def bce_of_true_positive(y_true,
y_pred,
from_logits=False,
_sentinel=None,
name=None):
if not from_logits:
_epsilon = tf.convert_to_tensor(epsilon(), y_pred.dtype.base_dtype)
output = tf.clip_by_value(y_pred, _epsilon, 1 - _epsilon)
output = tf.log(output / (1 - output))
# alteration of sigmoid_crossentroy_with_logits
nn_ops._ensure_xent_args("sigmoid_cross_entropy_with_logits", _sentinel,
y_true, y_pred)
with ops.name_scope(name, "logistic_loss_over_true_positives",
[y_pred, y_true]) as name:
logits = ops.convert_to_tensor(y_pred, name="logits")
labels = ops.convert_to_tensor(y_true, name="labels")
try:
labels.get_shape().merge_with(logits.get_shape())
except ValueError:
raise ValueError(
"Logits and labels must have the same shape (%s vs %s)" %
(logits.get_shape(), labels.get_shape()))
zeros = array_ops.zeros_like(logits, dtype=logits.dtype)
cond = (logits >= zeros)
relu_logits = array_ops.where(cond, logits, zeros)
neg_abs_logits = array_ops.where(cond, -logits, logits)
# here we calculate the mean to be in-line with Keras' binary crossentropy.
return K.mean(
math_ops.multiply(-labels,
math_ops.log1p(math_ops.exp(neg_abs_logits)),
name=name))
def sigmoid_balanced_cross_entropy_with_logits(_sentinel=None,
labels=None,
logits=None,
beta=None,
name=None):
nn_ops._ensure_xent_args("sigmoid_cross_entropy_with_logits", _sentinel,
labels, logits)
with ops.name_scope(name, "logistic_loss", [logits, labels]) as name:
logits = ops.convert_to_tensor(logits, name="logits")
labels = ops.convert_to_tensor(labels, name="labels")
try:
labels.get_shape().merge_with(logits.get_shape())
except ValueError:
raise ValueError(
"logits and labels must have the same shape (%s vs %s)" %
(logits.get_shape(), labels.get_shape()))
zeros = array_ops.zeros_like(logits, dtype=logits.dtype)
cond = (logits >= zeros)
relu_logits = array_ops.where(cond, logits, zeros)
neg_abs_logits = array_ops.where(cond, -logits, logits)
#beta=0.5
balanced_cross_entropy = relu_logits * (
1. - beta) - logits * labels * (1. - beta) + math_ops.log1p(
math_ops.exp(neg_abs_logits)) * ((1. - beta) *
(1. - labels) + beta * labels)
return tf.reduce_mean(balanced_cross_entropy)
def sigmoid_cross_entropy_with_logits( # pylint: disable=invalid-name
_sentinel=None,
labels=None,
logits=None,
name=None,
fp_rate=None,
fn_rate=None):
"""Computes sigmoid cross entropy given `logits`.
Measures the probability error in discrete classification tasks in which each
class is independent and not mutually exclusive. For instance, one could
perform multilabel classification where a picture can contain both an elephant
and a dog at the same time.
For brevity, let `x = logits`, `z = labels`. The logistic loss is
z * -log(sigmoid(x)) + (1 - z) * -log(1 - sigmoid(x))
= z * -log(1 / (1 + exp(-x))) + (1 - z) * -log(exp(-x) / (1 + exp(-x)))
= z * log(1 + exp(-x)) + (1 - z) * (-log(exp(-x)) + log(1 + exp(-x)))
= z * log(1 + exp(-x)) + (1 - z) * (x + log(1 + exp(-x))
= (1 - z) * x + log(1 + exp(-x))
= x - x * z + log(1 + exp(-x))
For x < 0, to avoid overflow in exp(-x), we reformulate the above
x - x * z + log(1 + exp(-x))
= log(exp(x)) - x * z + log(1 + exp(-x))
= - x * z + log(1 + exp(x))
Hence, to ensure stability and avoid overflow, the implementation uses this
equivalent formulation
max(x, 0) - x * z + log(1 + exp(-abs(x)))
`logits` and `labels` must have the same type and shape.
Args:
_sentinel: Used to prevent positional parameters. Internal, do not use.
labels: A `Tensor` of the same type and shape as `logits`.
logits: A `Tensor` of type `float32` or `float64`.
name: A name for the operation (optional).
Returns:
A `Tensor` of the same shape as `logits` with the componentwise
logistic losses.
