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pearson.py
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pearson.py
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# Copyright The PyTorch 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 Any, List, Tuple
import torch
from torch import Tensor
from torchmetrics.functional.regression.pearson import _pearson_corrcoef_compute, _pearson_corrcoef_update
from torchmetrics.metric import Metric
def _final_aggregation(
means_x: Tensor,
means_y: Tensor,
vars_x: Tensor,
vars_y: Tensor,
corrs_xy: Tensor,
nbs: Tensor,
) -> Tuple[Tensor, Tensor, Tensor, Tensor, Tensor, Tensor]:
"""Aggregate the statistics from multiple devices.
Formula taken from here: `Aggregate the statistics from multiple devices`_
"""
if len(means_x) == 1:
return means_x[0], means_y[0], vars_x[0], vars_y[0], corrs_xy[0], nbs[0]
mx1, my1, vx1, vy1, cxy1, n1 = means_x[0], means_y[0], vars_x[0], vars_y[0], corrs_xy[0], nbs[0]
for i in range(1, len(means_x)):
mx2, my2, vx2, vy2, cxy2, n2 = means_x[i], means_y[i], vars_x[i], vars_y[i], corrs_xy[i], nbs[i]
nb = n1 + n2
mean_x = (n1 * mx1 + n2 * mx2) / nb
mean_y = (n1 * my1 + n2 * my2) / nb
# var_x
element_x1 = (n1 + 1) * mean_x - n1 * mx1
vx1 += (element_x1 - mx1) * (element_x1 - mean_x) - (element_x1 - mean_x) ** 2
element_x2 = (n2 + 1) * mean_x - n2 * mx2
vx2 += (element_x2 - mx2) * (element_x2 - mean_x) - (element_x2 - mean_x) ** 2
var_x = vx1 + vx2
# var_y
element_y1 = (n1 + 1) * mean_y - n1 * my1
vy1 += (element_y1 - my1) * (element_y1 - mean_y) - (element_y1 - mean_y) ** 2
element_y2 = (n2 + 1) * mean_y - n2 * my2
vy2 += (element_y2 - my2) * (element_y2 - mean_y) - (element_y2 - mean_y) ** 2
var_y = vy1 + vy2
# corr
cxy1 += (element_x1 - mx1) * (element_y1 - mean_y) - (element_x1 - mean_x) * (element_y1 - mean_y)
cxy2 += (element_x2 - mx2) * (element_y2 - mean_y) - (element_x2 - mean_x) * (element_y2 - mean_y)
corr_xy = cxy1 + cxy2
mx1, my1, vx1, vy1, cxy1, n1 = mean_x, mean_y, var_x, var_y, corr_xy, nb
return mean_x, mean_y, var_x, var_y, corr_xy, nb
class PearsonCorrCoef(Metric):
r"""Computes `Pearson Correlation Coefficient`_:
.. math::
P_{corr}(x,y) = \frac{cov(x,y)}{\sigma_x \sigma_y}
Where :math:`y` is a tensor of target values, and :math:`x` is a tensor of predictions.
As input to ``forward`` and ``update`` the metric accepts the following input:
- ``preds`` (:class:`~torch.Tensor`): either single output float tensor with shape ``(N,)``
or multioutput float tensor of shape ``(N,d)``
- ``target`` (:class:`~torch.Tensor`): either single output tensor with shape ``(N,)``
or multioutput tensor of shape ``(N,d)``
As output of ``forward`` and ``compute`` the metric returns the following output:
- ``pearson`` (:class:`~torch.Tensor`): A tensor with the Pearson Correlation Coefficient
Args:
num_outputs: Number of outputs in multioutput setting
kwargs: Additional keyword arguments, see :ref:`Metric kwargs` for more info.
Example (single output regression):
>>> from torchmetrics import PearsonCorrCoef
>>> target = torch.tensor([3, -0.5, 2, 7])
>>> preds = torch.tensor([2.5, 0.0, 2, 8])
>>> pearson = PearsonCorrCoef()
>>> pearson(preds, target)
tensor(0.9849)
Example (multi output regression):
>>> from torchmetrics import PearsonCorrCoef
>>> target = torch.tensor([[3, -0.5], [2, 7]])
>>> preds = torch.tensor([[2.5, 0.0], [2, 8]])
>>> pearson = PearsonCorrCoef(num_outputs=2)
>>> pearson(preds, target)
tensor([1., 1.])
"""
is_differentiable = True
higher_is_better = None # both -1 and 1 are optimal
full_state_update: bool = True
preds: List[Tensor]
target: List[Tensor]
mean_x: Tensor
mean_y: Tensor
var_x: Tensor
var_y: Tensor
corr_xy: Tensor
n_total: Tensor
def __init__(
self,
num_outputs: int = 1,
**kwargs: Any,
) -> None:
super().__init__(**kwargs)
if not isinstance(num_outputs, int) and num_outputs < 1:
raise ValueError("Expected argument `num_outputs` to be an int larger than 0, but got {num_outputs}")
self.num_outputs = num_outputs
self.add_state("mean_x", default=torch.zeros(self.num_outputs), dist_reduce_fx=None)
self.add_state("mean_y", default=torch.zeros(self.num_outputs), dist_reduce_fx=None)
self.add_state("var_x", default=torch.zeros(self.num_outputs), dist_reduce_fx=None)
self.add_state("var_y", default=torch.zeros(self.num_outputs), dist_reduce_fx=None)
self.add_state("corr_xy", default=torch.zeros(self.num_outputs), dist_reduce_fx=None)
self.add_state("n_total", default=torch.zeros(self.num_outputs), dist_reduce_fx=None)
def update(self, preds: Tensor, target: Tensor) -> None:
"""Update state with predictions and targets."""
self.mean_x, self.mean_y, self.var_x, self.var_y, self.corr_xy, self.n_total = _pearson_corrcoef_update(
preds,
target,
self.mean_x,
self.mean_y,
self.var_x,
self.var_y,
self.corr_xy,
self.n_total,
self.num_outputs,
)
def compute(self) -> Tensor:
"""Computes pearson correlation coefficient over state."""
if (self.num_outputs == 1 and self.mean_x.numel() > 1) or (self.num_outputs > 1 and self.mean_x.ndim > 1):
# multiple devices, need further reduction
_, _, var_x, var_y, corr_xy, n_total = _final_aggregation(
self.mean_x, self.mean_y, self.var_x, self.var_y, self.corr_xy, self.n_total
)
else:
var_x = self.var_x
var_y = self.var_y
corr_xy = self.corr_xy
n_total = self.n_total
return _pearson_corrcoef_compute(var_x, var_y, corr_xy, n_total)