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# Copyright The Lightning team.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
from typing import Union
import torch
from torch import Tensor
from torchmetrics.utilities import rank_zero_warn
from torchmetrics.utilities.checks import _check_same_shape
def _r2_score_update(preds: Tensor, target: Tensor) -> tuple[Tensor, Tensor, Tensor, int]:
"""Update and returns variables required to compute R2 score.
Check for same shape and 1D/2D input tensors.
Args:
preds: Predicted tensor
target: Ground truth tensor
"""
_check_same_shape(preds, target)
if preds.ndim > 2:
raise ValueError(
"Expected both prediction and target to be 1D or 2D tensors,"
f" but received tensors with dimension {preds.shape}"
)
sum_obs = torch.sum(target, dim=0)
sum_squared_obs = torch.sum(target * target, dim=0)
residual = target - preds
rss = torch.sum(residual * residual, dim=0)
return sum_squared_obs, sum_obs, rss, target.size(0)
def _r2_score_compute(
sum_squared_obs: Tensor,
sum_obs: Tensor,
rss: Tensor,
num_obs: Union[int, Tensor],
adjusted: int = 0,
multioutput: str = "uniform_average",
) -> Tensor:
"""Compute R2 score.
Args:
sum_squared_obs: Sum of square of all observations
sum_obs: Sum of all observations
rss: Residual sum of squares
num_obs: Number of predictions or observations
adjusted: number of independent regressors for calculating adjusted r2 score.
multioutput: Defines aggregation in the case of multiple output scores. Can be one of the following strings:
* `'raw_values'` returns full set of scores
* `'uniform_average'` scores are uniformly averaged
* `'variance_weighted'` scores are weighted by their individual variances
Example:
>>> target = torch.tensor([[0.5, 1], [-1, 1], [7, -6]])
>>> preds = torch.tensor([[0, 2], [-1, 2], [8, -5]])
>>> sum_squared_obs, sum_obs, rss, num_obs = _r2_score_update(preds, target)
>>> _r2_score_compute(sum_squared_obs, sum_obs, rss, num_obs, multioutput="raw_values")
tensor([0.9654, 0.9082])
"""
if num_obs < 2:
raise ValueError("Needs at least two samples to calculate r2 score.")
mean_obs = sum_obs / num_obs
tss = sum_squared_obs - sum_obs * mean_obs
# Account for near constant targets
cond_rss = ~torch.isclose(rss, torch.zeros_like(rss), atol=1e-4)
cond_tss = ~torch.isclose(tss, torch.zeros_like(tss), atol=1e-4)
cond = cond_rss & cond_tss
raw_scores = torch.ones_like(rss)
raw_scores[cond] = 1 - (rss[cond] / tss[cond])
raw_scores[cond_rss & ~cond_tss] = 0.0
if multioutput == "raw_values":
r2 = raw_scores
elif multioutput == "uniform_average":
r2 = torch.mean(raw_scores)
elif multioutput == "variance_weighted":
tss_sum = torch.sum(tss)
r2 = torch.sum(tss / tss_sum * raw_scores)
else:
raise ValueError(
"Argument `multioutput` must be either `raw_values`,"
f" `uniform_average` or `variance_weighted`. Received {multioutput}."
)
if adjusted < 0 or not isinstance(adjusted, int):
raise ValueError("`adjusted` parameter should be an integer larger or equal to 0.")
if adjusted != 0:
if adjusted > num_obs - 1:
rank_zero_warn(
"More independent regressions than data points in adjusted r2 score. Falls back to standard r2 score.",
UserWarning,
)
elif adjusted == num_obs - 1:
rank_zero_warn("Division by zero in adjusted r2 score. Falls back to standard r2 score.", UserWarning)
else:
return 1 - (1 - r2) * (num_obs - 1) / (num_obs - adjusted - 1)
return r2
def r2_score(
preds: Tensor,
target: Tensor,
adjusted: int = 0,
multioutput: str = "uniform_average",
) -> Tensor:
r"""Compute r2 score also known as `R2 Score_Coefficient Determination`_.
.. math:: R^2 = 1 - \frac{SS_{res}}{SS_{tot}}
where :math:`SS_{res}=\sum_i (y_i - f(x_i))^2` is the sum of residual squares, and
:math:`SS_{tot}=\sum_i (y_i - \bar{y})^2` is total sum of squares. Can also calculate
adjusted r2 score given by
.. math:: R^2_{adj} = 1 - \frac{(1-R^2)(n-1)}{n-k-1}
where the parameter :math:`k` (the number of independent regressors) should
be provided as the ``adjusted`` argument.
Args:
preds: estimated labels
target: ground truth labels
adjusted: number of independent regressors for calculating adjusted r2 score.
multioutput: Defines aggregation in the case of multiple output scores. Can be one of the following strings:
* ``'raw_values'`` returns full set of scores
* ``'uniform_average'`` scores are uniformly averaged
* ``'variance_weighted'`` scores are weighted by their individual variances
Raises:
ValueError:
If both ``preds`` and ``targets`` are not ``1D`` or ``2D`` tensors.
ValueError:
If ``len(preds)`` is less than ``2`` since at least ``2`` samples are needed to calculate r2 score.
ValueError:
If ``multioutput`` is not one of ``raw_values``, ``uniform_average`` or ``variance_weighted``.
ValueError:
If ``adjusted`` is not an ``integer`` greater than ``0``.
Example:
>>> from torchmetrics.functional.regression import r2_score
>>> target = torch.tensor([3, -0.5, 2, 7])
>>> preds = torch.tensor([2.5, 0.0, 2, 8])
>>> r2_score(preds, target)
tensor(0.9486)
>>> target = torch.tensor([[0.5, 1], [-1, 1], [7, -6]])
>>> preds = torch.tensor([[0, 2], [-1, 2], [8, -5]])
>>> r2_score(preds, target, multioutput='raw_values')
tensor([0.9654, 0.9082])
"""
sum_squared_obs, sum_obs, rss, num_obs = _r2_score_update(preds, target)
return _r2_score_compute(sum_squared_obs, sum_obs, rss, num_obs, adjusted, multioutput)
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