deel.lip.losses module

This module contains losses used in wasserstein distance estimation. See https://arxiv.org/abs/2006.06520 for more information.

class deel.lip.losses.HKR(alpha, min_margin=1.0, reduction='auto', name='HKR')

Bases: keras.losses.Loss

Wasserstein loss with a regularization param based on hinge loss.

\[\inf_{f \in Lip_1(\Omega)} \underset{\textbf{x} \sim P_-}{\mathbb{E}} \left[f(\textbf{x} )\right] - \underset{\textbf{x} \sim P_+} {\mathbb{E}} \left[f(\textbf{x} )\right] + \alpha \underset{\textbf{x}}{\mathbb{E}} \left(\text{min_margin} -Yf(\textbf{x})\right)_+\]
Parameters

  • alpha – regularization factor

  • min_margin – minimal margin ( see hinge_margin_loss )

  • consistent (Kantorovich-rubinstein term of the loss. In order to be) –

  • KR (between hinge and) –

  • class (the first label must yield the positve) –

  • class. (while the second yields negative) –

  • reduction – passed to tf.keras.Loss constructor

  • name – passed to tf.keras.Loss constructor

Returns

a function that compute the regularized Wasserstein loss

call(y_true, y_pred)
get_config()

Returns the config dictionary for a Loss instance.

class deel.lip.losses.HingeMargin(min_margin=1.0, reduction='auto', name='HingeMargin')

Bases: keras.losses.Loss

Compute the hinge margin loss.

\[\underset{\textbf{x}}{\mathbb{E}} \left(\text{min_margin} -Yf(\textbf{x})\right)_+\]
Parameters

  • min_margin – the minimal margin to enforce.

  • reduction – passed to tf.keras.Loss constructor

  • name – passed to tf.keras.Loss constructor

Returns

a function that compute the hinge loss.

call(y_true, y_pred)
get_config()

Returns the config dictionary for a Loss instance.

deel.lip.losses.KR(y_true, y_pred)

Loss to estimate wasserstein-1 distance using Kantorovich-Rubinstein duality. The Kantorovich-Rubinstein duality is formulated as following:

\[W_1(\mu, \nu) = \sup_{f \in Lip_1(\Omega)} \underset{\textbf{x} \sim \mu}{\mathbb{E}} \left[f(\textbf{x} )\right] - \underset{\textbf{x} \sim \nu}{\mathbb{E}} \left[f(\textbf{x} )\right]\]

Where mu and nu stands for the two distributions, the distribution where the label is 1 and the rest.

Returns

Callable, the function to compute Wasserstein loss

class deel.lip.losses.MultiMargin(min_margin=1, reduction='auto', name='MultiMargin')

Bases: keras.losses.Loss

Compute the mean hinge margin loss for multi class (equivalent to Pytorch

multi_margin_loss)

Parameters

  • min_margin – the minimal margin to enforce.

  • reduction – passed to tf.keras.Loss constructor

  • name – passed to tf.keras.Loss constructor

Notes

y_true has to be to_categorical

Returns

Callable, the function to compute multi margin loss

call(y_true, y_pred)
get_config()

Returns the config dictionary for a Loss instance.

class deel.lip.losses.MulticlassHKR(alpha=10.0, min_margin=1.0, reduction='auto', name='MulticlassHKR')

Bases: keras.losses.Loss

The multiclass version of HKR. This is done by computing the HKR term over each class and averaging the results.

Parameters

  • alpha – regularization factor

  • min_margin – minimal margin ( see Hinge_multiclass_loss )

  • reduction – passed to tf.keras.Loss constructor

  • name – passed to tf.keras.Loss constructor

Returns

Callable, the function to compute HKR loss #Note y_true has to be one hot encoded

call(y_true, y_pred)
get_config()

Returns the config dictionary for a Loss instance.

class deel.lip.losses.MulticlassHinge(min_margin=1.0, reduction='auto', name='MulticlassHinge')

Bases: keras.losses.Loss

Loss to estimate the Hinge loss in a multiclass setup. It compute the elementwise hinge term. Note that this formulation differs from the one commonly found in tensorflow/pytorch (with marximise the difference between the two largest logits). This formulation is consistent with the binary classification loss used in a multiclass fashion. Note y_true should be one hot encoded. labels in (1,0)

Parameters

  • min_margin – positive float, margin to enforce.

  • reduction – passed to tf.keras.Loss constructor

  • name – passed to tf.keras.Loss constructor

Returns

Callable, the function to compute multiclass Hinge loss #Note y_true has to be one hot encoded

call(y_true, y_pred)
get_config()

Returns the config dictionary for a Loss instance.

class deel.lip.losses.MulticlassKR(reduction='auto', name='MulticlassKR')

Bases: keras.losses.Loss

Loss to estimate average of W1 distance using Kantorovich-Rubinstein duality over outputs. Note y_true should be one hot encoding (labels being 1s and 0s ). In this multiclass setup thr KR term is computed for each class and then averaged.

Parameters

  • reduction – passed to tf.keras.Loss constructor

  • name – passed to tf.keras.Loss constructor

Returns

Callable, the function to compute Wasserstein multiclass loss. #Note y_true has to be one hot encoded

call(y_true, y_pred)
get_config()

Returns the config dictionary for a Loss instance.

deel.lip.losses.negative_KR(y_true, y_pred)

Loss to compute the negative wasserstein-1 distance using Kantorovich-Rubinstein duality. This allows the maximisation of the term using conventional optimizer.

Returns

Callable, the function to compute negative Wasserstein loss