Fix corner case for R2Score

CHANGELOG.md

@@ -92,6 +92,9 @@ and this project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0
 - Fixed the use of `ignore_index` in `MulticlassJaccardIndex` ([#1386](https://github.com/Lightning-AI/metrics/pull/1386))
 
 
+- Fixed evaluation of `R2Score` with near constant target ([#1576](https://github.com/Lightning-AI/metrics/pull/1576))
+
+
 ## [0.11.2] - 2023-02-21
 
 ### Fixed

src/torchmetrics/functional/regression/r2.py

@@ -41,7 +41,6 @@ def _r2_score_update(preds: Tensor, target: Tensor) -> Tuple[Tensor, Tensor, Ten
     residual = target - preds
     rss = torch.sum(residual * residual, dim=0)
     n_obs = target.size(0)
-
     return sum_squared_obs, sum_obs, rss, n_obs
 
 
@@ -79,7 +78,15 @@ def _r2_score_compute(
 
     mean_obs = sum_obs / n_obs
     tss = sum_squared_obs - sum_obs * mean_obs
-    raw_scores = 1 - (rss / tss)
+
+    # 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

src/torchmetrics/regression/r2.py

@@ -32,6 +32,9 @@ class R2Score(Metric):
     .. 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.
+    The score is only proper defined when :math:`SS_{tot}\neq 0`, which can happen for near constant targets. In this
+    case a score of 0 is returned. By definition the score is bounded between 0 and 1, where 1 corresponds to the
+    predictions exactly matching the targets.
 
     As input to ``forward`` and ``update`` the metric accepts the following input:
 

tests/unittests/regression/test_r2.py

@@ -159,3 +159,11 @@ def test_warning_on_too_large_adjusted(metric_class=R2Score):
 
     with pytest.warns(UserWarning, match="Division by zero in adjusted r2 score. Falls back to" " standard r2 score."):
         metric(torch.randn(11), torch.randn(11))
+
+
+def test_constant_target():
+    """Check for a near constant target that a value of 0 is returned."""
+    y_true = torch.tensor([-5.1608, -5.1609, -5.1608, -5.1608, -5.1608, -5.1608])
+    y_pred = torch.tensor([-3.9865, -5.4648, -5.0238, -4.3899, -5.6672, -4.7336])
+    score = r2_score(preds=y_pred, target=y_true)
+    assert score == 0