# ROC¶

## Module Interface¶

class torchmetrics.ROC(**kwargs)[source]

Compute the Receiver Operating Characteristic (ROC).

The curve consist of multiple pairs of true positive rate (TPR) and false positive rate (FPR) values evaluated at different thresholds, such that the tradeoff between the two values can be seen.

This function is a simple wrapper to get the task specific versions of this metric, which is done by setting the task argument to either 'binary', 'multiclass' or multilabel. See the documentation of BinaryROC, MulticlassROC and MultilabelROC for the specific details of each argument influence and examples.

Legacy Example:
>>> from torch import tensor
>>> pred = tensor([0.0, 1.0, 2.0, 3.0])
>>> target = tensor([0, 1, 1, 1])
>>> fpr, tpr, thresholds = roc(pred, target)
>>> fpr
tensor([0., 0., 0., 0., 1.])
>>> tpr
tensor([0.0000, 0.3333, 0.6667, 1.0000, 1.0000])
>>> thresholds
tensor([1.0000, 0.9526, 0.8808, 0.7311, 0.5000])

>>> pred = tensor([[0.75, 0.05, 0.05, 0.05],
...                [0.05, 0.75, 0.05, 0.05],
...                [0.05, 0.05, 0.75, 0.05],
...                [0.05, 0.05, 0.05, 0.75]])
>>> target = tensor([0, 1, 3, 2])
>>> fpr, tpr, thresholds = roc(pred, target)
>>> fpr
[tensor([0., 0., 1.]), tensor([0., 0., 1.]), tensor([0.0000, 0.3333, 1.0000]), tensor([0.0000, 0.3333, 1.0000])]
>>> tpr
[tensor([0., 1., 1.]), tensor([0., 1., 1.]), tensor([0., 0., 1.]), tensor([0., 0., 1.])]
>>> thresholds
[tensor([1.0000, 0.7500, 0.0500]),
tensor([1.0000, 0.7500, 0.0500]),
tensor([1.0000, 0.7500, 0.0500]),
tensor([1.0000, 0.7500, 0.0500])]

>>> pred = tensor([[0.8191, 0.3680, 0.1138],
...                [0.3584, 0.7576, 0.1183],
...                [0.2286, 0.3468, 0.1338],
...                [0.8603, 0.0745, 0.1837]])
>>> target = tensor([[1, 1, 0], [0, 1, 0], [0, 0, 0], [0, 1, 1]])
>>> fpr, tpr, thresholds = roc(pred, target)
>>> fpr
[tensor([0.0000, 0.3333, 0.3333, 0.6667, 1.0000]),
tensor([0., 0., 0., 1., 1.]),
tensor([0.0000, 0.0000, 0.3333, 0.6667, 1.0000])]
>>> tpr
[tensor([0., 0., 1., 1., 1.]),
tensor([0.0000, 0.3333, 0.6667, 0.6667, 1.0000]),
tensor([0., 1., 1., 1., 1.])]
>>> thresholds
[tensor([1.0000, 0.8603, 0.8191, 0.3584, 0.2286]),
tensor([1.0000, 0.7576, 0.3680, 0.3468, 0.0745]),
tensor([1.0000, 0.1837, 0.1338, 0.1183, 0.1138])]

static __new__(cls, task, thresholds=None, num_classes=None, num_labels=None, ignore_index=None, validate_args=True, **kwargs)[source]

Return type:

Metric

### BinaryROC¶

class torchmetrics.classification.BinaryROC(thresholds=None, ignore_index=None, validate_args=True, **kwargs)[source]

The curve consist of multiple pairs of true positive rate (TPR) and false positive rate (FPR) values evaluated at different thresholds, such that the tradeoff between the two values can be seen.

As input to forward and update the metric accepts the following input:

• preds (Tensor): A float tensor of shape (N, ...). Preds should be a tensor containing probabilities or logits for each observation. If preds has values outside [0,1] range we consider the input to be logits and will auto apply sigmoid per element.

• target (Tensor): An int tensor of shape (N, ...). Target should be a tensor containing ground truth labels, and therefore only contain {0,1} values (except if ignore_index is specified). The value 1 always encodes the positive class.

Note

Additional dimension ... will be flattened into the batch dimension.

