.shape : (batch_size, seq_len) or None
mask = self.dataset.symb_mask
# mu.shape = (batch_size, seq_len, K, M, target_dims)
mu = model_output[:, :, :, :, 0:3]
# sigma.shape = (batch_size, seq_len, K, M, target_dims)
sigma = model_output[:, :, :, :, 3:6]
# Stack K targets for each input (sliding window style)
# targets.shape = (batch_size, seq_len, K, target_dims)
targets = T.stack([
self.dataset.symb_targets[:, i:(-self.model.k + i + 1) or None]
for i in range(self.model.k)
],
axis=2)
# Add new axis for sum over M
# targets.shape = (batch_size, seq_len, K, 1, target_dims)
targets = targets[:, :, :, None, :]
# For monitoring the L2 error of using $mu$ as the predicted direction (should be comparable to MICCAI's work).
normalized_mu = mu[:, :, 0, 0] / l2distance(
mu[:, :, 0, 0], keepdims=True, eps=1e-8)
normalized_targets = targets[:, :, 0, 0] / l2distance(
targets[:, :, 0, 0], keepdims=True, eps=1e-8)
self.L2_error_per_item = T.sqrt(
T.sum(((normalized_mu - normalized_targets)**2), axis=2))
if mask is not None:
self.mean_sqr_error = T.sum(self.L2_error_per_item * mask,
axis=1) / T.sum(mask, axis=1)
else:
self.mean_sqr_error = T.mean(self.L2_error_per_item, axis=1)
# Likelihood of multivariate gaussian (n dimensions) is :
# ((2 \pi)^D |\Sigma|)^{-1/2} exp(-1/2 (x - \mu)^T \Sigma^-1 (x - \mu))
# We suppose a diagonal covariance matrix, so we have :
# => |\Sigma| = \prod_n \sigma_n^2
# => (x - \mu)^T \Sigma^-1 (x - \mu) = \sum_n ((x_n - \mu_n) / \sigma_n)^2
m_log_likelihoods = -np.float32(
(self.target_dims / 2.) * np.log(2 * np.pi)) + T.sum(
-T.log(sigma) - 0.5 * T.sqr((targets - mu) / sigma), axis=4)
# k_losses_per_timestep.shape : (batch_size, seq_len, K)
self.k_losses_per_timestep = T.log(self.m) - logsumexp(
m_log_likelihoods, axis=3, keepdims=False)
# loss_per_timestep.shape : (batch_size, seq_len)
self.loss_per_time_step = T.mean(self.k_losses_per_timestep, axis=2)
# Average over sequence steps.
# k_nlls_per_seq.shape :(batch_size, K)
if mask is not None:
self.k_losses_per_seq = T.sum(
self.k_losses_per_timestep * mask[:, :, None], axis=1) / T.sum(
mask, axis=1, keepdims=True)
else:
self.k_losses_per_seq = T.mean(self.k_losses_per_timestep, axis=1)
# Average over K
# loss_per_seq.shape :(batch_size,)
self.loss_per_seq = T.mean(self.k_losses_per_seq, axis=1)
return self.loss_per_seq
