scikit-learn · lorentzenchr · Apr 16, 2025 · May 30, 2024 · May 30, 2024 · May 30, 2024
diff --git a/doc/whats_new/upcoming_changes/sklearn.metrics/29151.enhancement.rst b/doc/whats_new/upcoming_changes/sklearn.metrics/29151.enhancement.rst
@@ -0,0 +1,6 @@
+- :func:`metrics.det_curve`, :class:`metrics.DetCurveDisplay.from_estimator`,
+  and :class:`metrics.DetCurveDisplay.from_estimator` now accept a
+  `drop_intermediate` option to drop thresholds where true positives (tp) do not
+  change from the previous or subsequent thresholds. All points with the same tp
+  value have the same `fnr` and thus same y coordinate in a DET curve.
+  :pr:`29151` by :user:`Arturo Amor <ArturoAmorQ>`.
diff --git a/doc/whats_new/upcoming_changes/sklearn.metrics/29151.fix.rst b/doc/whats_new/upcoming_changes/sklearn.metrics/29151.fix.rst
@@ -0,0 +1,4 @@
+- :func:`metrics.det_curve` and :class:`metrics.DetCurveDisplay` now return an
+  extra threshold at infinity where the classifier always predicts the negative
+  class i.e. tps = fps = 0.
+  :pr:`29151` by :user:`Arturo Amor <ArturoAmorQ>`.
diff --git a/examples/model_selection/plot_det.py b/examples/model_selection/plot_det.py
@@ -60,24 +60,24 @@
 # ----------------------
 #
 # Here we define two different classifiers. The goal is to visually compare their
-# statistical performance across thresholds using the ROC and DET curves. There
-# is no particular reason why these classifiers are chosen other classifiers
-# available in scikit-learn.
+# statistical performance across thresholds using the ROC and DET curves.
 
+from sklearn.dummy import DummyClassifier
 from sklearn.ensemble import RandomForestClassifier
 from sklearn.pipeline import make_pipeline
 from sklearn.svm import LinearSVC
 
 classifiers = {
     "Linear SVM": make_pipeline(StandardScaler(), LinearSVC(C=0.025)),
     "Random Forest": RandomForestClassifier(
-        max_depth=5, n_estimators=10, max_features=1
+        max_depth=5, n_estimators=10, max_features=1, random_state=0
     ),
+    "Non-informative baseline": DummyClassifier(),
 }
 
 # %%
-# Plot ROC and DET curves
-# -----------------------
+# Compare ROC and DET curves
+# --------------------------
 #
 # DET curves are commonly plotted in normal deviate scale. To achieve this the
 # DET display transforms the error rates as returned by the
@@ -86,22 +86,29 @@
 
 import matplotlib.pyplot as plt
 
+from sklearn.dummy import DummyClassifier
 from sklearn.metrics import DetCurveDisplay, RocCurveDisplay
 
 fig, [ax_roc, ax_det] = plt.subplots(1, 2, figsize=(11, 5))
 
-for name, clf in classifiers.items():
-    clf.fit(X_train, y_train)
-
-    RocCurveDisplay.from_estimator(clf, X_test, y_test, ax=ax_roc, name=name)
-    DetCurveDisplay.from_estimator(clf, X_test, y_test, ax=ax_det, name=name)
-
 ax_roc.set_title("Receiver Operating Characteristic (ROC) curves")
 ax_det.set_title("Detection Error Tradeoff (DET) curves")
 
 ax_roc.grid(linestyle="--")
 ax_det.grid(linestyle="--")
 
+for name, clf in classifiers.items():
+    (color, linestyle) = (
+        ("black", "--") if name == "Non-informative baseline" else (None, None)
+    )
+    clf.fit(X_train, y_train)
+    RocCurveDisplay.from_estimator(
+        clf, X_test, y_test, ax=ax_roc, name=name, color=color, linestyle=linestyle
+    )
+    DetCurveDisplay.from_estimator(
+        clf, X_test, y_test, ax=ax_det, name=name, color=color, linestyle=linestyle
+    )
+
 plt.legend()
 plt.show()
 