As output to forward and compute the metric returns a tuple of 3 tensors containing:

• fpr (Tensor): A 1d tensor of size (n_thresholds+1, ) with false positive rate values

• tpr (Tensor): A 1d tensor of size (n_thresholds+1, ) with true positive rate values

• thresholds (Tensor): A 1d tensor of size (n_thresholds, ) with decreasing threshold values

Note

The implementation both supports calculating the metric in a non-binned but accurate version and a binned version that is less accurate but more memory efficient. Setting the thresholds argument to None will activate the non-binned version that uses memory of size $$\mathcal{O}(n_{samples})$$ whereas setting the thresholds argument to either an integer, list or a 1d tensor will use a binned version that uses memory of size $$\mathcal{O}(n_{thresholds})$$ (constant memory).

Note

The outputted thresholds will be in reversed order to ensure that they corresponds to both fpr and tpr which are sorted in reversed order during their calculation, such that they are monotome increasing.

Parameters:
• Can be one of:

• If set to None, will use a non-binned approach where thresholds are dynamically calculated from all the data. Most accurate but also most memory consuming approach.

• If set to an int (larger than 1), will use that number of thresholds linearly spaced from 0 to 1 as bins for the calculation.

• If set to an list of floats, will use the indicated thresholds in the list as bins for the calculation

• If set to an 1d tensor of floats, will use the indicated thresholds in the tensor as bins for the calculation.

• ignore_index (Optional[int]) – Specifies a target value that is ignored and does not contribute to the metric calculation

• validate_args (bool) – bool indicating if input arguments and tensors should be validated for correctness. Set to False for faster computations.

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

Example

>>> from torch import tensor
>>> from torchmetrics.classification import BinaryROC
>>> preds = tensor([0, 0.5, 0.7, 0.8])
>>> target = tensor([0, 1, 1, 0])
>>> metric = BinaryROC(thresholds=None)
>>> metric(preds, target)
(tensor([0.0000, 0.5000, 0.5000, 0.5000, 1.0000]),
tensor([0.0000, 0.0000, 0.5000, 1.0000, 1.0000]),
tensor([1.0000, 0.8000, 0.7000, 0.5000, 0.0000]))
>>> broc = BinaryROC(thresholds=5)
>>> broc(preds, target)
(tensor([0.0000, 0.5000, 0.5000, 0.5000, 1.0000]),
tensor([0., 0., 1., 1., 1.]),
tensor([1.0000, 0.7500, 0.5000, 0.2500, 0.0000]))

plot(curve=None, score=None, ax=None)[source]

Plot a single or multiple values from the metric.

Parameters:
Return type:
Returns:

Figure and Axes object

Raises:

ModuleNotFoundError – If matplotlib is not installed

>>> from torch import rand, randint
>>> from torchmetrics.classification import BinaryROC
>>> preds = rand(20)
>>> target = randint(2, (20,))
>>> metric = BinaryROC()
>>> metric.update(preds, target)
>>> fig_, ax_ = metric.plot(score=True)


### MulticlassROC¶

class torchmetrics.classification.MulticlassROC(num_classes, thresholds=None, average=None, ignore_index=None, validate_args=True, **kwargs)[source]

The curve consist of multiple pairs of true positive rate (TPR) and false positive rate (FPR) values evaluated at different thresholds, such that the tradeoff between the two values can be seen.

For multiclass the metric is calculated by iteratively treating each class as the positive class and all other classes as the negative, which is referred to as the one-vs-rest approach. One-vs-one is currently not supported by this metric.

As input to forward and update the metric accepts the following input:

• preds (Tensor): A float tensor of shape (N, C, ...). Preds should be a tensor containing probabilities or logits for each observation. If preds has values outside [0,1] range we consider the input to be logits and will auto apply softmax per sample.

• target (Tensor): An int tensor of shape (N, ...). Target should be a tensor containing ground truth labels, and therefore only contain values in the [0, n_classes-1] range (except if ignore_index is specified).

Note

Additional dimension ... will be flattened into the batch dimension.

As output to forward and compute the metric returns a tuple of either 3 tensors or 3 lists containing

• fpr (Tensor): if thresholds=None a list for each class is returned with an 1d tensor of size (n_thresholds+1, ) with false positive rate values (length may differ between classes). If thresholds is set to something else, then a single 2d tensor of size (n_classes, n_thresholds+1) with false positive rate values is returned.

• tpr (Tensor): if thresholds=None a list for each class is returned with an 1d tensor of size (n_thresholds+1, ) with true positive rate values (length may differ between classes). If thresholds is set to something else, then a single 2d tensor of size (n_classes, n_thresholds+1) with true positive rate values is returned.

• thresholds (Tensor): if thresholds=None a list for each class is returned with an 1d tensor of size (n_thresholds, ) with decreasing threshold values (length may differ between classes). If threshold is set to something else, then a single 1d tensor of size (n_thresholds, ) is returned with shared threshold values for all classes.

