---
title: ROC
description: Compute the Receiver Operating Characteristic (ROC).
canonical: 'https://lightning.ai/docs/torchmetrics/stable/classification/roc'
---
# ROC {#roc}

## Module Interface {#module-interface}

### `class torchmetrics.ROC(**kwargs)` {#torchmetrics.ROC}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/classification/roc.py#L508-L596)

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`](#torchmetrics.classification.BinaryROC "torchmetrics.classification.BinaryROC"), [`MulticlassROC`](#torchmetrics.classification.MulticlassROC "torchmetrics.classification.MulticlassROC") and [`MultilabelROC`](#torchmetrics.classification.MultilabelROC "torchmetrics.classification.MultilabelROC") for the specific details of each argument influence and examples.

Legacy Example:

```python
>>> from torch import tensor
>>> pred = tensor([0.0, 1.0, 2.0, 3.0])
>>> target = tensor([0, 1, 1, 1])
>>> roc = ROC(task="binary")
>>> 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])
```

```python
>>> 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])
>>> roc = ROC(task="multiclass", num_classes=4)
>>> 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])]
```

```python
>>> 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]])
>>> roc = ROC(task='multilabel', num_labels=3)
>>> 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)` {#torchmetrics.ROC.__new__}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/classification/roc.py#L573-L596)

Initialize task metric.

Return type:

[`Metric`](/docs/torchmetrics/1.9.0/api-reference/metric.md#torchmetrics.Metric "torchmetrics.metric.Metric")

### BinaryROC {#binaryroc}

### `class torchmetrics.classification.BinaryROC(thresholds=None, ignore_index=None, validate_args=True, normalization='sigmoid', **kwargs)` {#torchmetrics.classification.BinaryROC}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/classification/roc.py#L42-L172)

Compute the Receiver Operating Characteristic (ROC) for binary tasks.

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`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): 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`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): 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.
    

Tip

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`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): A 1d tensor of size `(n_thresholds+1, )` with false positive rate values
    
*   `tpr` ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): A 1d tensor of size `(n_thresholds+1, )` with true positive rate values
    
*   `thresholds` ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): 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).

Attention

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

Parameters:

*   **thresholds** (`Union`\[[`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)"), [`list`](https://docs.python.org/3/builtins/stdtypes.html#list "(in Python v3.15)")\[[`float`](https://docs.python.org/3/builtins/functions.html#float "(in Python v3.15)")\], [`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)"), [`None`](https://docs.python.org/3/builtins/constants.html#None "(in Python v3.15)")\]) –
    
    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`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.15)")\[[`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)")\]) – Specifies a target value that is ignored and does not contribute to the metric calculation
    
*   **validate\_args** ([`bool`](https://docs.python.org/3/builtins/functions.html#bool "(in Python v3.15)")) – bool indicating if input arguments and tensors should be validated for correctness. Set to `False` for faster computations.
    
*   **kwargs** ([`Any`](https://docs.python.org/3/library/typing.html#typing.Any "(in Python v3.15)")) – Additional keyword arguments, see [Advanced metric settings](/docs/torchmetrics/1.9.0/user-guide/overview.md#metric-kwargs) for more info.
    

Example

```python
>>> 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)` {#torchmetrics.classification.BinaryROC.plot}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/classification/roc.py#L125-L172)

Plot a single or multiple values from the metric.

Parameters:

*   **curve** ([`Optional`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.15)")\[[`tuple`](https://docs.python.org/3/builtins/stdtypes.html#tuple "(in Python v3.15)")\[[`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)"), [`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)"), [`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")\]\]) – the output of either metric.compute or metric.forward. If no value is provided, will automatically call metric.compute and plot that result.
    
*   **score** (`Union`\[[`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)"), [`bool`](https://docs.python.org/3/builtins/functions.html#bool "(in Python v3.15)"), [`None`](https://docs.python.org/3/builtins/constants.html#None "(in Python v3.15)")\]) – Provide a area-under-the-curve score to be displayed on the plot. If True and no curve is provided, will automatically compute the score. The score is computed by using the trapezoidal rule to compute the area under the curve.
    