Raises:
ValueError: If `logits` and `labels` do not have the same shape.
"""
# pylint: disable=protected-access
nn_ops._ensure_xent_args("sigmoid_cross_entropy_with_logits", _sentinel,
labels, logits)
# pylint: enable=protected-access
with ops.name_scope(name, "logistic_loss", [logits, labels]) as name:
logits = ops.convert_to_tensor(logits, name="logits")
labels = ops.convert_to_tensor(labels, name="labels")
try:
labels.get_shape().merge_with(logits.get_shape())
except ValueError:
raise ValueError(
"logits and labels must have the same shape (%s vs %s)" %
(logits.get_shape(), labels.get_shape()))
# The logistic loss formula from above is
# x - x * z + log(1 + exp(-x))
# For x < 0, a more numerically stable formula is
# -x * z + log(1 + exp(x))
# Note that these two expressions can be combined into the following:
# max(x, 0) - x * z + log(1 + exp(-abs(x)))
# To allow computing gradients at zero, we define custom versions of max and
# abs functions.
zeros = array_ops.zeros_like(logits, dtype=logits.dtype)
ones = array_ops.ones_like(logits, dtype=logits.dtype)
cond = (logits >= zeros)
#print (cond)
relu_logits = array_ops.where(cond, logits, zeros)
neg_abs_logits = array_ops.where(cond, -logits, logits)
fn_cond = math_ops.logical_and(labels > zeros, logits < zeros)
fp_cond = math_ops.logical_and(labels <= zeros, logits >= zeros)
fn_cost = fn_rate * math_ops.cast(fn_cond, dtypes.float32)
fp_cost = fp_rate * math_ops.cast(fp_cond, dtypes.float32)
pos_loss = logits - logits * labels + labels * math_ops.log1p(
math_ops.exp(-logits + fn_cost)) + (
(ones - labels) *
math_ops.log1p(math_ops.exp(-logits + fp_cost)))
neg_loss = -logits * labels + labels * math_ops.log(
math_ops.exp(logits) + math_ops.exp(fn_cost)) + (
(ones - labels) *
math_ops.log(math_ops.exp(logits) + math_ops.exp(fp_cost)))
return array_ops.where(cond, pos_loss, neg_loss,
name=name), fn_cost, fp_cost
def weighted_cel(
_sentinel=None,
labels=None,
logits=None,
bound=2.0,
name=None):
"""
Inspired strongly by tensorflow :sigmoid_cross_entropy_with_logits
https://github.com/tensorflow/tensorflow/blob/v2.3.1/tensorflow/python/ops/nn_impl.py#L196-L244
Version with weighted CEL(Cross-Entropy Loss)
https://arxiv.org/pdf/1705.02315
Starting from CEL from TF
For brevity, let `x = logits`, `z = labels`. The logistic loss is
z * -log(sigmoid(x)) + (1 - z) * -log(1 - sigmoid(x))
= z * -log(1 / (1 + exp(-x))) + (1 - z) * -log(exp(-x) / (1 + exp(-x)))
= z * log(1 + exp(-x)) + (1 - z) * (-log(exp(-x)) + log(1 + exp(-x)))
= z * log(1 + exp(-x)) + (1 - z) * (x + log(1 + exp(-x)) (4)
= (1 - z) * x + log(1 + exp(-x))
= x - x * z + log(1 + exp(-x))
For x < 0, to avoid overflow in exp(-x), we reformulate the above
x - x * z + log(1 + exp(-x))
= log(exp(x)) - x * z + log(1 + exp(-x))
= - x * z + log(1 + exp(x))
Hence, to ensure stability and avoid overflow, the implementation uses this
equivalent formulation
max(x, 0) - x * z + log(1 + exp(-abs(x)))
weighted CEL:
For x > 0 (from (4)):
= B_p * [z * -log( 1 + exp(-x) )] + B_n * [(1 - z) * (x + log(1 + exp(-x)))]
For x < 0 (from (4)):
= B_p * [z * log( exp(x) / (1 + exp(x)) )] + B_n * [(1 - z) *(x + log( exp(x) / (1 + exp(x))))]
= B_p * [z * log(1 + exp(x)) - x] + B_n * [(1 - z) * log( (1 + exp(x))))]
Hence, to ensure stability and avoid overflow, the implementation uses this
equivalent formulation
= B_p * [z * log(1 + exp(-x)) + min(0,x) ] + B_n * [(1 - z) * (max(0,x) + log( (1 + exp(-x)))))]
Args:
_sentinel: Used to prevent positional parameters. Internal, do not use.
labels: A `Tensor` of the same type and shape as `logits`.
logits: A `Tensor` of type `float32` or `float64`.
name: A name for the operation (optional).