Note

The implementation both supports calculating the metric in a non-binned but accurate version and a binned version that is less accurate but more memory efficient. Setting the thresholds argument to None will activate the non-binned version that uses memory of size $$\mathcal{O}(n_{samples})$$ whereas setting the thresholds argument to either an integer, list or a 1d tensor will use a binned version that uses memory of size $$\mathcal{O}(n_{thresholds} \times n_{classes})$$ (constant memory).

Note

Note that outputted thresholds will be in reversed order to ensure that they corresponds to both fpr and tpr which are sorted in reversed order during their calculation, such that they are monotome increasing.

Parameters:
• num_classes (int) – Integer specifying the number of classes

• Can be one of:

• If set to None, will use a non-binned approach where thresholds are dynamically calculated from all the data. Most accurate but also most memory consuming approach.

• If set to an int (larger than 1), will use that number of thresholds linearly spaced from 0 to 1 as bins for the calculation.

• If set to an list of floats, will use the indicated thresholds in the list as bins for the calculation

• If set to an 1d tensor of floats, will use the indicated thresholds in the tensor as bins for the calculation.

• average (Optional[Literal['micro', 'macro']]) – If aggregation of curves should be applied. By default, the curves are not aggregated and a curve for each class is returned. If average is set to "micro", the metric will aggregate the curves by one hot encoding the targets and flattening the predictions, considering all classes jointly as a binary problem. If average is set to "macro", the metric will aggregate the curves by first interpolating the curves from each class at a combined set of thresholds and then average over the classwise interpolated curves. See averaging curve objects for more info on the different averaging methods.

• ignore_index (Optional[int]) – Specifies a target value that is ignored and does not contribute to the metric calculation

• validate_args (bool) – bool indicating if input arguments and tensors should be validated for correctness. Set to False for faster computations.

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

Example

>>> from torch import tensor
>>> from torchmetrics.classification import MulticlassROC
>>> preds = tensor([[0.75, 0.05, 0.05, 0.05, 0.05],
...                 [0.05, 0.75, 0.05, 0.05, 0.05],
...                 [0.05, 0.05, 0.75, 0.05, 0.05],
...                 [0.05, 0.05, 0.05, 0.75, 0.05]])
>>> target = tensor([0, 1, 3, 2])
>>> metric = MulticlassROC(num_classes=5, thresholds=None)
>>> fpr, tpr, thresholds = metric(preds, target)
>>> fpr
[tensor([0., 0., 1.]), tensor([0., 0., 1.]), tensor([0.0000, 0.3333, 1.0000]),
tensor([0.0000, 0.3333, 1.0000]), tensor([0., 1.])]
>>> tpr
[tensor([0., 1., 1.]), tensor([0., 1., 1.]), tensor([0., 0., 1.]), tensor([0., 0., 1.]), tensor([0., 0.])]
>>> thresholds
[tensor([1.0000, 0.7500, 0.0500]), tensor([1.0000, 0.7500, 0.0500]),
tensor([1.0000, 0.7500, 0.0500]), tensor([1.0000, 0.7500, 0.0500]), tensor([1.0000, 0.0500])]
>>> mcroc = MulticlassROC(num_classes=5, thresholds=5)
>>> mcroc(preds, target)
(tensor([[0.0000, 0.0000, 0.0000, 0.0000, 1.0000],
[0.0000, 0.0000, 0.0000, 0.0000, 1.0000],
[0.0000, 0.3333, 0.3333, 0.3333, 1.0000],
[0.0000, 0.3333, 0.3333, 0.3333, 1.0000],
[0.0000, 0.0000, 0.0000, 0.0000, 1.0000]]),
tensor([[0., 1., 1., 1., 1.],
[0., 1., 1., 1., 1.],
[0., 0., 0., 0., 1.],
[0., 0., 0., 0., 1.],
[0., 0., 0., 0., 0.]]),
tensor([1.0000, 0.7500, 0.5000, 0.2500, 0.0000]))

plot(curve=None, score=None, ax=None)[source]

Plot a single or multiple values from the metric.

Parameters:
Return type:
Returns:

Figure and Axes object

Raises:

ModuleNotFoundError – If matplotlib is not installed

>>> from torch import randn, randint
>>> from torchmetrics.classification import MulticlassROC
>>> preds = randn(20, 3).softmax(dim=-1)
>>> target = randint(3, (20,))
>>> metric = MulticlassROC(num_classes=3)
>>> metric.update(preds, target)
>>> fig_, ax_ = metric.plot(score=True)


### MultilabelROC¶

class torchmetrics.classification.MultilabelROC(num_labels, thresholds=None, ignore_index=None, validate_args=True, **kwargs)[source]

The curve consist of multiple pairs of true positive rate (TPR) and false positive rate (FPR) values evaluated at different thresholds, such that the tradeoff between the two values can be seen.