*   **ax** ([`Optional`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.15)")\[[`Axes`](https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.html#matplotlib.axes.Axes "(in Matplotlib v3.11.2)")\]) – An matplotlib axis object. If provided will add plot to that axis
    

Return type:

[`tuple`](https://docs.python.org/3/builtins/stdtypes.html#tuple "(in Python v3.15)")\[[`Figure`](https://matplotlib.org/stable/api/_as_gen/matplotlib.figure.Figure.html#matplotlib.figure.Figure "(in Matplotlib v3.11.2)"), `Union`\[[`Axes`](https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.html#matplotlib.axes.Axes "(in Matplotlib v3.11.2)"), [`ndarray`](https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray "(in NumPy v2.5)")\]\]

Returns:

Figure and Axes object

Raises:

[**ModuleNotFoundError**](https://docs.python.org/3/builtins/exceptions.html#ModuleNotFoundError "(in Python v3.15)") – If matplotlib is not installed

```python
>>> 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)
```

[![../../\_images/roc-1.png](/docs/torchmetrics/1.9.0/static/_images/roc-1.png)](/docs/torchmetrics/1.9.0/static/_images/roc-1.png)

### MulticlassROC {#multiclassroc}

### `class torchmetrics.classification.MulticlassROC(num_classes, thresholds=None, average=None, ignore_index=None, validate_args=True, **kwargs)` {#torchmetrics.classification.MulticlassROC}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/classification/roc.py#L175-L343)

Compute the Receiver Operating Characteristic (ROC) for binary tasks.

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`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): 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`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): 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).
    

Tip

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`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): 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`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): 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`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): 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).

Attention

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

Parameters:

*   **num\_classes** ([`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)")) – Integer specifying the number of classes
    
*   **thresholds** (`Union`\[[`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)"), [`list`](https://docs.python.org/3/builtins/stdtypes.html#list "(in Python v3.15)")\[[`float`](https://docs.python.org/3/builtins/functions.html#float "(in Python v3.15)")\], [`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)"), [`None`](https://docs.python.org/3/builtins/constants.html#None "(in Python v3.15)")\]) –
    
    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`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.15)")\[[`Literal`](https://docs.python.org/3/library/typing.html#typing.Literal "(in Python v3.15)")\[`'micro'`, `'macro'`\]\]) – 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](https://scikit-learn.org/stable/auto_examples/model_selection/plot_roc.html) for more info on the different averaging methods.
    
*   **ignore\_index** ([`Optional`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.15)")\[[`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)")\]) – Specifies a target value that is ignored and does not contribute to the metric calculation
    
*   **validate\_args** ([`bool`](https://docs.python.org/3/builtins/functions.html#bool "(in Python v3.15)")) – bool indicating if input arguments and tensors should be validated for correctness. Set to `False` for faster computations.
    
*   **kwargs** ([`Any`](https://docs.python.org/3/library/typing.html#typing.Any "(in Python v3.15)")) – Additional keyword arguments, see [Advanced metric settings](/docs/torchmetrics/1.9.0/user-guide/overview.md#metric-kwargs) for more info.
    

