MeanSquaredError
class
keras.losses.MeanSquaredError(
reduction="sum_over_batch_size", name="mean_squared_error"
)
Computes the mean of squares of errors between labels and predictions.
Formula:
loss = mean(square(y_true - y_pred))
Arguments
- reduction: Type of reduction to apply to the loss. In almost all cases this should be
"sum_over_batch_size"
. Supported options are"sum"
,"sum_over_batch_size"
orNone
. - name: Optional name for the loss instance.
MeanAbsoluteError
class
keras.losses.MeanAbsoluteError(
reduction="sum_over_batch_size", name="mean_absolute_error"
)
Computes the mean of absolute difference between labels and predictions.
Formula:
loss = mean(abs(y_true - y_pred))
Arguments
- reduction: Type of reduction to apply to the loss. In almost all cases this should be
"sum_over_batch_size"
. Supported options are"sum"
,"sum_over_batch_size"
orNone
. - name: Optional name for the loss instance.
MeanAbsolutePercentageError
class
keras.losses.MeanAbsolutePercentageError(
reduction="sum_over_batch_size", name="mean_absolute_percentage_error"
)
Computes the mean absolute percentage error between y_true
& y_pred
.
Formula:
loss = 100 * mean(abs((y_true - y_pred) / y_true))
Arguments
- reduction: Type of reduction to apply to the loss. In almost all cases this should be
"sum_over_batch_size"
. Supported options are"sum"
,"sum_over_batch_size"
orNone
. - name: Optional name for the loss instance.
MeanSquaredLogarithmicError
class
keras.losses.MeanSquaredLogarithmicError(
reduction="sum_over_batch_size", name="mean_squared_logarithmic_error"
)
Computes the mean squared logarithmic error between y_true
& y_pred
.
Formula:
loss = mean(square(log(y_true + 1) - log(y_pred + 1)))
Arguments
- reduction: Type of reduction to apply to the loss. In almost all cases this should be
"sum_over_batch_size"
. Supported options are"sum"
,"sum_over_batch_size"
orNone
. - name: Optional name for the loss instance.
CosineSimilarity
class
keras.losses.CosineSimilarity(
axis=-1, reduction="sum_over_batch_size", name="cosine_similarity"
)
Computes the cosine similarity between y_true
& y_pred
.
Note that it is a number between -1 and 1. When it is a negative number between -1 and 0, 0 indicates orthogonality and values closer to -1 indicate greater similarity. This makes it usable as a loss function in a setting where you try to maximize the proximity between predictions and targets. If either y_true
or y_pred
is a zero vector, cosine similarity will be 0 regardless of the proximity between predictions and targets.
Formula:
loss = -sum(l2_norm(y_true) * l2_norm(y_pred))
Arguments
- axis: The axis along which the cosine similarity is computed (the features axis). Defaults to
-1
. - reduction: Type of reduction to apply to the loss. In almost all cases this should be
"sum_over_batch_size"
. Supported options are"sum"
,"sum_over_batch_size"
orNone
. - name: Optional name for the loss instance.
mean_squared_error
function
keras.losses.mean_squared_error(y_true, y_pred)
Computes the mean squared error between labels and predictions.
Formula:
loss = mean(square(y_true - y_pred), axis=-1)
Example
>>> y_true = np.random.randint(0, 2, size=(2, 3))
>>> y_pred = np.random.random(size=(2, 3))
>>> loss = keras.losses.mean_squared_error(y_true, y_pred)
Arguments
- y_true: Ground truth values with shape =
[batch_size, d0, .. dN]
. - y_pred: The predicted values with shape =
[batch_size, d0, .. dN]
.
Returns
Mean squared error values with shape = [batch_size, d0, .. dN-1]
.
mean_absolute_error
function
keras.losses.mean_absolute_error(y_true, y_pred)
Computes the mean absolute error between labels and predictions.
loss = mean(abs(y_true - y_pred), axis=-1)
Arguments
- y_true: Ground truth values with shape =
[batch_size, d0, .. dN]
. - y_pred: The predicted values with shape =
[batch_size, d0, .. dN]
.
Returns
Mean absolute error values with shape = [batch_size, d0, .. dN-1]
.
Example
>>> y_true = np.random.randint(0, 2, size=(2, 3))
>>> y_pred = np.random.random(size=(2, 3))
>>> loss = keras.losses.mean_absolute_error(y_true, y_pred)
mean_absolute_percentage_error
function
keras.losses.mean_absolute_percentage_error(y_true, y_pred)
Computes the mean absolute percentage error between y_true
& y_pred
.
Formula:
loss = 100 * mean(abs((y_true - y_pred) / y_true), axis=-1)
Division by zero is prevented by dividing by maximum(y_true, epsilon)
where epsilon = keras.backend.epsilon()
(default to 1e-7
).
Arguments
- y_true: Ground truth values with shape =
[batch_size, d0, .. dN]
. - y_pred: The predicted values with shape =
[batch_size, d0, .. dN]
.
Returns
Mean absolute percentage error values with shape = [batch_size, d0, .. dN-1]
.