As input to forward and update the metric accepts the following input:

• preds (Tensor): A float tensor of shape (N, C, ...). Preds should be a tensor containing probabilities or logits for each observation. If preds has values outside [0,1] range we consider the input to be logits and will auto apply sigmoid per element.

• target (Tensor): An int tensor of shape (N, C, ...). Target should be a tensor containing ground truth labels, and therefore only contain {0,1} values (except if ignore_index is specified).

Note

Additional dimension ... will be flattened into the batch dimension.

As output to forward and compute the metric returns a tuple of either 3 tensors or 3 lists containing

• fpr (Tensor): if thresholds=None a list for each label is returned with an 1d tensor of size (n_thresholds+1, ) with false positive rate values (length may differ between labels). If thresholds is set to something else, then a single 2d tensor of size (n_labels, n_thresholds+1) with false positive rate values is returned.

• tpr (Tensor): if thresholds=None a list for each label is returned with an 1d tensor of size (n_thresholds+1, ) with true positive rate values (length may differ between labels). If thresholds is set to something else, then a single 2d tensor of size (n_labels, n_thresholds+1) with true positive rate values is returned.

• thresholds (Tensor): if thresholds=None a list for each label is returned with an 1d tensor of size (n_thresholds, ) with decreasing threshold values (length may differ between labels). If threshold is set to something else, then a single 1d tensor of size (n_thresholds, ) is returned with shared threshold values for all labels.

Note

The implementation both supports calculating the metric in a non-binned but accurate version and a binned version that is less accurate but more memory efficient. Setting the thresholds argument to None will activate the non-binned version that uses memory of size $$\mathcal{O}(n_{samples})$$ whereas setting the thresholds argument to either an integer, list or a 1d tensor will use a binned version that uses memory of size $$\mathcal{O}(n_{thresholds} \times n_{labels})$$ (constant memory).

Note

The outputted thresholds will be in reversed order to ensure that they corresponds to both fpr and tpr which are sorted in reversed order during their calculation, such that they are monotome increasing.

Parameters:
• num_labels (int) – Integer specifying the number of labels

• Can be one of:

• If set to None, will use a non-binned approach where thresholds are dynamically calculated from all the data. Most accurate but also most memory consuming approach.

• If set to an int (larger than 1), will use that number of thresholds linearly spaced from 0 to 1 as bins for the calculation.

• If set to an list of floats, will use the indicated thresholds in the list as bins for the calculation

• If set to an 1d tensor of floats, will use the indicated thresholds in the tensor as bins for the calculation.

• ignore_index (Optional[int]) – Specifies a target value that is ignored and does not contribute to the metric calculation

• validate_args (bool) – bool indicating if input arguments and tensors should be validated for correctness. Set to False for faster computations.

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

Example

>>> from torch import tensor
>>> from torchmetrics.classification import MultilabelROC
>>> preds = tensor([[0.75, 0.05, 0.35],
...                 [0.45, 0.75, 0.05],
...                 [0.05, 0.55, 0.75],
...                 [0.05, 0.65, 0.05]])
>>> target = tensor([[1, 0, 1],
...                  [0, 0, 0],
...                  [0, 1, 1],
...                  [1, 1, 1]])
>>> metric = MultilabelROC(num_labels=3, thresholds=None)
>>> fpr, tpr, thresholds = metric(preds, target)
>>> fpr
[tensor([0.0000, 0.0000, 0.5000, 1.0000]),
tensor([0.0000, 0.5000, 0.5000, 0.5000, 1.0000]),
tensor([0., 0., 0., 1.])]
>>> tpr
[tensor([0.0000, 0.5000, 0.5000, 1.0000]),
tensor([0.0000, 0.0000, 0.5000, 1.0000, 1.0000]),
tensor([0.0000, 0.3333, 0.6667, 1.0000])]
>>> thresholds
[tensor([1.0000, 0.7500, 0.4500, 0.0500]),
tensor([1.0000, 0.7500, 0.6500, 0.5500, 0.0500]),
tensor([1.0000, 0.7500, 0.3500, 0.0500])]
>>> mlroc = MultilabelROC(num_labels=3, thresholds=5)
>>> mlroc(preds, target)
(tensor([[0.0000, 0.0000, 0.0000, 0.5000, 1.0000],
[0.0000, 0.5000, 0.5000, 0.5000, 1.0000],
[0.0000, 0.0000, 0.0000, 0.0000, 1.0000]]),
tensor([[0.0000, 0.5000, 0.5000, 0.5000, 1.0000],
[0.0000, 0.0000, 1.0000, 1.0000, 1.0000],
[0.0000, 0.3333, 0.3333, 0.6667, 1.0000]]),
tensor([1.0000, 0.7500, 0.5000, 0.2500, 0.0000]))

plot(curve=None, score=None, ax=None)[source]

Plot a single or multiple values from the metric.