Example

```python
>>> 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, labels=None)` {#torchmetrics.classification.MulticlassROC.plot}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/classification/roc.py#L295-L343)

Plot a single or multiple values from the metric.

Parameters:

*   **curve** (`Union`\[[`tuple`](https://docs.python.org/3/builtins/stdtypes.html#tuple "(in Python v3.15)")\[[`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)"), [`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)"), [`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")\], [`tuple`](https://docs.python.org/3/builtins/stdtypes.html#tuple "(in Python v3.15)")\[[`List`](https://docs.python.org/3/library/typing.html#typing.List "(in Python v3.15)")\[[`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")\], [`List`](https://docs.python.org/3/library/typing.html#typing.List "(in Python v3.15)")\[[`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")\], [`List`](https://docs.python.org/3/library/typing.html#typing.List "(in Python v3.15)")\[[`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")\]\], [`None`](https://docs.python.org/3/builtins/constants.html#None "(in Python v3.15)")\]) – the output of either metric.compute or metric.forward. If no value is provided, will automatically call metric.compute and plot that result.
    
*   **score** (`Union`\[[`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)"), [`bool`](https://docs.python.org/3/builtins/functions.html#bool "(in Python v3.15)"), [`None`](https://docs.python.org/3/builtins/constants.html#None "(in Python v3.15)")\]) – Provide a area-under-the-curve score to be displayed on the plot. If True and no curve is provided, will automatically compute the score. The score is computed by using the trapezoidal rule to compute the area under the curve.
    
*   **ax** ([`Optional`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.15)")\[[`Axes`](https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.html#matplotlib.axes.Axes "(in Matplotlib v3.11.2)")\]) – An matplotlib axis object. If provided will add plot to that axis
    
*   **labels** ([`Optional`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.15)")\[[`list`](https://docs.python.org/3/builtins/stdtypes.html#list "(in Python v3.15)")\[[`str`](https://docs.python.org/3/builtins/stdtypes.html#str "(in Python v3.15)")\]\]) – a list of strings, if provided will be added to the plot to indicate the different classes
    

Return type:

[`tuple`](https://docs.python.org/3/builtins/stdtypes.html#tuple "(in Python v3.15)")\[[`Figure`](https://matplotlib.org/stable/api/_as_gen/matplotlib.figure.Figure.html#matplotlib.figure.Figure "(in Matplotlib v3.11.2)"), `Union`\[[`Axes`](https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.html#matplotlib.axes.Axes "(in Matplotlib v3.11.2)"), [`ndarray`](https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray "(in NumPy v2.5)")\]\]

Returns:

Figure and Axes object

Raises:

[**ModuleNotFoundError**](https://docs.python.org/3/builtins/exceptions.html#ModuleNotFoundError "(in Python v3.15)") – If matplotlib is not installed

```python
>>> 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)
```

[![../../\_images/roc-2.png](/docs/torchmetrics/1.9.0/static/_images/roc-2.png)](/docs/torchmetrics/1.9.0/static/_images/roc-2.png)

### MultilabelROC {#multilabelroc}

### `class torchmetrics.classification.MultilabelROC(num_labels, thresholds=None, ignore_index=None, validate_args=True, **kwargs)` {#torchmetrics.classification.MultilabelROC}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/classification/roc.py#L346-L505)

Compute the Receiver Operating Characteristic (ROC) for binary tasks.

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`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): 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`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): 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).
    

Tip

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`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): 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`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): 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`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")): 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).

Attention

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

Parameters:

*   **num\_labels** ([`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)")) – Integer specifying the number of labels
    
*   **thresholds** (`Union`\[[`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)"), [`list`](https://docs.python.org/3/builtins/stdtypes.html#list "(in Python v3.15)")\[[`float`](https://docs.python.org/3/builtins/functions.html#float "(in Python v3.15)")\], [`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)"), [`None`](https://docs.python.org/3/builtins/constants.html#None "(in Python v3.15)")\]) –
    
    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`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.15)")\[[`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)")\]) – Specifies a target value that is ignored and does not contribute to the metric calculation
    
*   **validate\_args** ([`bool`](https://docs.python.org/3/builtins/functions.html#bool "(in Python v3.15)")) – bool indicating if input arguments and tensors should be validated for correctness. Set to `False` for faster computations.
    
*   **kwargs** ([`Any`](https://docs.python.org/3/library/typing.html#typing.Any "(in Python v3.15)")) – Additional keyword arguments, see [Advanced metric settings](/docs/torchmetrics/1.9.0/user-guide/overview.md#metric-kwargs) for more info.
    

Example

```python
>>> 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, labels=None)` {#torchmetrics.classification.MultilabelROC.plot}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/classification/roc.py#L457-L505)

Plot a single or multiple values from the metric.

Parameters:

*   **curve** (`Union`\[[`tuple`](https://docs.python.org/3/builtins/stdtypes.html#tuple "(in Python v3.15)")\[[`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)"), [`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)"), [`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")\], [`tuple`](https://docs.python.org/3/builtins/stdtypes.html#tuple "(in Python v3.15)")\[[`List`](https://docs.python.org/3/library/typing.html#typing.List "(in Python v3.15)")\[[`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")\], [`List`](https://docs.python.org/3/library/typing.html#typing.List "(in Python v3.15)")\[[`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")\], [`List`](https://docs.python.org/3/library/typing.html#typing.List "(in Python v3.15)")\[[`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")\]\], [`None`](https://docs.python.org/3/builtins/constants.html#None "(in Python v3.15)")\]) – the output of either metric.compute or metric.forward. If no value is provided, will automatically call metric.compute and plot that result.
    