Returns:
A `Tensor` of the same shape as `logits` with the componentwise
logistic losses.
Raises:
ValueError: If `logits` and `labels` do not have the same shape.
"""
nn_ops._ensure_xent_args("sigmoid_cross_entropy_with_logits", _sentinel,
labels, logits)
with ops.name_scope(name, "weighted_logistic_loss", [logits, labels]) as name:
logits = ops.convert_to_tensor(logits, name="logits")
labels = ops.convert_to_tensor(labels, name="labels")
try:
labels.get_shape().merge_with(logits.get_shape())
except ValueError:
raise ValueError("logits and labels must have the same shape (%s vs %s)" %
(logits.get_shape(), labels.get_shape()))
cnt_one = tf.cast(tf.reduce_sum(labels),tf.float32)
cnt_zero = tf.cast(tf.size(logits),tf.float32) - cnt_one
beta_p = tf.cast((cnt_one + cnt_zero) / cnt_one, tf.float32)
beta_n = tf.cast((cnt_one + cnt_zero) / cnt_zero, tf.float32)
beta_n = math_ops.minimum(bound, beta_n)
beta_p = math_ops.minimum(bound, beta_p)
zeros = array_ops.zeros_like(logits, dtype=logits.dtype)
cond = (logits >= zeros)
relu_logits = array_ops.where(cond, logits, zeros)
not_relu_logits = array_ops.where(cond, zeros, logits)
abs_logits = math_ops.abs(logits)
A = beta_p * (labels * (math_ops.log1p(math_ops.exp(-abs_logits)) - not_relu_logits))
B = beta_n * ((1.0-labels) * (relu_logits + math_ops.log1p(math_ops.exp(-abs_logits))))
return math_ops.add(A, B, name=name)
def sigmoid_cross_entropy_with_logits(_sentinel=None, # pylint: disable=invalid-name
labels=None, logits=None,
name=None):
"""Computes sigmoid cross entropy given `logits`.
Measures the probability error in discrete classification tasks in which each
class is independent and not mutually exclusive. For instance, one could
perform multilabel classification where a picture can contain both an elephant
and a dog at the same time.
For brevity, let `x = logits`, `z = labels`. The logistic loss is
z * -log(sigmoid(x)) + (1 - z) * -log(1 - sigmoid(x))
= z * -log(1 / (1 + exp(-x))) + (1 - z) * -log(exp(-x) / (1 + exp(-x)))
= z * log(1 + exp(-x)) + (1 - z) * (-log(exp(-x)) + log(1 + exp(-x)))
= z * log(1 + exp(-x)) + (1 - z) * (x + log(1 + exp(-x))
= (1 - z) * x + log(1 + exp(-x))
= x - x * z + log(1 + exp(-x))
For x < 0, to avoid overflow in exp(-x), we reformulate the above
x - x * z + log(1 + exp(-x))
= log(exp(x)) - x * z + log(1 + exp(-x))
= - x * z + log(1 + exp(x))
Hence, to ensure stability and avoid overflow, the implementation uses this
equivalent formulation
max(x, 0) - x * z + log(1 + exp(-abs(x)))
`logits` and `labels` must have the same type and shape.
Args:
_sentinel: Used to prevent positional parameters. Internal, do not use.
labels: A `Tensor` of the same type and shape as `logits`.
logits: A `Tensor` of type `float32` or `float64`.
name: A name for the operation (optional).
Returns:
A `Tensor` of the same shape as `logits` with the componentwise
logistic losses.
Raises:
ValueError: If `logits` and `labels` do not have the same shape.