Parameters:
Return type:
Returns:

Figure and Axes object

Raises:

ModuleNotFoundError – If matplotlib is not installed

>>> from torch import rand, randint
>>> from torchmetrics.classification import MultilabelROC
>>> preds = rand(20, 3)
>>> target = randint(2, (20,3))
>>> metric = MultilabelROC(num_labels=3)
>>> metric.update(preds, target)
>>> fig_, ax_ = metric.plot(score=True)


## Functional Interface¶

torchmetrics.functional.roc(preds, target, task, thresholds=None, num_classes=None, num_labels=None, average=None, ignore_index=None, validate_args=True)[source]

Compute the Receiver Operating Characteristic (ROC).

The curve consist of multiple pairs of true positive rate (TPR) and false positive rate (FPR) values evaluated at different thresholds, such that the tradeoff between the two values can be seen.

This function is a simple wrapper to get the task specific versions of this metric, which is done by setting the task argument to either 'binary', 'multiclass' or multilabel. See the documentation of binary_roc(), multiclass_roc() and multilabel_roc() for the specific details of each argument influence and examples.

Return type:
Legacy Example:
>>> pred = torch.tensor([0.0, 1.0, 2.0, 3.0])
>>> target = torch.tensor([0, 1, 1, 1])
>>> fpr, tpr, thresholds = roc(pred, target, task='binary')
>>> fpr
tensor([0., 0., 0., 0., 1.])
>>> tpr
tensor([0.0000, 0.3333, 0.6667, 1.0000, 1.0000])
>>> thresholds
tensor([1.0000, 0.9526, 0.8808, 0.7311, 0.5000])

>>> pred = torch.tensor([[0.75, 0.05, 0.05, 0.05],
...                      [0.05, 0.75, 0.05, 0.05],
...                      [0.05, 0.05, 0.75, 0.05],
...                      [0.05, 0.05, 0.05, 0.75]])
>>> target = torch.tensor([0, 1, 3, 2])
>>> fpr, tpr, thresholds = roc(pred, target, task='multiclass', num_classes=4)
>>> fpr
[tensor([0., 0., 1.]), tensor([0., 0., 1.]), tensor([0.0000, 0.3333, 1.0000]), tensor([0.0000, 0.3333, 1.0000])]
>>> tpr
[tensor([0., 1., 1.]), tensor([0., 1., 1.]), tensor([0., 0., 1.]), tensor([0., 0., 1.])]
>>> thresholds
[tensor([1.0000, 0.7500, 0.0500]),
tensor([1.0000, 0.7500, 0.0500]),
tensor([1.0000, 0.7500, 0.0500]),
tensor([1.0000, 0.7500, 0.0500])]

>>> pred = torch.tensor([[0.8191, 0.3680, 0.1138],
...                      [0.3584, 0.7576, 0.1183],
...                      [0.2286, 0.3468, 0.1338],
...                      [0.8603, 0.0745, 0.1837]])
>>> target = torch.tensor([[1, 1, 0], [0, 1, 0], [0, 0, 0], [0, 1, 1]])
>>> fpr, tpr, thresholds = roc(pred, target, task='multilabel', num_labels=3)
>>> fpr
[tensor([0.0000, 0.3333, 0.3333, 0.6667, 1.0000]),
tensor([0., 0., 0., 1., 1.]),
tensor([0.0000, 0.0000, 0.3333, 0.6667, 1.0000])]
>>> tpr
[tensor([0., 0., 1., 1., 1.]), tensor([0.0000, 0.3333, 0.6667, 0.6667, 1.0000]), tensor([0., 1., 1., 1., 1.])]
>>> thresholds
[tensor([1.0000, 0.8603, 0.8191, 0.3584, 0.2286]),
tensor([1.0000, 0.7576, 0.3680, 0.3468, 0.0745]),
tensor([1.0000, 0.1837, 0.1338, 0.1183, 0.1138])]


### binary_roc¶

torchmetrics.functional.classification.binary_roc(preds, target, thresholds=None, ignore_index=None, validate_args=True)[source]

The curve consist of multiple pairs of true positive rate (TPR) and false positive rate (FPR) values evaluated at different thresholds, such that the tradeoff between the two values can be seen.