@@ -117,3 +124,35 @@
 # DET curves give direct feedback of the detection error tradeoff to aid in
 # operating point analysis. The user can then decide the FNR they are willing to
 # accept at the expense of the FPR (or vice-versa).
+#
+# Non-informative classifier baseline for the ROC and DET curves
+# --------------------------------------------------------------
+#
+# The diagonal black-dotted lines in the plots above correspond to a
+# :class:`~sklearn.dummy.DummyClassifier` using the default "prior" strategy, to
+# serve as baseline for comparison with other classifiers. This classifier makes
+# constant predictions, independent of the input features in `X`, making it a
+# non-informative classifier.
+#
+# To further understand the non-informative baseline of the ROC and DET curves,
+# we recall the following mathematical definitions:
+#
+# :math:`\text{FPR} = \frac{\text{FP}}{\text{FP} + \text{TN}}`
+#
+# :math:`\text{FNR} = \frac{\text{FN}}{\text{TP} + \text{FN}}`
+#
+# :math:`\text{TPR} = \frac{\text{TP}}{\text{TP} + \text{FN}}`
+#
+# A classifier that always predict the positive class would have no true
+# negatives nor false negatives, giving :math:`\text{FPR} = \text{TPR} = 1` and
+# :math:`\text{FNR} = 0`, i.e.:
+#
+# - a single point in the upper right corner of the ROC plane,
+# - a single point in the lower right corner of the DET plane.
+#
+# Similarly, a classifier that always predict the negative class would have no
+# true positives nor false positives, thus :math:`\text{FPR} = \text{TPR} = 0`
+# and :math:`\text{FNR} = 1`, i.e.:
+#
+# - a single point in the lower left corner of the ROC plane,
+# - a single point in the upper left corner of the DET plane.
diff --git a/sklearn/metrics/_plot/det_curve.py b/sklearn/metrics/_plot/det_curve.py
@@ -1,20 +1,21 @@
 # Authors: The scikit-learn developers
 # SPDX-License-Identifier: BSD-3-Clause
 
+import numpy as np
 import scipy as sp
 
 from ...utils._plotting import _BinaryClassifierCurveDisplayMixin
 from .._ranking import det_curve
 
 
 class DetCurveDisplay(_BinaryClassifierCurveDisplayMixin):
-    """DET curve visualization.
+    """Detection Error Tradeoff (DET) curve visualization.
 
     It is recommend to use :func:`~sklearn.metrics.DetCurveDisplay.from_estimator`
     or :func:`~sklearn.metrics.DetCurveDisplay.from_predictions` to create a
     visualizer. All parameters are stored as attributes.
 
-    Read more in the :ref:`User Guide <visualizations>`.
+    Read more in the :ref:`User Guide <det_curve>`.
 
     .. versionadded:: 0.24
 
@@ -86,6 +87,7 @@ def from_estimator(
         y,
         *,
         sample_weight=None,
+        drop_intermediate=True,
         response_method="auto",
         pos_label=None,
         name=None,
@@ -94,7 +96,7 @@ def from_estimator(
     ):
         """Plot DET curve given an estimator and data.
 
-        Read more in the :ref:`User Guide <visualizations>`.
+        Read more in the :ref:`User Guide <det_curve>`.
 
         .. versionadded:: 1.0
 
@@ -113,6 +115,11 @@ def from_estimator(
         sample_weight : array-like of shape (n_samples,), default=None
             Sample weights.
 
+        drop_intermediate : bool, default=True
+            Whether to drop thresholds where true positives (tp) do not change
+            from the previous or subsequent threshold. All points with the same
+            tp value have the same `fnr` and thus same y coordinate.
+
         response_method : {'predict_proba', 'decision_function', 'auto'} \
                 default='auto'
             Specifies whether to use :term:`predict_proba` or
@@ -176,6 +183,7 @@ def from_estimator(
             y_true=y,
             y_pred=y_pred,
             sample_weight=sample_weight,
+            drop_intermediate=drop_intermediate,
             name=name,
             ax=ax,
             pos_label=pos_label,
@@ -189,14 +197,15 @@ def from_predictions(
         y_pred,
         *,
         sample_weight=None,
+        drop_intermediate=True,
         pos_label=None,
         name=None,
         ax=None,
         **kwargs,
     ):
         """Plot the DET curve given the true and predicted labels.
 
