Objective Functions¶

Objective functions are used measure the performance of a model.

Featured Objectives¶

`HingeLoss`	Hinge Loss
`KLDivergence`	KL Divergence
`MeanSquaredError`	Mean Squared error (MSE)
`HellingerDistance`	Hellinger Distance
`BinaryCrossEntropy`	Binary Cross Entropy
`CategoricalCrossEntropy`	Categorical Cross Entropy

Function Descriptions¶

class ztlearn.objectives.BinaryCrossEntropy[source]¶

Bases: ztlearn.objectives.Objective

Binary Cross Entropy

Binary CrossEntropy measures the performance of a classification model whose output is a probability value between 0 & 1. ‘Binary’ is meant for discrete classification tasks in which the classes are independent and not mutually exclusive. Targets here could be either 0 or 1 scalar

References

[1] Cross Entropy

[Wikipedia Article] https://en.wikipedia.org/wiki/Cross_entropy

accuracy(predictions, targets, threshold=0.5)[source]¶

Calculates the BinaryCrossEntropy Accuracy Score given prediction and targets

Parameters:	predictions (numpy.array) – the predictions numpy array targets (numpy.array) – the targets numpy array threshold (numpy.float32) – the threshold value
Returns:	the output of BinaryCrossEntropy Accuracy Score
Return type:	numpy.float32

derivative(predictions, targets, np_type)[source]¶

Applies the BinaryCrossEntropy Derivative to prediction and targets provided

Parameters:	predictions (numpy.array) – the predictions numpy array targets (numpy.array) – the targets numpy array
Returns:	the output of BinaryCrossEntropy Derivative to prediction and targets
Return type:	numpy.array

loss(predictions, targets, np_type)[source]¶

Applies the BinaryCrossEntropy Loss to prediction and targets provided

Parameters:	predictions (numpy.array) – the predictions numpy array targets (numpy.array) – the targets numpy array
Returns:	the output of BinaryCrossEntropy Loss to prediction and targets
Return type:	numpy.array

objective_name¶

class ztlearn.objectives.CategoricalCrossEntropy[source]¶

Bases: ztlearn.objectives.Objective

Categorical Cross Entropy

Categorical Cross Entropy measures the performance of a classification model whose output is a probability value between 0 and 1. ‘Categorical’ is meant for discrete classification tasks in which the classes are mutually exclusive.

References

[1] Cross Entropy

[Wikipedia Article] https://en.wikipedia.org/wiki/Cross_entropy

accuracy(predictions, targets)[source]¶

Calculates the CategoricalCrossEntropy Accuracy Score given prediction and targets

Parameters:	predictions (numpy.array) – the predictions numpy array targets (numpy.array) – the targets numpy array
Returns:	the output of CategoricalCrossEntropy Accuracy Score
Return type:	numpy.float32

derivative(predictions, targets, np_type)[source]¶

Applies the CategoricalCrossEntropy Derivative to prediction and targets provided

Parameters:	predictions (numpy.array) – the predictions numpy array targets (numpy.array) – the targets numpy array
Returns:	the output of CategoricalCrossEntropy Derivative to prediction and targets
Return type:	numpy.array

loss(predictions, targets, np_type)[source]¶

Applies the CategoricalCrossEntropy Loss to prediction and targets provided

Parameters:	predictions (numpy.array) – the predictions numpy array targets (numpy.array) – the targets numpy array
Returns:	the output of CategoricalCrossEntropy Loss to prediction and targets
Return type:	numpy.array

objective_name¶

class ztlearn.objectives.HellingerDistance[source]¶

Bases: object

Hellinger Distance

Hellinger Distance is used to quantify the similarity between two probability distributions.

References

[1] Hellinger Distance

[Wikipedia Article] https://en.wikipedia.org/wiki/Hellinger_distance

SQRT_2 = 1.4142135623730951¶

accuracy(predictions, targets, threshold=0.5)[source]¶

derivative(predictions, targets, np_type)[source]¶

Applies the HellingerDistance Derivative to prediction and targets provided

Parameters:	predictions (numpy.array) – the predictions numpy array targets (numpy.array) – the targets numpy array
Returns:	the output of HellingerDistance Derivative to prediction and targets
Return type:	numpy.array

loss(predictions, targets, np_type)[source]¶

Applies the HellingerDistance Loss to prediction and targets provided

Parameters:	predictions (numpy.array) – the predictions numpy array targets (numpy.array) – the targets numpy array
Returns:	the output of HellingerDistance Loss to prediction and targets
Return type:	numpy.array

objective_name¶

sqrt_difference(predictions, targets)[source]¶

class ztlearn.objectives.HingeLoss[source]¶

Bases: object

Hinge Loss

Hinge Loss also known as SVM Loss is used “maximum-margin” classification, most notably for support vector machines (SVMs)