Accepts the following input tensors:

• preds (float tensor): (N, ...). Preds should be a tensor containing probabilities or logits for each observation. If preds has values outside [0,1] range we consider the input to be logits and will auto apply sigmoid per element.

• target (int tensor): (N, ...). Target should be a tensor containing ground truth labels, and therefore only contain {0,1} values (except if ignore_index is specified). The value 1 always encodes the positive class.

Additional dimension ... will be flattened into the batch dimension.

The implementation both supports calculating the metric in a non-binned but accurate version and a binned version that is less accurate but more memory efficient. Setting the thresholds argument to None will activate the non-binned version that uses memory of size $$\mathcal{O}(n_{samples})$$ whereas setting the thresholds argument to either an integer, list or a 1d tensor will use a binned version that uses memory of size $$\mathcal{O}(n_{thresholds})$$ (constant memory).

Note that outputted thresholds will be in reversed order to ensure that they corresponds to both fpr and tpr which are sorted in reversed order during their calculation, such that they are monotome increasing.

Parameters:
• preds (Tensor) – Tensor with predictions

• target (Tensor) – Tensor with true labels

• Can be one of:

• If set to None, will use a non-binned approach where thresholds are dynamically calculated from all the data. Most accurate but also most memory consuming approach.

• If set to an int (larger than 1), will use that number of thresholds linearly spaced from 0 to 1 as bins for the calculation.

• If set to an list of floats, will use the indicated thresholds in the list as bins for the calculation

• If set to an 1d tensor of floats, will use the indicated thresholds in the tensor as bins for the calculation.

• ignore_index (Optional[int]) – Specifies a target value that is ignored and does not contribute to the metric calculation

• validate_args (bool) – bool indicating if input arguments and tensors should be validated for correctness. Set to False for faster computations.

Returns:

a tuple of 3 tensors containing:

• fpr: an 1d tensor of size (n_thresholds+1, ) with false positive rate values

• tpr: an 1d tensor of size (n_thresholds+1, ) with true positive rate values

• thresholds: an 1d tensor of size (n_thresholds, ) with decreasing threshold values

Return type:

(tuple)

Example

>>> from torchmetrics.functional.classification import binary_roc
>>> preds = torch.tensor([0, 0.5, 0.7, 0.8])
>>> target = torch.tensor([0, 1, 1, 0])
>>> binary_roc(preds, target, thresholds=None)
(tensor([0.0000, 0.5000, 0.5000, 0.5000, 1.0000]),
tensor([0.0000, 0.0000, 0.5000, 1.0000, 1.0000]),
tensor([1.0000, 0.8000, 0.7000, 0.5000, 0.0000]))
>>> binary_roc(preds, target, thresholds=5)
(tensor([0.0000, 0.5000, 0.5000, 0.5000, 1.0000]),
tensor([0., 0., 1., 1., 1.]),
tensor([1.0000, 0.7500, 0.5000, 0.2500, 0.0000]))


### multiclass_roc¶

torchmetrics.functional.classification.multiclass_roc(preds, target, num_classes, thresholds=None, average=None, ignore_index=None, validate_args=True)[source]

The curve consist of multiple pairs of true positive rate (TPR) and false positive rate (FPR) values evaluated at different thresholds, such that the tradeoff between the two values can be seen.

Accepts the following input tensors:

• preds (float tensor): (N, C, ...). Preds should be a tensor containing probabilities or logits for each observation. If preds has values outside [0,1] range we consider the input to be logits and will auto apply softmax per sample.

• target (int tensor): (N, ...). Target should be a tensor containing ground truth labels, and therefore only contain values in the [0, n_classes-1] range (except if ignore_index is specified).

Additional dimension ... will be flattened into the batch dimension.

The implementation both supports calculating the metric in a non-binned but accurate version and a binned version that is less accurate but more memory efficient. Setting the thresholds argument to None will activate the non-binned version that uses memory of size $$\mathcal{O}(n_{samples})$$ whereas setting the thresholds argument to either an integer, list or a 1d tensor will use a binned version that uses memory of size $$\mathcal{O}(n_{thresholds} \times n_{classes})$$ (constant memory).

Note that outputted thresholds will be in reversed order to ensure that they corresponds to both fpr and tpr which are sorted in reversed order during their calculation, such that they are monotome increasing.

Parameters:
• preds (Tensor) – Tensor with predictions

• target (Tensor) – Tensor with true labels

• num_classes (int) – Integer specifying the number of classes

• Can be one of:

• If set to None, will use a non-binned approach where thresholds are dynamically calculated from all the data. Most accurate but also most memory consuming approach.

