# 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)