from typing import Literal
import torch
import torch.nn.functional as F
from torch import Tensor
from torchmetrics import Metric
from torchmetrics.utilities.data import dim_zero_cat
[docs]
class BrierScore(Metric):
is_differentiable = True
higher_is_better = False
full_state_update = False
def __init__(
self,
num_classes: int,
top_class: bool = False,
reduction: Literal["mean", "sum", "none", None] = "mean",
**kwargs,
) -> None:
r"""Compute the Brier score.
The Brier Score measures the mean squared difference between predicted
probabilities and actual target values. It is used to evaluate the
accuracy of probabilistic predictions, where a lower score indicates
better calibration and prediction quality.
Args:
num_classes (int): Number of classes.
top_class (bool, optional): If True, computes the Brier score for the
top predicted class only. Defaults to ``False``.
reduction (str, optional): Determines how to reduce the score across the
batch dimension:
- ``'mean'`` [default]: Averages the score across samples.
- ``'sum'``: Sums the score across samples.
- ``'none'`` or ``None``: Returns the score for each sample.
kwargs: Additional keyword arguments, see `Advanced metric settings
<https://torchmetrics.readthedocs.io/en/stable/pages/overview.html#metric-kwargs>`_.
Inputs:
- :attr:`probs`: :math:`(B, C)` or :math:`(B, N, C)`
Predicted probabilities for each class.
- :attr:`target`: :math:`(B)` or :math:`(B, C)`
Ground truth class labels or one-hot encoded targets.
where:
:math:`B` is the batch size,
:math:`C` is the number of classes,
:math:`N` is the number of estimators.
Note:
If :attr:`probs` is a 3D tensor, the metric computes the mean of
the Brier score over the estimators, as:
:math:`t = \frac{1}{N} \sum_{i=0}^{N-1} BrierScore(probs[:,i,:], target)`.
Warning:
Ensure that the probabilities in :attr:`probs` are normalized to sum
to one before passing them to the metric.
Raises:
ValueError: If :attr:`reduction` is not one of ``'mean'``, ``'sum'``,
``'none'`` or ``None``.
Examples:
>>> from torch_uncertainty.metrics.classification.brier_score import BrierScore
# Example 1: Binary Classification
>>> probs = torch.tensor([[0.8, 0.2], [0.3, 0.7]])
>>> target = torch.tensor([0, 1])
>>> metric = BrierScore(num_classes=2)
>>> metric.update(probs, target)
>>> score = metric.compute()
>>> print(score)
tensor(0.1299)
# Example 2: Multi-Class Classification
>>> probs = torch.tensor([[0.6, 0.3, 0.1], [0.2, 0.5, 0.3]])
>>> target = torch.tensor([0, 2])
>>> metric = BrierScore(num_classes=3, reduction="mean")
>>> metric.update(probs, target)
>>> score = metric.compute()
>>> print(score)
tensor(0.5199)
References:
[1] `Wikipedia entry for the Brier score
<https://en.wikipedia.org/wiki/Brier_score>`_.
"""
super().__init__(**kwargs)
allowed_reduction = ("sum", "mean", "none", None)
if reduction not in allowed_reduction:
raise ValueError(
"Expected argument `reduction` to be one of ",
f"{allowed_reduction} but got {reduction}",
)
self.num_classes = num_classes
self.top_class = top_class
self.reduction = reduction
self.num_estimators = 1
if self.reduction in ["mean", "sum"]:
self.add_state("values", default=torch.tensor(0.0), dist_reduce_fx="sum")
else:
self.add_state("values", default=[], dist_reduce_fx="cat")
self.add_state("total", default=torch.tensor(0), dist_reduce_fx="sum")
[docs]
def update(self, probs: Tensor, target: Tensor) -> None:
"""Update the current Brier score with a new tensor of probabilities.
Args:
probs (Tensor): A probability tensor of shape
(batch, num_estimators, num_classes) or
(batch, num_classes)
target (Tensor): A tensor of ground truth labels of shape
(batch, num_classes) or (batch)
"""
if target.ndim == 1 and self.num_classes > 1:
target = F.one_hot(target, self.num_classes)
if probs.ndim <= 2:
batch_size = probs.size(0)
elif probs.ndim == 3:
batch_size = probs.size(0)
self.num_estimators = probs.size(1)
target = target.unsqueeze(1).repeat(1, self.num_estimators, 1)
else:
raise ValueError(
f"Expected `probs` to be of shape (batch, num_classes) or "
f"(batch, num_estimators, num_classes) but got {probs.shape}"
)
if self.top_class:
probs, indices = probs.max(dim=-1)
target = target.gather(-1, indices.unsqueeze(-1)).squeeze(-1)
brier_score = F.mse_loss(probs, target, reduction="none")
else:
brier_score = F.mse_loss(probs, target, reduction="none").sum(dim=-1)
if self.reduction is None or self.reduction == "none":
self.values.append(brier_score)
else:
self.values += brier_score.sum()
self.total += batch_size
[docs]
def compute(self) -> Tensor:
"""Compute the final Brier score based on inputs passed to ``update``.
Returns:
Tensor: The final value(s) for the Brier score
"""
values = dim_zero_cat(self.values)
if self.reduction == "sum":
return values.sum(dim=-1) / self.num_estimators
if self.reduction == "mean":
return values.sum(dim=-1) / self.total / self.num_estimators
return values