"""
# pylint: disable=protected-access
nn_ops._ensure_xent_args("sigmoid_cross_entropy_with_logits",
_sentinel, labels, logits)
# pylint: enable=protected-access
with ops.name_scope(name, "logistic_loss", [logits, labels]) as name:
logits = ops.convert_to_tensor(logits, name="logits")
labels = ops.convert_to_tensor(labels, name="labels")
try:
labels.get_shape().merge_with(logits.get_shape())
except ValueError:
raise ValueError("logits and labels must have the same shape (%s vs %s)"
% (logits.get_shape(), labels.get_shape()))
# The logistic loss formula from above is
# x - x * z + log(1 + exp(-x))
# For x < 0, a more numerically stable formula is
# -x * z + log(1 + exp(x))
# Note that these two expressions can be combined into the following:
# max(x, 0) - x * z + log(1 + exp(-abs(x)))
# To allow computing gradients at zero, we define custom versions of max and
# abs functions.
zeros = array_ops.zeros_like(logits, dtype=logits.dtype)
cond = (logits >= zeros)
relu_logits = array_ops.where(cond, logits, zeros)
neg_abs_logits = array_ops.where(cond, -logits, logits)
return math_ops.add(relu_logits - logits * labels,
math_ops.log1p(math_ops.exp(neg_abs_logits)),
name=name)
def focal_sigmoid_cross_entropy_with_logits( # pylint: disable=invalid-name
_sentinel=None,
labels=None,
logits=None,
alpha=0.5,
gamma=0.0,
name=None):
"""Computes focal sigmoid cross entropy given `logits`.
Measures the probability error in discrete classification tasks in which each
class is independent and not mutually exclusive. For instance, one could
perform multilabel classification where a picture can contain both an elephant
and a dog at the same time.
For brevity, let `x = logits`, `z = labels`. For `every row`, the logistic loss is
If the background label(z[baich_i][0]) is 0:
row_result = - labels * alpha * tf.pow(1.0 - sigmoid_x, gamma_array) * tf.log(sigmoid_x) \
- (1.0 - labels) * alpha * tf.pow(sigmoid_x, gamma_array) * tf.log(1.0 - sigmoid_x)
If the background label(z[baich_i][0]) is 1:
row_result = - labels * (1.0 - alpha) * tf.pow(1.0 - sigmoid_x, gamma_array) * tf.log(sigmoid_x) \
- (1.0 - labels) * (1.0 - alpha) * tf.pow(sigmoid_x, gamma_array) * tf.log(1.0 - sigmoid_x)
`logits` and `labels` must have the same type and shape.
Args:
_sentinel: Used to prevent positional parameters. Internal, do not use.
labels: A `Tensor` of the same type and shape as `logits`.
logits: A `Tensor` of type `float32` or `float64`.
It must be a tensor of shape [num_batch, num_classes], and first class is background.
alpha: weighting factor for positive class.
gamma: focusing parameter in focal loss.
name: A name for the operation (optional).
Returns:
A `Tensor` of the same shape as `logits` with the componentwise
logistic losses.
Raises:
ValueError: If `logits` and `labels` do not have the same shape.
"""
# pylint: disable=protected-access
nn_ops._ensure_xent_args("focal_sigmoid_cross_entropy_with_logits",
_sentinel, labels, logits)
# pylint: enable=protected-access
with ops.name_scope(name, "logistic_loss", [logits, labels]) as name:
logits = ops.convert_to_tensor(logits, name="logits")
labels = ops.convert_to_tensor(labels, name="labels")
try:
labels.get_shape().merge_with(logits.get_shape())
except ValueError:
raise ValueError(
"logits and labels must have the same shape (%s vs %s)" %
(logits.get_shape(), labels.get_shape()))
if len(labels.get_shape().as_list()) != 2:
raise ValueError(
"logits and labels must have two dim: [num_batch, num_classes], but the shape is %s "
% (logits.get_shape()))
sigmoid_x = tf.sigmoid(logits)
log_sigmoid_x = tf.log_sigmoid(logits)
background_col = tf.slice(labels, [0, 0], [-1, 1])
num_classes = labels.get_shape().as_list()[1]
background_col = tf.matmul(
background_col, tf.ones([1, num_classes], dtype=labels.dtype))
is_pos_label_row = background_col < 0.5
alpha_tmp = alpha * tf.ones_like(logits, dtype=logits.dtype)
alpha_array = tf.where(is_pos_label_row, alpha_tmp, 1.0 - alpha_tmp)
gamma_array = gamma * tf.ones_like(logits, dtype=logits.dtype)
pos_part = -labels * alpha_array * tf.pow(1.0 - sigmoid_x,
gamma_array) * log_sigmoid_x
neg_part = -(1.0 - labels) * alpha_array * tf.pow(
sigmoid_x, gamma_array) * -tf.log(1.0 + tf.exp(logits))
### tf.log(1.0 - sigmoid_x) = - tf.log(1.0 + tf.exp(logits))
return tf.add(pos_part, neg_part, name=name)