References

[1] Hinge loss

[Wikipedia Article] https://en.wikipedia.org/wiki/Hinge_loss

accuracy(predictions, targets, threshold=0.5)[source]¶

Calculates the Hinge-Loss Accuracy Score given prediction and targets

Parameters:	predictions (numpy.array) – the predictions numpy array targets (numpy.array) – the targets numpy array
Returns:	the output of Hinge-Loss Accuracy Score
Return type:	numpy.float32

derivative(predictions, targets, np_type)[source]¶

Applies the Hinge-Loss Derivative to prediction and targets provided

Parameters:	predictions (numpy.array) – the predictions numpy array targets (numpy.array) – the targets numpy array
Returns:	the output of Hinge-Loss Derivative to prediction and targets
Return type:	numpy.array

loss(predictions, targets, np_type)[source]¶

Applies the Hinge-Loss to Loss prediction and targets provided

Parameters:	predictions (numpy.array) – the predictions numpy array targets (numpy.array) – the targets numpy array
Returns:	the output of Hinge-Loss Loss to prediction and targets
Return type:	numpy.array

objective_name¶

class ztlearn.objectives.HuberLoss[source]¶

Bases: ztlearn.objectives.Objective

Huber Loss

Huber Loss: is a loss function used in robust regression where it is found to be less sensitive to outliers in data than the squared error loss.

References:

[1] Huber Loss

[Wikipedia Article] https://en.wikipedia.org/wiki/Huber_loss

[2] Huber loss

[Wikivisually Article] https://wikivisually.com/wiki/Huber_loss

accuracy(predictions, targets)[source]¶

Calculates the HuberLoss Accuracy Score given prediction and targets

Parameters:	predictions (numpy.array) – the predictions numpy array targets (numpy.array) – the targets numpy array
Returns:	the output of KLDivergence Accuracy Score
Return type:	numpy.float32

derivative(predictions, targets, np_type, delta=1.0)[source]¶

Applies the HuberLoss Derivative to prediction and targets provided

Parameters:	predictions (numpy.array) – the predictions numpy array targets (numpy.array) – the targets numpy array
Returns:	the output of KLDivergence Derivative to prediction and targets
Return type:	numpy.array

loss(predictions, targets, np_type, delta=1.0)[source]¶

Applies the HuberLoss Loss to prediction and targets provided

Parameters:	predictions (numpy.array) – the predictions numpy array targets (numpy.array) – the targets numpy array
Returns:	the output of KLDivergence Loss to prediction and targets
Return type:	numpy.array

objective_name¶

class ztlearn.objectives.KLDivergence[source]¶

Bases: ztlearn.objectives.Objective

KL Divergence

Kullback–Leibler divergence (also called relative entropy) is a measure of divergence between two probability distributions.

accuracy(predictions, targets)[source]¶

Calculates the KLDivergence Accuracy Score given prediction and targets

Parameters:	predictions (numpy.array) – the predictions numpy array targets (numpy.array) – the targets numpy array
Returns:	the output of KLDivergence Accuracy Score
Return type:	numpy.float32

derivative(predictions, targets, np_type)[source]¶

Applies the KLDivergence Derivative to prediction and targets provided

Parameters:	predictions (numpy.array) – the predictions numpy array targets (numpy.array) – the targets numpy array
Returns:	the output of KLDivergence Derivative to prediction and targets
Return type:	numpy.array

loss(predictions, targets, np_type)[source]¶

Applies the KLDivergence Loss to prediction and targets provided

Parameters:	predictions (numpy.array) – the predictions numpy array targets (numpy.array) – the targets numpy array
Returns:	the output of KLDivergence Loss to prediction and targets
Return type:	numpy.array

objective_name¶

class ztlearn.objectives.MeanSquaredError[source]¶

Bases: object

Mean Squared error (MSE)

MSE measures the average squared difference between the predictions and the targets. The closer the predictions are to the targets the more efficient the estimator.

References

[1] Mean Squared error

[Wikipedia Article] https://en.wikipedia.org/wiki/Mean_squared_error

accuracy(predictions, targets, threshold=0.5)[source]¶

derivative(predictions, targets, np_type)[source]¶

Applies the MeanSquaredError Derivative to prediction and targets provided

Parameters:	predictions (numpy.array) – the predictions numpy array targets (numpy.array) – the targets numpy array
Returns:	the output of MeanSquaredError Derivative to prediction and targets
Return type:	numpy.array

loss(predictions, targets, np_type)[source]¶

Applies the MeanSquaredError Loss to prediction and targets provided

Parameters:	predictions (numpy.array) – the predictions numpy array targets (numpy.array) – the targets numpy array
Returns:	the output of MeanSquaredError Loss to prediction and targets
Return type:	numpy.array

objective_name¶

class ztlearn.objectives.Objective[source]¶

Bases: object

add_fuzz_factor(np_array, epsilon=1e-05)[source]¶

clip(predictions, epsilon=1e-15)[source]¶

error(predictions, targets)[source]¶

objective_name¶

class ztlearn.objectives.ObjectiveFunction(name)[source]¶

Bases: object

accuracy(predictions, targets)[source]¶

backward(predictions, targets, np_type=<class 'numpy.float32'>)[source]¶

forward(predictions, targets, np_type=<class 'numpy.float32'>)[source]¶

name¶