*   **score** (`Union`\[[`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)"), [`bool`](https://docs.python.org/3/builtins/functions.html#bool "(in Python v3.15)"), [`None`](https://docs.python.org/3/builtins/constants.html#None "(in Python v3.15)")\]) – Provide a area-under-the-curve score to be displayed on the plot. If True and no curve is provided, will automatically compute the score. The score is computed by using the trapezoidal rule to compute the area under the curve.
    
*   **ax** ([`Optional`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.15)")\[[`Axes`](https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.html#matplotlib.axes.Axes "(in Matplotlib v3.11.2)")\]) – An matplotlib axis object. If provided will add plot to that axis
    
*   **labels** ([`Optional`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.15)")\[[`list`](https://docs.python.org/3/builtins/stdtypes.html#list "(in Python v3.15)")\[[`str`](https://docs.python.org/3/builtins/stdtypes.html#str "(in Python v3.15)")\]\]) – a list of strings, if provided will be added to the plot to indicate the different classes
    

Return type:

[`tuple`](https://docs.python.org/3/builtins/stdtypes.html#tuple "(in Python v3.15)")\[[`Figure`](https://matplotlib.org/stable/api/_as_gen/matplotlib.figure.Figure.html#matplotlib.figure.Figure "(in Matplotlib v3.11.2)"), `Union`\[[`Axes`](https://matplotlib.org/stable/api/_as_gen/matplotlib.axes.Axes.html#matplotlib.axes.Axes "(in Matplotlib v3.11.2)"), [`ndarray`](https://numpy.org/doc/stable/reference/generated/numpy.ndarray.html#numpy.ndarray "(in NumPy v2.5)")\]\]

Returns:

Figure and Axes object

Raises:

[**ModuleNotFoundError**](https://docs.python.org/3/builtins/exceptions.html#ModuleNotFoundError "(in Python v3.15)") – If matplotlib is not installed

```python
>>> 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)
```

[![../../\_images/roc-3.png](/docs/torchmetrics/1.9.0/static/_images/roc-3.png)](/docs/torchmetrics/1.9.0/static/_images/roc-3.png)

## Functional Interface {#functional-interface}

### `torchmetrics.functional.roc(preds, target, task, thresholds=None, num_classes=None, num_labels=None, average=None, ignore_index=None, validate_args=True)` {#torchmetrics.functional.roc}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/functional/classification/roc.py#L471-L550)

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()`](#torchmetrics.functional.classification.binary_roc "torchmetrics.functional.classification.binary_roc"), [`multiclass_roc()`](#torchmetrics.functional.classification.multiclass_roc "torchmetrics.functional.classification.multiclass_roc") and [`multilabel_roc()`](#torchmetrics.functional.classification.multilabel_roc "torchmetrics.functional.classification.multilabel_roc") for the specific details of each argument influence and examples.

Return type:

`Union`\[[`tuple`](https://docs.python.org/3/builtins/stdtypes.html#tuple "(in Python v3.15)")\[[`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)"), [`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)"), [`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")\], [`tuple`](https://docs.python.org/3/builtins/stdtypes.html#tuple "(in Python v3.15)")\[[`List`](https://docs.python.org/3/library/typing.html#typing.List "(in Python v3.15)")\[[`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")\], [`List`](https://docs.python.org/3/library/typing.html#typing.List "(in Python v3.15)")\[[`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")\], [`List`](https://docs.python.org/3/library/typing.html#typing.List "(in Python v3.15)")\[[`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")\]\]\]

