Improve calculations in Pearson (#1729)

* fixing
* changelog
* fix condition in multi case

CHANGELOG.md

@@ -128,6 +128,8 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 - Changed FID matrix square root calculation from `scipy` to `torch` ([#1708](https://github.com/Lightning-AI/torchmetrics/pull/1708))
 
 
+- Changed calculation in `PearsonCorrCoeff` to be more robust in certain cases ([#1729](https://github.com/Lightning-AI/torchmetrics/pull/1729))
+
 ### Deprecated
 
 - Deprecated domain metrics import from package root (

src/torchmetrics/functional/regression/pearson.py

@@ -49,13 +49,25 @@ def _pearson_corrcoef_update(
  # Data checking
  _check_same_shape(preds, target)
  _check_data_shape_to_num_outputs(preds, target, num_outputs)
+ cond = n_prior.mean() > 0
 
  n_obs = preds.shape[0]
- mx_new = (n_prior * mean_x + preds.mean(0) * n_obs) / (n_prior + n_obs)
- my_new = (n_prior * mean_y + target.mean(0) * n_obs) / (n_prior + n_obs)
+ if cond:
+ mx_new = (n_prior * mean_x + preds.sum(0)) / (n_prior + n_obs)
+ my_new = (n_prior * mean_y + target.sum(0)) / (n_prior + n_obs)
+ else:
+ mx_new = preds.mean(0)
+ my_new = target.mean(0)
+
  n_prior += n_obs
- var_x += ((preds - mx_new) * (preds - mean_x)).sum(0)
- var_y += ((target - my_new) * (target - mean_y)).sum(0)
+
+ if cond:
+ var_x += ((preds - mx_new) * (preds - mean_x)).sum(0)
+ var_y += ((target - my_new) * (target - mean_y)).sum(0)
+
+ else:
+ var_x += preds.var(0) * (n_obs - 1)
+ var_y += target.var(0) * (n_obs - 1)
  corr_xy += ((preds - mx_new) * (target - mean_y)).sum(0)
  mean_x = mx_new
  mean_y = my_new