• If set to an int (larger than 1), will use that number of thresholds linearly spaced from 0 to 1 as bins for the calculation.

• If set to an list of floats, will use the indicated thresholds in the list as bins for the calculation

• If set to an 1d tensor of floats, will use the indicated thresholds in the tensor as bins for the calculation.

• average (Optional[Literal['micro', 'macro']]) – If aggregation of curves should be applied. By default, the curves are not aggregated and a curve for each class is returned. If average is set to "micro", the metric will aggregate the curves by one hot encoding the targets and flattening the predictions, considering all classes jointly as a binary problem. If average is set to "macro", the metric will aggregate the curves by first interpolating the curves from each class at a combined set of thresholds and then average over the classwise interpolated curves. See averaging curve objects for more info on the different averaging methods.

• ignore_index (Optional[int]) – Specifies a target value that is ignored and does not contribute to the metric calculation

• validate_args (bool) – bool indicating if input arguments and tensors should be validated for correctness. Set to False for faster computations.

Returns:

a tuple of either 3 tensors or 3 lists containing

• fpr: if thresholds=None a list for each class is returned with an 1d tensor of size (n_thresholds+1, ) with false positive rate values (length may differ between classes). If thresholds is set to something else, then a single 2d tensor of size (n_classes, n_thresholds+1) with false positive rate values is returned.

• tpr: if thresholds=None a list for each class is returned with an 1d tensor of size (n_thresholds+1, ) with true positive rate values (length may differ between classes). If thresholds is set to something else, then a single 2d tensor of size (n_classes, n_thresholds+1) with true positive rate values is returned.

• thresholds: if thresholds=None a list for each class is returned with an 1d tensor of size (n_thresholds, ) with decreasing threshold values (length may differ between classes). If threshold is set to something else, then a single 1d tensor of size (n_thresholds, ) is returned with shared threshold values for all classes.

Return type:

(tuple)

Example

>>> from torchmetrics.functional.classification import multiclass_roc
>>> preds = torch.tensor([[0.75, 0.05, 0.05, 0.05, 0.05],
...                       [0.05, 0.75, 0.05, 0.05, 0.05],
...                       [0.05, 0.05, 0.75, 0.05, 0.05],
...                       [0.05, 0.05, 0.05, 0.75, 0.05]])
>>> target = torch.tensor([0, 1, 3, 2])
>>> fpr, tpr, thresholds = multiclass_roc(
...    preds, target, num_classes=5, thresholds=None
... )
>>> fpr
[tensor([0., 0., 1.]), tensor([0., 0., 1.]), tensor([0.0000, 0.3333, 1.0000]),
tensor([0.0000, 0.3333, 1.0000]), tensor([0., 1.])]
>>> tpr
[tensor([0., 1., 1.]), tensor([0., 1., 1.]), tensor([0., 0., 1.]), tensor([0., 0., 1.]), tensor([0., 0.])]
>>> thresholds
[tensor([1.0000, 0.7500, 0.0500]), tensor([1.0000, 0.7500, 0.0500]),
tensor([1.0000, 0.7500, 0.0500]), tensor([1.0000, 0.7500, 0.0500]), tensor([1.0000, 0.0500])]
>>> multiclass_roc(
...     preds, target, num_classes=5, thresholds=5
... )
(tensor([[0.0000, 0.0000, 0.0000, 0.0000, 1.0000],
[0.0000, 0.0000, 0.0000, 0.0000, 1.0000],
[0.0000, 0.3333, 0.3333, 0.3333, 1.0000],
[0.0000, 0.3333, 0.3333, 0.3333, 1.0000],
[0.0000, 0.0000, 0.0000, 0.0000, 1.0000]]),
tensor([[0., 1., 1., 1., 1.],
[0., 1., 1., 1., 1.],
[0., 0., 0., 0., 1.],
[0., 0., 0., 0., 1.],
[0., 0., 0., 0., 0.]]),
tensor([1.0000, 0.7500, 0.5000, 0.2500, 0.0000]))


### multilabel_roc¶

torchmetrics.functional.classification.multilabel_roc(preds, target, num_labels, thresholds=None, ignore_index=None, validate_args=True)[source]

The curve consist of multiple pairs of true positive rate (TPR) and false positive rate (FPR) values evaluated at different thresholds, such that the tradeoff between the two values can be seen.

Accepts the following input tensors:

• preds (float tensor): (N, C, ...). Preds should be a tensor containing probabilities or logits for each observation. If preds has values outside [0,1] range we consider the input to be logits and will auto apply sigmoid per element.

