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Calibration Error

Module Interface

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

Top-label Calibration Error.

The expected calibration error can be used to quantify how well a given model is calibrated e.g. how well the predicted output probabilities of the model matches the actual probabilities of the ground truth distribution. Three different norms are implemented, each corresponding to variations on the calibration error metric.

\[\text{ECE} = \sum_i^N b_i \|(p_i - c_i)\|, \text{L1 norm (Expected Calibration Error)}\]
\[\text{MCE} = \max_{i} (p_i - c_i), \text{Infinity norm (Maximum Calibration Error)}\]
\[\text{RMSCE} = \sqrt{\sum_i^N b_i(p_i - c_i)^2}, \text{L2 norm (Root Mean Square Calibration Error)}\]

Where \(p_i\) is the top-1 prediction accuracy in bin \(i\), \(c_i\) is the average confidence of predictions in bin \(i\), and \(b_i\) is the fraction of data points in bin \(i\). Bins are constructed in an uniform way in the [0,1] range.

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' or 'multiclass'. See the documentation of BinaryCalibrationError and MulticlassCalibrationError for the specific details of each argument influence and examples.

static __new__(cls, task, n_bins=15, norm='l1', num_classes=None, ignore_index=None, validate_args=True, **kwargs)[source]

Initialize task metric.

Return type:

Metric

BinaryCalibrationError

class torchmetrics.classification.BinaryCalibrationError(n_bins=15, norm='l1', ignore_index=None, validate_args=True, **kwargs)[source]

Top-label Calibration Error for binary tasks.

The expected calibration error can be used to quantify how well a given model is calibrated e.g. how well the predicted output probabilities of the model matches the actual probabilities of the ground truth distribution. Three different norms are implemented, each corresponding to variations on the calibration error metric.

\[\text{ECE} = \sum_i^N b_i \|(p_i - c_i)\|, \text{L1 norm (Expected Calibration Error)}\]
\[\text{MCE} = \max_{i} (p_i - c_i), \text{Infinity norm (Maximum Calibration Error)}\]
\[\text{RMSCE} = \sqrt{\sum_i^N b_i(p_i - c_i)^2}, \text{L2 norm (Root Mean Square Calibration Error)}\]

Where \(p_i\) is the top-1 prediction accuracy in bin \(i\), \(c_i\) is the average confidence of predictions in bin \(i\), and \(b_i\) is the fraction of data points in bin \(i\). Bins are constructed in an uniform way in the [0,1] range.

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

  • preds (Tensor): A float tensor of shape (N, ...) 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, ...) 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.

As output to forward and compute the metric returns the following output:

  • bce (Tensor): A scalar tensor containing the calibration error

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

Parameters:

  • n_bins (int) – Number of bins to use when computing the metric.

  • norm (Literal['l1', 'l2', 'max']) – Norm used to compare empirical and expected probability bins.

  • 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 BinaryCalibrationError
>>> preds = tensor([0.25, 0.25, 0.55, 0.75, 0.75])
>>> target = tensor([0, 0, 1, 1, 1])
>>> metric = BinaryCalibrationError(n_bins=2, norm='l1')
>>> metric(preds, target)
tensor(0.2900)
>>> bce = BinaryCalibrationError(n_bins=2, norm='l2')
>>> bce(preds, target)
tensor(0.2918)
>>> bce = BinaryCalibrationError(n_bins=2, norm='max')
>>> bce(preds, target)
tensor(0.3167)
plot(val=None, ax=None)[source]

Plot a single or multiple values from the metric.

Parameters:

  • val (Union[Tensor, Sequence[Tensor], None]) – Either a single result from calling metric.forward or metric.compute or a list of these results. If no value is provided, will automatically call metric.compute and plot that result.

  • ax (Optional[Axes]) – An matplotlib axis object. If provided will add plot to that axis

Return type:

tuple[Figure, Union[Axes, ndarray]]

Returns:

Figure object and Axes object

Raises:

ModuleNotFoundError – If matplotlib is not installed

>>> from torch import rand, randint
>>> # Example plotting a single value
>>> from torchmetrics.classification import BinaryCalibrationError
>>> metric = BinaryCalibrationError(n_bins=2, norm='l1')
>>> metric.update(rand(10), randint(2,(10,)))
>>> fig_, ax_ = metric.plot()
../_images/calibration_error-1.png 
>>> from torch import rand, randint
>>> # Example plotting multiple values
>>> from torchmetrics.classification import BinaryCalibrationError
>>> metric = BinaryCalibrationError(n_bins=2, norm='l1')
>>> values = [ ]
>>> for _ in range(10):
...     values.append(metric(rand(10), randint(2,(10,))))
>>> fig_, ax_ = metric.plot(values)
../_images/calibration_error-2.png

MulticlassCalibrationError

class torchmetrics.classification.MulticlassCalibrationError(num_classes, n_bins=15, norm='l1', ignore_index=None, validate_args=True, **kwargs)[source]

Top-label Calibration Error for multiclass tasks.