-        Read more in the :ref:`User Guide <visualizations>`.
+        Read more in the :ref:`User Guide <det_curve>`.
 
         .. versionadded:: 1.0
 
@@ -213,6 +222,11 @@ def from_predictions(
         sample_weight : array-like of shape (n_samples,), default=None
             Sample weights.
 
+        drop_intermediate : bool, default=True
+            Whether to drop thresholds where true positives (tp) do not change
+            from the previous or subsequent threshold. All points with the same
+            tp value have the same `fnr` and thus same y coordinate.
+
         pos_label : int, float, bool or str, default=None
             The label of the positive class. When `pos_label=None`, if `y_true`
             is in {-1, 1} or {0, 1}, `pos_label` is set to 1, otherwise an
@@ -266,6 +280,7 @@ def from_predictions(
             y_pred,
             pos_label=pos_label,
             sample_weight=sample_weight,
+            drop_intermediate=drop_intermediate,
         )
 
         viz = cls(
@@ -303,6 +318,14 @@ def plot(self, ax=None, *, name=None, **kwargs):
         line_kwargs = {} if name is None else {"label": name}
         line_kwargs.update(**kwargs)
 
+        # We have the following bounds:
+        # sp.stats.norm.ppf(0.0) = -np.inf
+        # sp.stats.norm.ppf(1.0) = np.inf
+        # We therefore clip to eps and 1 - eps to not provide infinity to matplotlib.
+        eps = np.finfo(self.fpr.dtype).eps
+        self.fpr = self.fpr.clip(eps, 1 - eps)
+        self.fnr = self.fnr.clip(eps, 1 - eps)
+
         (self.line_,) = self.ax_.plot(
             sp.stats.norm.ppf(self.fpr),
             sp.stats.norm.ppf(self.fnr),

diff --git a/sklearn/metrics/_plot/tests/test_det_curve_display.py b/sklearn/metrics/_plot/tests/test_det_curve_display.py
@@ -10,9 +10,15 @@
 @pytest.mark.parametrize("constructor_name", ["from_estimator", "from_predictions"])
 @pytest.mark.parametrize("response_method", ["predict_proba", "decision_function"])
 @pytest.mark.parametrize("with_sample_weight", [True, False])
+@pytest.mark.parametrize("drop_intermediate", [True, False])
 @pytest.mark.parametrize("with_strings", [True, False])
 def test_det_curve_display(
-    pyplot, constructor_name, response_method, with_sample_weight, with_strings
+    pyplot,
+    constructor_name,
+    response_method,
+    with_sample_weight,
+    drop_intermediate,
+    with_strings,
 ):
     X, y = load_iris(return_X_y=True)
     # Binarize the data with only the two first classes
@@ -42,6 +48,7 @@ def test_det_curve_display(
         "name": lr.__class__.__name__,
         "alpha": 0.8,
         "sample_weight": sample_weight,
+        "drop_intermediate": drop_intermediate,
         "pos_label": pos_label,
     }
     if constructor_name == "from_estimator":
@@ -53,11 +60,12 @@ def test_det_curve_display(
         y,
         y_pred,
         sample_weight=sample_weight,
+        drop_intermediate=drop_intermediate,
         pos_label=pos_label,
     )
 
-    assert_allclose(disp.fpr, fpr)
-    assert_allclose(disp.fnr, fnr)
+    assert_allclose(disp.fpr, fpr, atol=1e-7)
+    assert_allclose(disp.fnr, fnr, atol=1e-7)
 
     assert disp.estimator_name == "LogisticRegression"
 

diff --git a/sklearn/metrics/_ranking.py b/sklearn/metrics/_ranking.py
@@ -271,11 +271,14 @@ def _binary_uninterpolated_average_precision(
         "y_score": ["array-like"],
         "pos_label": [Real, str, "boolean", None],
         "sample_weight": ["array-like", None],
+        "drop_intermediate": ["boolean"],
     },
     prefer_skip_nested_validation=True,
 )
-def det_curve(y_true, y_score, pos_label=None, sample_weight=None):
-    """Compute error rates for different probability thresholds.
+def det_curve(
+    y_true, y_score, pos_label=None, sample_weight=None, drop_intermediate=False
+):
+    """Compute Detection Error Tradeoff (DET) for different probability thresholds.
 