• target (int tensor): (N, C, ...). Target should be a tensor containing ground truth labels, and therefore only contain {0,1} values (except if ignore_index is specified).

Additional dimension ... will be flattened into the batch dimension.

The implementation both supports calculating the metric in a non-binned but accurate version and a binned version that is less accurate but more memory efficient. Setting the thresholds argument to None will activate the non-binned version that uses memory of size $$\mathcal{O}(n_{samples})$$ whereas setting the thresholds argument to either an integer, list or a 1d tensor will use a binned version that uses memory of size $$\mathcal{O}(n_{thresholds} \times n_{labels})$$ (constant memory).

Note that outputted thresholds will be in reversed order to ensure that they corresponds to both fpr and tpr which are sorted in reversed order during their calculation, such that they are monotome increasing.

Parameters:
• preds (Tensor) – Tensor with predictions

• target (Tensor) – Tensor with true labels

• num_labels (int) – Integer specifying the number of labels

• Can be one of:

• If set to None, will use a non-binned approach where thresholds are dynamically calculated from all the data. Most accurate but also most memory consuming approach.

• If set to an int (larger than 1), will use that number of thresholds linearly spaced from 0 to 1 as bins for the calculation.

• If set to an list of floats, will use the indicated thresholds in the list as bins for the calculation

• If set to an 1d tensor of floats, will use the indicated thresholds in the tensor as bins for the calculation.

• ignore_index (Optional[int]) – Specifies a target value that is ignored and does not contribute to the metric calculation

• validate_args (bool) – bool indicating if input arguments and tensors should be validated for correctness. Set to False for faster computations.

Returns:

a tuple of either 3 tensors or 3 lists containing

• fpr: if thresholds=None a list for each label is returned with an 1d tensor of size (n_thresholds+1, ) with false positive rate values (length may differ between labels). If thresholds is set to something else, then a single 2d tensor of size (n_labels, n_thresholds+1) with false positive rate values is returned.

• tpr: if thresholds=None a list for each label is returned with an 1d tensor of size (n_thresholds+1, ) with true positive rate values (length may differ between labels). If thresholds is set to something else, then a single 2d tensor of size (n_labels, n_thresholds+1) with true positive rate values is returned.

• thresholds: if thresholds=None a list for each label is returned with an 1d tensor of size (n_thresholds, ) with decreasing threshold values (length may differ between labels). If threshold is set to something else, then a single 1d tensor of size (n_thresholds, ) is returned with shared threshold values for all labels.

Return type:

(tuple)

Example

>>> from torchmetrics.functional.classification import multilabel_roc
>>> preds = torch.tensor([[0.75, 0.05, 0.35],
...                       [0.45, 0.75, 0.05],
...                       [0.05, 0.55, 0.75],
...                       [0.05, 0.65, 0.05]])
>>> target = torch.tensor([[1, 0, 1],
...                        [0, 0, 0],
...                        [0, 1, 1],
...                        [1, 1, 1]])
>>> fpr, tpr, thresholds = multilabel_roc(
...    preds, target, num_labels=3, thresholds=None
... )
>>> fpr
[tensor([0.0000, 0.0000, 0.5000, 1.0000]),
tensor([0.0000, 0.5000, 0.5000, 0.5000, 1.0000]),
tensor([0., 0., 0., 1.])]
>>> tpr
[tensor([0.0000, 0.5000, 0.5000, 1.0000]),
tensor([0.0000, 0.0000, 0.5000, 1.0000, 1.0000]),
tensor([0.0000, 0.3333, 0.6667, 1.0000])]
>>> thresholds
[tensor([1.0000, 0.7500, 0.4500, 0.0500]),
tensor([1.0000, 0.7500, 0.6500, 0.5500, 0.0500]),
tensor([1.0000, 0.7500, 0.3500, 0.0500])]
>>> multilabel_roc(
...     preds, target, num_labels=3, thresholds=5
... )
(tensor([[0.0000, 0.0000, 0.0000, 0.5000, 1.0000],
[0.0000, 0.5000, 0.5000, 0.5000, 1.0000],
[0.0000, 0.0000, 0.0000, 0.0000, 1.0000]]),
tensor([[0.0000, 0.5000, 0.5000, 0.5000, 1.0000],
[0.0000, 0.0000, 1.0000, 1.0000, 1.0000],
[0.0000, 0.3333, 0.3333, 0.6667, 1.0000]]),
tensor([1.0000, 0.7500, 0.5000, 0.2500, 0.0000]))