The expected calibration error can be used to quantify how well a given model is calibrated e.g. how well the predicted output probabilities of the model matches the actual probabilities of the ground truth distribution. Three different norms are implemented, each corresponding to variations on the calibration error metric.

\[\text{ECE} = \sum_i^N b_i \|(p_i - c_i)\|, \text{L1 norm (Expected Calibration Error)}\]
\[\text{MCE} = \max_{i} (p_i - c_i), \text{Infinity norm (Maximum Calibration Error)}\]
\[\text{RMSCE} = \sqrt{\sum_i^N b_i(p_i - c_i)^2}, \text{L2 norm (Root Mean Square Calibration Error)}\]

Where \(p_i\) is the top-1 prediction accuracy in bin \(i\), \(c_i\) is the average confidence of predictions in bin \(i\), and \(b_i\) is the fraction of data points in bin \(i\). Bins are constructed in an uniform way in the [0,1] range.

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

  • preds (Tensor): A float tensor of shape (N, C, ...) 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, ...) 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 the following output:

  • mcce (Tensor): A scalar tensor containing the calibration error

Parameters:

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

  • n_bins (int) – Number of bins to use when computing the metric.

  • norm (Literal['l1', 'l2', 'max']) – Norm used to compare empirical and expected probability bins.

  • 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 MulticlassCalibrationError
>>> preds = tensor([[0.25, 0.20, 0.55],
...                 [0.55, 0.05, 0.40],
...                 [0.10, 0.30, 0.60],
...                 [0.90, 0.05, 0.05]])
>>> target = tensor([0, 1, 2, 0])
>>> metric = MulticlassCalibrationError(num_classes=3, n_bins=3, norm='l1')
>>> metric(preds, target)
tensor(0.2000)
>>> mcce = MulticlassCalibrationError(num_classes=3, n_bins=3, norm='l2')
>>> mcce(preds, target)
tensor(0.2082)
>>> mcce = MulticlassCalibrationError(num_classes=3, n_bins=3, norm='max')
>>> mcce(preds, target)
tensor(0.2333)
plot(val=None, ax=None)[source]

Plot a single or multiple values from the metric.

Parameters:

  • val (Union[Tensor, Sequence[Tensor], None]) – Either a single result from calling metric.forward or metric.compute or a list of these results. If no value is provided, will automatically call metric.compute and plot that result.

  • ax (Optional[Axes]) – An matplotlib axis object. If provided will add plot to that axis

Return type:

tuple[Figure, Union[Axes, ndarray]]

Returns:

Figure object and Axes object

Raises:

ModuleNotFoundError – If matplotlib is not installed

>>> from torch import randn, randint
>>> # Example plotting a single value
>>> from torchmetrics.classification import MulticlassCalibrationError
>>> metric = MulticlassCalibrationError(num_classes=3, n_bins=3, norm='l1')
>>> metric.update(randn(20,3).softmax(dim=-1), randint(3, (20,)))
>>> fig_, ax_ = metric.plot()
../_images/calibration_error-3.png 
>>> from torch import randn, randint
>>> # Example plotting a multiple values
>>> from torchmetrics.classification import MulticlassCalibrationError
>>> metric = MulticlassCalibrationError(num_classes=3, n_bins=3, norm='l1')
>>> values = []
>>> for _ in range(20):
...     values.append(metric(randn(20,3).softmax(dim=-1), randint(3, (20,))))
>>> fig_, ax_ = metric.plot(values)
../_images/calibration_error-4.png

Functional Interface

torchmetrics.functional.calibration_error(preds, target, task, n_bins=15, norm='l1', num_classes=None, ignore_index=None, validate_args=True)[source]

Top-label Calibration Error.

The expected calibration error can be used to quantify how well a given model is calibrated e.g. how well the predicted output probabilities of the model matches the actual probabilities of the ground truth distribution. Three different norms are implemented, each corresponding to variations on the calibration error metric. :rtype: Tensor

\[\text{ECE} = \sum_i^N b_i \|(p_i - c_i)\|, \text{L1 norm (Expected Calibration Error)}\]
\[\text{MCE} = \max_{i} (p_i - c_i), \text{Infinity norm (Maximum Calibration Error)}\]
\[\text{RMSCE} = \sqrt{\sum_i^N b_i(p_i - c_i)^2}, \text{L2 norm (Root Mean Square Calibration Error)}\]

Where \(p_i\) is the top-1 prediction accuracy in bin \(i\), \(c_i\) is the average confidence of predictions in bin \(i\), and \(b_i\) is the fraction of data points in bin \(i\). Bins are constructed in an uniform way in the [0,1] range.

