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

doc/source/user_guide/indexing.rst

@@ -710,32 +710,6 @@ When applied to a DataFrame, you can use a column of the DataFrame as sampling w
 (provided you are sampling rows and not columns) by simply passing the name of the column
 as a string.
 
-.. ipython:: python
-
-    df2 = pd.DataFrame({'col1': [9, 8, 7, 6],
-                        'weight_column': [0.5, 0.4, 0.1, 0]})
-    df2.sample(n=3, weights='weight_column')
-
-``sample`` also allows users to sample columns instead of rows using the ``axis`` argument.
-
-.. ipython:: python
-
-    df3 = pd.DataFrame({'col1': [1, 2, 3], 'col2': [2, 3, 4]})
-    df3.sample(n=1, axis=1)
-
-Finally, one can also set a seed for ``sample``'s random number generator using the ``random_state`` argument, which will accept either an integer (as a seed) or a NumPy RandomState object.
-
-.. ipython:: python
-
-    df4 = pd.DataFrame({'col1': [1, 2, 3], 'col2': [2, 3, 4]})
-
-    # With a given seed, the sample will always draw the same rows.
-    df4.sample(n=2, random_state=2)
-    df4.sample(n=2, random_state=2)
-
-
-
-Setting with enlargement
 ------------------------
 
 The ``.loc/[]`` operations can perform enlargement when setting a non-existent key for that axis.

doc/source/whatsnew/v3.0.0.rst

@@ -890,6 +890,7 @@ 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")
 
+    if weights is not None:
+        is_max_weight_dominating = size * weights.max() > 1
+        if is_max_weight_dominating and not replace:
+            raise ValueError(
+                "Invalid weights: If `replace`=False, "
+                "total 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

@@ -113,9 +113,6 @@ def test_sample_invalid_weight_lengths(self, obj):
         with pytest.raises(ValueError, match=msg):
             obj.sample(n=3, weights=[0.5] * 11)
 
-        with pytest.raises(ValueError, match="Fewer non-zero entries in p than size"):
-            obj.sample(n=4, weights=Series([0, 0, 0.2]))
-
     def test_sample_negative_weights(self, obj):
         # Check won't accept negative weights
         bad_weights = [-0.1] * 10
@@ -137,6 +134,28 @@ def test_sample_inf_weights(self, obj):
         with pytest.raises(ValueError, match=msg):
             obj.sample(n=3, weights=weights_with_ninf)
 
+    def test_sample_unit_probabilities_raises(self, obj):
+        # GH#61516
+        high_variance_weights = [1] * 10
+        high_variance_weights[0] = 100
+        msg = (
+            "Invalid weights: If `replace`=False, "
+            "total unit probabilities have to be less than 1"
+        )
+        with pytest.raises(ValueError, match=msg):
+            obj.sample(n=2, weights=high_variance_weights, replace=False)
+
+        # edge case, n*max(weights)/sum(weights) == 1
+        edge_variance_weights = [1] * 10
+        edge_variance_weights[0] = 9
+        # should not raise
+        obj.sample(n=2, weights=edge_variance_weights, replace=False)
+
+        low_variance_weights = [1] * 10
+        low_variance_weights[0] = 8
+        # should not raise
+        obj.sample(n=2, weights=low_variance_weights, replace=False)
+
     def test_sample_zero_weights(self, obj):
         # All zeros raises errors