Legacy Example:

```python
>>> 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])
```

```python
>>> 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])]
```

```python
>>> 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 {#binary-roc}

### `torchmetrics.functional.classification.binary_roc(preds, target, thresholds=None, ignore_index=None, validate_args=True)` {#torchmetrics.functional.classification.binary_roc}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/functional/classification/roc.py#L83-L159)

Compute the Receiver Operating Characteristic (ROC) for binary tasks.

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`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")) – Tensor with predictions
    
*   **target** ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")) – Tensor with true labels
    
*   **thresholds** (`Union`\[[`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)"), [`list`](https://docs.python.org/3/builtins/stdtypes.html#list "(in Python v3.15)")\[[`float`](https://docs.python.org/3/builtins/functions.html#float "(in Python v3.15)")\], [`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)"), [`None`](https://docs.python.org/3/builtins/constants.html#None "(in Python v3.15)")\]) –
    
    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`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.15)")\[[`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)")\]) – Specifies a target value that is ignored and does not contribute to the metric calculation
    
*   **validate\_args** ([`bool`](https://docs.python.org/3/builtins/functions.html#bool "(in Python v3.15)")) – 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](https://docs.python.org/3/builtins/stdtypes.html#tuple "(in Python v3.15)"))

Example

```python
>>> 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 {#multiclass-roc}

### `torchmetrics.functional.classification.multiclass_roc(preds, target, num_classes, thresholds=None, average=None, ignore_index=None, validate_args=True)` {#torchmetrics.functional.classification.multiclass_roc}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/functional/classification/roc.py#L207-L326)

Compute the Receiver Operating Characteristic (ROC) for multiclass tasks.

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`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")) – Tensor with predictions
    
*   **target** ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")) – Tensor with true labels
    
*   **num\_classes** ([`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)")) – Integer specifying the number of classes
    
*   **thresholds** (`Union`\[[`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)"), [`list`](https://docs.python.org/3/builtins/stdtypes.html#list "(in Python v3.15)")\[[`float`](https://docs.python.org/3/builtins/functions.html#float "(in Python v3.15)")\], [`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)"), [`None`](https://docs.python.org/3/builtins/constants.html#None "(in Python v3.15)")\]) –
    
    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`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.15)")\[[`Literal`](https://docs.python.org/3/library/typing.html#typing.Literal "(in Python v3.15)")\[`'micro'`, `'macro'`\]\]) – 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](https://scikit-learn.org/stable/auto_examples/model_selection/plot_roc.html) for more info on the different averaging methods.
    
*   **ignore\_index** ([`Optional`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.15)")\[[`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)")\]) – Specifies a target value that is ignored and does not contribute to the metric calculation
    
*   **validate\_args** ([`bool`](https://docs.python.org/3/builtins/functions.html#bool "(in Python v3.15)")) – 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](https://docs.python.org/3/builtins/stdtypes.html#tuple "(in Python v3.15)"))

Example

```python
>>> 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 {#multilabel-roc}

### `torchmetrics.functional.classification.multilabel_roc(preds, target, num_labels, thresholds=None, ignore_index=None, validate_args=True)` {#torchmetrics.functional.classification.multilabel_roc}

[\[source\]](https://github.com/Lightning-AI/torchmetrics/blob/v1.9.0/src/torchmetrics/functional/classification/roc.py#L359-L468)

Compute the Receiver Operating Characteristic (ROC) for multilabel tasks.

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`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")) – Tensor with predictions
    
*   **target** ([`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)")) – Tensor with true labels
    
*   **num\_labels** ([`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)")) – Integer specifying the number of labels
    
*   **thresholds** (`Union`\[[`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)"), [`list`](https://docs.python.org/3/builtins/stdtypes.html#list "(in Python v3.15)")\[[`float`](https://docs.python.org/3/builtins/functions.html#float "(in Python v3.15)")\], [`Tensor`](https://docs.pytorch.org/docs/stable/tensors.html#torch.Tensor "(in PyTorch v2.15)"), [`None`](https://docs.python.org/3/builtins/constants.html#None "(in Python v3.15)")\]) –
    
    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`](https://docs.python.org/3/library/typing.html#typing.Optional "(in Python v3.15)")\[[`int`](https://docs.python.org/3/builtins/functions.html#int "(in Python v3.15)")\]) – Specifies a target value that is ignored and does not contribute to the metric calculation
    
*   **validate\_args** ([`bool`](https://docs.python.org/3/builtins/functions.html#bool "(in Python v3.15)")) – 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](https://docs.python.org/3/builtins/stdtypes.html#tuple "(in Python v3.15)"))

Example

```python
>>> 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]))
```

---

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- Parent: [Classification](/docs/torchmetrics/1.9.0/classification.md)