     .. note::
        This metric is used for evaluation of ranking and error tradeoffs of
@@ -285,6 +288,11 @@ def det_curve(y_true, y_score, pos_label=None, sample_weight=None):
 
     .. versionadded:: 0.24
 
+    .. versionchanged:: 1.7
+       An arbitrary threshold at infinity is added to represent a classifier
+       that always predicts the negative class, i.e. `fpr=0` and `fnr=1`, unless
+       `fpr=0` is already reached at a finite threshold.
+
     Parameters
     ----------
     y_true : ndarray of shape (n_samples,)
@@ -306,6 +314,13 @@ def det_curve(y_true, y_score, pos_label=None, sample_weight=None):
     sample_weight : array-like of shape (n_samples,), default=None
         Sample weights.
 
+    drop_intermediate : bool, default=False
+        Whether to drop thresholds where true positives (tp) do not change from
+        the previous or subsequent threshold. All points with the same tp value
+        have the same `fnr` and thus same y coordinate.
+
+        .. versionadded:: 1.7
+
     Returns
     -------
     fpr : ndarray of shape (n_thresholds,)
@@ -319,7 +334,9 @@ def det_curve(y_true, y_score, pos_label=None, sample_weight=None):
         referred to as false rejection or miss rate.
 
     thresholds : ndarray of shape (n_thresholds,)
-        Decreasing score values.
+        Decreasing thresholds on the decision function (either `predict_proba`
+        or `decision_function`) used to compute FPR and FNR. An arbitrary
+        threshold at infinity is added for the case `fpr=0` and `fnr=1`.
 
     See Also
     --------
@@ -349,6 +366,28 @@ def det_curve(y_true, y_score, pos_label=None, sample_weight=None):
         y_true, y_score, pos_label=pos_label, sample_weight=sample_weight
     )
 
+    # add a threshold at inf where the clf always predicts the negative class
+    # i.e. tps = fps = 0
+    tps = np.concatenate(([0], tps))
+    fps = np.concatenate(([0], fps))
+    thresholds = np.concatenate(([np.inf], thresholds))
+
+    if drop_intermediate and len(fps) > 2:
+        # Drop thresholds where true positives (tp) do not change from the
+        # previous or subsequent threshold. As tp + fn, is fixed for a dataset,
+        # this means the false negative rate (fnr) remains constant while the
+        # false positive rate (fpr) changes, producing horizontal line segments
+        # in the transformed (normal deviate) scale. These intermediate points
+        # can be dropped to create lighter DET curve plots.
+        optimal_idxs = np.where(
+            np.concatenate(
+                [[True], np.logical_or(np.diff(tps[:-1]), np.diff(tps[1:])), [True]]
+            )
+        )[0]
+        fps = fps[optimal_idxs]
+        tps = tps[optimal_idxs]
+        thresholds = thresholds[optimal_idxs]
+
     if len(np.unique(y_true)) != 2:
         raise ValueError(
             "Only one class is present in y_true. Detection error "
@@ -359,7 +398,7 @@ def det_curve(y_true, y_score, pos_label=None, sample_weight=None):
     p_count = tps[-1]
     n_count = fps[-1]
 
-    # start with false positives zero
+    # start with false positives zero, which may be at a finite threshold
     first_ind = (
         fps.searchsorted(fps[0], side="right") - 1
         if fps.searchsorted(fps[0], side="right") > 0
@@ -1121,9 +1160,8 @@ def roc_curve(
     are reversed upon returning them to ensure they correspond to both ``fpr``
     and ``tpr``, which are sorted in reversed order during their calculation.
 
-    An arbitrary threshold is added for the case `tpr=0` and `fpr=0` to
-    ensure that the curve starts at `(0, 0)`. This threshold corresponds to the
-    `np.inf`.
+    An arbritrary threshold at infinity is added to represent a classifier
+    that always predicts the negative class, i.e. `fpr=0` and `tpr=0`.
 
     References
     ----------