BUG: Require sample weights to sum to less than 1 when replace = True

doc/source/whatsnew/v3.0.0.rst

@@ -888,6 +888,7 @@ Other
 - Bug in :meth:`DataFrame.query` where using duplicate column names led to a ``TypeError``. (:issue:`59950`)
 - Bug in :meth:`DataFrame.query` which raised an exception or produced incorrect results when expressions contained backtick-quoted column names containing the hash character ``#``, backticks, or characters that fall outside the ASCII range (U+0001..U+007F). (:issue:`59285`) (:issue:`49633`)
 - Bug in :meth:`DataFrame.query` which raised an exception when querying integer column names using backticks. (:issue:`60494`)
+- Bug in :meth:`DataFrame.sample` with ``replace=False`` and ``(n * max(weights) / sum(weights)) > 1``, the method would return biased results. Now raises ``ValueError``. (:issue:`61516`)
 - Bug in :meth:`DataFrame.shift` where passing a ``freq`` on a DataFrame with no columns did not shift the index correctly. (:issue:`60102`)
 - Bug in :meth:`DataFrame.sort_index` when passing ``axis="columns"`` and ``ignore_index=True`` and ``ascending=False`` not returning a :class:`RangeIndex` columns (:issue:`57293`)
 - Bug in :meth:`DataFrame.sort_values` where sorting by a column explicitly named ``None`` raised a ``KeyError`` instead of sorting by the column as expected. (:issue:`61512`)

pandas/core/generic.py

@@ -5815,6 +5815,8 @@ def sample(
             If weights do not sum to 1, they will be normalized to sum to 1.
             Missing values in the weights column will be treated as zero.
             Infinite values not allowed.
+            When replace = False will not allow ``(n * max(weights) / sum(weights)) > 1``,
+            in order to avoid biased results.
         random_state : int, array-like, BitGenerator, np.random.RandomState, np.random.Generator, optional
             If int, array-like, or BitGenerator, seed for random number generator.
             If np.random.RandomState or np.random.Generator, use as given.

pandas/core/sample.py

@@ -150,6 +150,14 @@ def sample(
         else:
             raise ValueError("Invalid weights: weights sum to zero")
 
+
+        is_max_weight_dominating = size * max(weights) > weight_sum
+        if is_max_weight_dominating and not replace:
+            raise ValueError(
+                "Invalid weights: If `replace`=False,"
+                " unit probabilities have to be less than 1"
+            )
+
     return random_state.choice(obj_len, size=size, replace=replace, p=weights).astype(
         np.intp, copy=False
     )

pandas/tests/frame/methods/test_sample.py

@@ -137,6 +137,17 @@ def test_sample_inf_weights(self, obj):
         with pytest.raises(ValueError, match=msg):
             obj.sample(n=3, weights=weights_with_ninf)
 
+    def test_sample_replacement_weight_sum(self, obj):
+        # GH#61516
+        weights_large_total = [1] * 10
+        weights_large_total[0] = 100
+        msg = (
+            "Invalid weights: If `replace`=False,"
+            " unit probabilities have to be less than 1"
+        )
+        with pytest.raises(ValueError, match=msg):
+            obj.sample(n=3, weights=weights_large_total, replace=False)
+
     def test_sample_zero_weights(self, obj):
         # All zeros raises errors