Example
>>> y_true = np.random.random(size=(2, 3))
>>> y_pred = np.random.random(size=(2, 3))
>>> loss = keras.losses.mean_absolute_percentage_error(y_true, y_pred)
mean_squared_logarithmic_error
function
keras.losses.mean_squared_logarithmic_error(y_true, y_pred)
Computes the mean squared logarithmic error between y_true
& y_pred
.
Formula:
loss = mean(square(log(y_true + 1) - log(y_pred + 1)), axis=-1)
Note that y_pred
and y_true
cannot be less or equal to 0. Negative values and 0 values will be replaced with keras.backend.epsilon()
(default to 1e-7
).
Arguments
- y_true: Ground truth values with shape =
[batch_size, d0, .. dN]
. - y_pred: The predicted values with shape =
[batch_size, d0, .. dN]
.
Returns
Mean squared logarithmic error values with shape = [batch_size, d0, .. dN-1]
.
Example
>>> y_true = np.random.randint(0, 2, size=(2, 3))
>>> y_pred = np.random.random(size=(2, 3))
>>> loss = keras.losses.mean_squared_logarithmic_error(y_true, y_pred)
cosine_similarity
function
keras.losses.cosine_similarity(y_true, y_pred, axis=-1)
Computes the cosine similarity between labels and predictions.
Formula:
loss = -sum(l2_norm(y_true) * l2_norm(y_pred))
Note that it is a number between -1 and 1. When it is a negative number between -1 and 0, 0 indicates orthogonality and values closer to -1 indicate greater similarity. This makes it usable as a loss function in a setting where you try to maximize the proximity between predictions and targets. If either y_true
or y_pred
is a zero vector, cosine similarity will be 0 regardless of the proximity between predictions and targets.
Arguments
- y_true: Tensor of true targets.
- y_pred: Tensor of predicted targets.
- axis: Axis along which to determine similarity. Defaults to
-1
.
Returns
Cosine similarity tensor.
Example
>>> y_true = [[0., 1.], [1., 1.], [1., 1.]]
>>> y_pred = [[1., 0.], [1., 1.], [-1., -1.]]
>>> loss = keras.losses.cosine_similarity(y_true, y_pred, axis=-1)
[-0., -0.99999994, 0.99999994]
Huber
class
keras.losses.Huber(delta=1.0, reduction="sum_over_batch_size", name="huber_loss")
Computes the Huber loss between y_true
& y_pred
.
Formula:
for x in error:
if abs(x) <= delta:
loss.append(0.5 * x^2)
elif abs(x) > delta:
loss.append(delta * abs(x) - 0.5 * delta^2)
loss = mean(loss, axis=-1)
Arguments
- delta: A float, the point where the Huber loss function changes from a quadratic to linear.
- reduction: Type of reduction to apply to loss. Options are
"sum"
,"sum_over_batch_size"
orNone
. Defaults to"sum_over_batch_size"
. - name: Optional name for the instance.
huber
function
keras.losses.huber(y_true, y_pred, delta=1.0)
Computes Huber loss value.
Formula:
for x in error:
if abs(x) <= delta:
loss.append(0.5 * x^2)
elif abs(x) > delta:
loss.append(delta * abs(x) - 0.5 * delta^2)
loss = mean(loss, axis=-1)
Example
>>> y_true = [[0, 1], [0, 0]]
>>> y_pred = [[0.6, 0.4], [0.4, 0.6]]
>>> loss = keras.losses.huber(y_true, y_pred)
0.155
Arguments
- y_true: tensor of true targets.
- y_pred: tensor of predicted targets.
- delta: A float, the point where the Huber loss function changes from a quadratic to linear. Defaults to
1.0
.
Returns
Tensor with one scalar loss entry per sample.
LogCosh
class
keras.losses.LogCosh(reduction="sum_over_batch_size", name="log_cosh")
Computes the logarithm of the hyperbolic cosine of the prediction error.
Formula:
error = y_pred - y_true
logcosh = mean(log((exp(error) + exp(-error))/2), axis=-1)`
where x is the error y_pred - y_true
.
Arguments
- reduction: Type of reduction to apply to loss. Options are
"sum"
,"sum_over_batch_size"
orNone
. Defaults to"sum_over_batch_size"
. - name: Optional name for the instance.
log_cosh
function
keras.losses.log_cosh(y_true, y_pred)
Logarithm of the hyperbolic cosine of the prediction error.
Formula:
loss = mean(log(cosh(y_pred - y_true)), axis=-1)
Note that log(cosh(x))
is approximately equal to (x ** 2) / 2
for small x
and to abs(x) - log(2)
for large x
. This means that ‘logcosh’ works mostly like the mean squared error, but will not be so strongly affected by the occasional wildly incorrect prediction.
Example
>>> y_true = [[0., 1.], [0., 0.]]
>>> y_pred = [[1., 1.], [0., 0.]]
>>> loss = keras.losses.log_cosh(y_true, y_pred)
0.108
Arguments
- y_true: Ground truth values with shape =
[batch_size, d0, .. dN]
. - y_pred: The predicted values with shape =
[batch_size, d0, .. dN]
.
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