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' or 'multiclass'. See the documentation of binary_calibration_error() and multiclass_calibration_error() for the specific details of each argument influence and examples.

binary_calibration_error

torchmetrics.functional.classification.binary_calibration_error(preds, target, n_bins=15, norm='l1', ignore_index=None, validate_args=True)[source]

Top-label Calibration Error for binary tasks.

The expected calibration error can be used to quantify how well a given model is calibrated e.g. how well the predicted output probabilities of the model matches the actual probabilities of the ground truth distribution. Three different norms are implemented, each corresponding to variations on the calibration error metric.

\[\text{ECE} = \sum_i^N b_i \|(p_i - c_i)\|, \text{L1 norm (Expected Calibration Error)}\]
\[\text{MCE} = \max_{i} (p_i - c_i), \text{Infinity norm (Maximum Calibration Error)}\]
\[\text{RMSCE} = \sqrt{\sum_i^N b_i(p_i - c_i)^2}, \text{L2 norm (Root Mean Square Calibration Error)}\]

Where \(p_i\) is the top-1 prediction accuracy in bin \(i\), \(c_i\) is the average confidence of predictions in bin \(i\), and \(b_i\) is the fraction of data points in bin \(i\). Bins are constructed in an uniform way in the [0,1] range.

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.

Parameters:

  • preds (Tensor) – Tensor with predictions

  • target (Tensor) – Tensor with true labels

  • n_bins (int) – Number of bins to use when computing the metric.

  • norm (Literal['l1', 'l2', 'max']) – Norm used to compare empirical and expected probability bins.

  • 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.

Return type:

Tensor

Example

>>> from torchmetrics.functional.classification import binary_calibration_error
>>> preds = torch.tensor([0.25, 0.25, 0.55, 0.75, 0.75])
>>> target = torch.tensor([0, 0, 1, 1, 1])
>>> binary_calibration_error(preds, target, n_bins=2, norm='l1')
tensor(0.2900)
>>> binary_calibration_error(preds, target, n_bins=2, norm='l2')
tensor(0.2918)
>>> binary_calibration_error(preds, target, n_bins=2, norm='max')
tensor(0.3167)

multiclass_calibration_error

torchmetrics.functional.classification.multiclass_calibration_error(preds, target, num_classes, n_bins=15, norm='l1', ignore_index=None, validate_args=True)[source]

Top-label Calibration Error for multiclass tasks.

The expected calibration error can be used to quantify how well a given model is calibrated e.g. how well the predicted output probabilities of the model matches the actual probabilities of the ground truth distribution. Three different norms are implemented, each corresponding to variations on the calibration error metric.

\[\text{ECE} = \sum_i^N b_i \|(p_i - c_i)\|, \text{L1 norm (Expected Calibration Error)}\]
\[\text{MCE} = \max_{i} (p_i - c_i), \text{Infinity norm (Maximum Calibration Error)}\]
\[\text{RMSCE} = \sqrt{\sum_i^N b_i(p_i - c_i)^2}, \text{L2 norm (Root Mean Square Calibration Error)}\]

Where \(p_i\) is the top-1 prediction accuracy in bin \(i\), \(c_i\) is the average confidence of predictions in bin \(i\), and \(b_i\) is the fraction of data points in bin \(i\). Bins are constructed in an uniform way in the [0,1] range.

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.

Parameters:

  • preds (Tensor) – Tensor with predictions

  • target (Tensor) – Tensor with true labels

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

  • n_bins (int) – Number of bins to use when computing the metric.

  • norm (Literal['l1', 'l2', 'max']) – Norm used to compare empirical and expected probability bins.

  • 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.

Return type:

Tensor

Example

>>> from torchmetrics.functional.classification import multiclass_calibration_error
>>> preds = torch.tensor([[0.25, 0.20, 0.55],
...                       [0.55, 0.05, 0.40],
...                       [0.10, 0.30, 0.60],
...                       [0.90, 0.05, 0.05]])
>>> target = torch.tensor([0, 1, 2, 0])
>>> multiclass_calibration_error(preds, target, num_classes=3, n_bins=3, norm='l1')
tensor(0.2000)
>>> multiclass_calibration_error(preds, target, num_classes=3, n_bins=3, norm='l2')
tensor(0.2082)
>>> multiclass_calibration_error(preds, target, num_classes=3, n_bins=3, norm='max')
tensor(0.2333)

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