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Hinge Loss

Module Interface

class torchmetrics.HingeLoss(squared=False, multiclass_mode=None, **kwargs)[source]

Computes the mean Hinge loss, typically used for Support Vector Machines (SVMs).

In the binary case it is defined as:

\text{Hinge loss} = \max(0, 1 - y \times \hat{y})

Where y \in {-1, 1} is the target, and \hat{y} \in \mathbb{R} is the prediction.

In the multi-class case, when multiclass_mode=None (default), multiclass_mode=MulticlassMode.CRAMMER_SINGER or multiclass_mode="crammer-singer", this metric will compute the multi-class hinge loss defined by Crammer and Singer as:

\text{Hinge loss} = \max\left(0, 1 - \hat{y}_y + \max_{i \ne y} (\hat{y}_i)\right)

Where y \in {0, ..., \mathrm{C}} is the target class (where \mathrm{C} is the number of classes), and \hat{y} \in \mathbb{R}^\mathrm{C} is the predicted output per class.

In the multi-class case when multiclass_mode=MulticlassMode.ONE_VS_ALL or multiclass_mode='one-vs-all', this metric will use a one-vs-all approach to compute the hinge loss, giving a vector of C outputs where each entry pits that class against all remaining classes.

This metric can optionally output the mean of the squared hinge loss by setting squared=True

Only accepts inputs with preds shape of (N) (binary) or (N, C) (multi-class) and target shape of (N).

Parameters
  • squared (bool) – If True, this will compute the squared hinge loss. Otherwise, computes the regular hinge loss (default).

  • multiclass_mode (Union[str, MulticlassMode, None]) – Which approach to use for multi-class inputs (has no effect in the binary case). None (default), MulticlassMode.CRAMMER_SINGER or "crammer-singer", uses the Crammer Singer multi-class hinge loss. MulticlassMode.ONE_VS_ALL or "one-vs-all" computes the hinge loss in a one-vs-all fashion.

  • kwargs (Any) – Additional keyword arguments, see Advanced metric settings for more info.

Raises

ValueError – If multiclass_mode is not: None, MulticlassMode.CRAMMER_SINGER, "crammer-singer", MulticlassMode.ONE_VS_ALL or "one-vs-all".

Example (binary case):
>>> import torch
>>> from torchmetrics import HingeLoss
>>> target = torch.tensor([0, 1, 1])
>>> preds = torch.tensor([-2.2, 2.4, 0.1])
>>> hinge = HingeLoss()
>>> hinge(preds, target)
tensor(0.3000)
Example (default / multiclass case):
>>> target = torch.tensor([0, 1, 2])
>>> preds = torch.tensor([[-1.0, 0.9, 0.2], [0.5, -1.1, 0.8], [2.2, -0.5, 0.3]])
>>> hinge = HingeLoss()
>>> hinge(preds, target)
tensor(2.9000)
Example (multiclass example, one vs all mode):
>>> target = torch.tensor([0, 1, 2])
>>> preds = torch.tensor([[-1.0, 0.9, 0.2], [0.5, -1.1, 0.8], [2.2, -0.5, 0.3]])
>>> hinge = HingeLoss(multiclass_mode="one-vs-all")
>>> hinge(preds, target)
tensor([2.2333, 1.5000, 1.2333])

Initializes internal Module state, shared by both nn.Module and ScriptModule.

compute()[source]

Override this method to compute the final metric value from state variables synchronized across the distributed backend.

Return type

Tensor

update(preds, target)[source]

Override this method to update the state variables of your metric class.

Return type

None

Functional Interface

torchmetrics.functional.hinge_loss(preds, target, squared=False, multiclass_mode=None)[source]

Computes the mean Hinge loss typically used for Support Vector Machines (SVMs).

In the binary case it is defined as:

\text{Hinge loss} = \max(0, 1 - y \times \hat{y})

Where y \in {-1, 1} is the target, and \hat{y} \in \mathbb{R} is the prediction.

In the multi-class case, when multiclass_mode=None (default), multiclass_mode=MulticlassMode.CRAMMER_SINGER or multiclass_mode="crammer-singer", this metric will compute the multi-class hinge loss defined by Crammer and Singer as:

\text{Hinge loss} = \max\left(0, 1 - \hat{y}_y + \max_{i \ne y} (\hat{y}_i)\right)

Where y \in {0, ..., \mathrm{C}} is the target class (where \mathrm{C} is the number of classes), and \hat{y} \in \mathbb{R}^\mathrm{C} is the predicted output per class.

In the multi-class case when multiclass_mode=MulticlassMode.ONE_VS_ALL or multiclass_mode='one-vs-all', this metric will use a one-vs-all approach to compute the hinge loss, giving a vector of C outputs where each entry pits that class against all remaining classes.

This metric can optionally output the mean of the squared hinge loss by setting squared=True

Only accepts inputs with preds shape of (N) (binary) or (N, C) (multi-class) and target shape of (N).

Parameters
  • preds (Tensor) – Predictions from model (as float outputs from decision function).

  • target (Tensor) – Ground truth labels.

  • squared (bool) – If True, this will compute the squared hinge loss. Otherwise, computes the regular hinge loss (default).

  • multiclass_mode (Union[str, MulticlassMode, None]) – Which approach to use for multi-class inputs (has no effect in the binary case). None (default), MulticlassMode.CRAMMER_SINGER or "crammer-singer", uses the Crammer Singer multi-class hinge loss. MulticlassMode.ONE_VS_ALL or "one-vs-all" computes the hinge loss in a one-vs-all fashion.

Raises
  • ValueError – If preds shape is not of size (N) or (N, C).

  • ValueError – If target shape is not of size (N).

  • ValueError – If multiclass_mode is not: None, MulticlassMode.CRAMMER_SINGER, "crammer-singer", MulticlassMode.ONE_VS_ALL or "one-vs-all".

Example (binary case):
>>> import torch
>>> from torchmetrics.functional import hinge_loss
>>> target = torch.tensor([0, 1, 1])
>>> preds = torch.tensor([-2.2, 2.4, 0.1])
>>> hinge_loss(preds, target)
tensor(0.3000)
Example (default / multiclass case):
>>> target = torch.tensor([0, 1, 2])
>>> preds = torch.tensor([[-1.0, 0.9, 0.2], [0.5, -1.1, 0.8], [2.2, -0.5, 0.3]])
>>> hinge_loss(preds, target)
tensor(2.9000)
Example (multiclass example, one vs all mode):
>>> target = torch.tensor([0, 1, 2])
>>> preds = torch.tensor([[-1.0, 0.9, 0.2], [0.5, -1.1, 0.8], [2.2, -0.5, 0.3]])
>>> hinge_loss(preds, target, multiclass_mode="one-vs-all")
tensor([2.2333, 1.5000, 1.2333])
Return type

Tensor

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