"""
======================================================
Post-hoc tuning the cut-off point of decision function
======================================================
Once a binary classifier is trained, the :term:`predict` method outputs class label
predictions corresponding to a thresholding of either the :term:`decision_function` or
the :term:`predict_proba` output. The default threshold is defined as a posterior
probability estimate of 0.5 or a decision score of 0.0. However, this default strategy
may not be optimal for the task at hand.
This example shows how to use the
:class:`~sklearn.model_selection.TunedThresholdClassifierCV` to tune the decision
threshold, depending on a metric of interest.
"""
# %%
# The diabetes dataset
# --------------------
#
# To illustrate the tuning of the decision threshold, we will use the diabetes dataset.
# This dataset is available on OpenML: https://www.openml.org/d/37. We use the
# :func:`~sklearn.datasets.fetch_openml` function to fetch this dataset.
from sklearn.datasets import fetch_openml
diabetes = fetch_openml(data_id=37, as_frame=True, parser="pandas")
data, target = diabetes.data, diabetes.target
# %%
# We look at the target to understand the type of problem we are dealing with.
target.value_counts()
# %%
# We can see that we are dealing with a binary classification problem. Since the
# labels are not encoded as 0 and 1, we make it explicit that we consider the class
# labeled "tested_negative" as the negative class (which is also the most frequent)
# and the class labeled "tested_positive" the positive as the positive class:
neg_label, pos_label = target.value_counts().index
# %%
# We can also observe that this binary problem is slightly imbalanced where we have
# around twice more samples from the negative class than from the positive class. When
# it comes to evaluation, we should consider this aspect to interpret the results.
#
# Our vanilla classifier
# ----------------------
#
# We define a basic predictive model composed of a scaler followed by a logistic
# regression classifier.
from sklearn.linear_model import LogisticRegression
from sklearn.pipeline import make_pipeline
from sklearn.preprocessing import StandardScaler
model = make_pipeline(StandardScaler(), LogisticRegression())
model
# %%
# We evaluate our model using cross-validation. We use the accuracy and the balanced
# accuracy to report the performance of our model. The balanced accuracy is a metric
# that is less sensitive to class imbalance and will allow us to put the accuracy
# score in perspective.
#
# Cross-validation allows us to study the variance of the decision threshold across
# different splits of the data. However, the dataset is rather small and it would be
# detrimental to use more than 5 folds to evaluate the dispersion. Therefore, we use
# a :class:`~sklearn.model_selection.RepeatedStratifiedKFold` where we apply several
# repetitions of 5-fold cross-validation.
import pandas as pd
from sklearn.model_selection import RepeatedStratifiedKFold, cross_validate
scoring = ["accuracy", "balanced_accuracy"]
cv_scores = [
"train_accuracy",
"test_accuracy",
"train_balanced_accuracy",
"test_balanced_accuracy",
]
cv = RepeatedStratifiedKFold(n_splits=5, n_repeats=10, random_state=42)
cv_results_vanilla_model = pd.DataFrame(
cross_validate(
model,
data,
target,
scoring=scoring,
cv=cv,
return_train_score=True,
return_estimator=True,
)
)
cv_results_vanilla_model[cv_scores].aggregate(["mean", "std"]).T
# %%
# Our predictive model succeeds to grasp the relationship between the data and the
# target. The training and testing scores are close to each other, meaning that our
# predictive model is not overfitting. We can also observe that the balanced accuracy is
# lower than the accuracy, due to the class imbalance previously mentioned.
#
# For this classifier, we let the decision threshold, used convert the probability of
# the positive class into a class prediction, to its default value: 0.5. However, this
# threshold might not be optimal. If our interest is to maximize the balanced accuracy,
# we should select another threshold that would maximize this metric.
#
# The :class:`~sklearn.model_selection.TunedThresholdClassifierCV` meta-estimator allows
# to tune the decision threshold of a classifier given a metric of interest.
#
# Tuning the decision threshold
# -----------------------------
#
# We create a :class:`~sklearn.model_selection.TunedThresholdClassifierCV` and
# configure it to maximize the balanced accuracy. We evaluate the model using the same
# cross-validation strategy as previously.
from sklearn.model_selection import TunedThresholdClassifierCV
tuned_model = TunedThresholdClassifierCV(estimator=model, scoring="balanced_accuracy")
cv_results_tuned_model = pd.DataFrame(
cross_validate(
tuned_model,
data,
target,
scoring=scoring,
cv=cv,
return_train_score=True,
return_estimator=True,
)
)
cv_results_tuned_model[cv_scores].aggregate(["mean", "std"]).T
# %%
# In comparison with the vanilla model, we observe that the balanced accuracy score
# increased. Of course, it comes at the cost of a lower accuracy score. It means that
# our model is now more sensitive to the positive class but makes more mistakes on the
# negative class.
#
# However, it is important to note that this tuned predictive model is internally the
# same model as the vanilla model: they have the same fitted coefficients.
import matplotlib.pyplot as plt
vanilla_model_coef = pd.DataFrame(
[est[-1].coef_.ravel() for est in cv_results_vanilla_model["estimator"]],
columns=diabetes.feature_names,
)
tuned_model_coef = pd.DataFrame(
[est.estimator_[-1].coef_.ravel() for est in cv_results_tuned_model["estimator"]],
columns=diabetes.feature_names,
)
fig, ax = plt.subplots(ncols=2, figsize=(12, 4), sharex=True, sharey=True)
vanilla_model_coef.boxplot(ax=ax[0])
ax[0].set_ylabel("Coefficient value")
ax[0].set_title("Vanilla model")
tuned_model_coef.boxplot(ax=ax[1])
ax[1].set_title("Tuned model")
_ = fig.suptitle("Coefficients of the predictive models")
# %%
# Only the decision threshold of each model was changed during the cross-validation.
decision_threshold = pd.Series(
[est.best_threshold_ for est in cv_results_tuned_model["estimator"]],
)
ax = decision_threshold.plot.kde()
ax.axvline(
decision_threshold.mean(),
color="k",
linestyle="--",
label=f"Mean decision threshold: {decision_threshold.mean():.2f}",
)
ax.set_xlabel("Decision threshold")
ax.legend(loc="upper right")
_ = ax.set_title(
"Distribution of the decision threshold \nacross different cross-validation folds"
)
# %%
# In average, a decision threshold around 0.32 maximizes the balanced accuracy, which is
# different from the default decision threshold of 0.5. Thus tuning the decision
# threshold is particularly important when the output of the predictive model
# is used to make decisions. Besides, the metric used to tune the decision threshold
# should be chosen carefully. Here, we used the balanced accuracy but it might not be
# the most appropriate metric for the problem at hand. The choice of the "right" metric
# is usually problem-dependent and might require some domain knowledge. Refer to the
# example entitled,
# :ref:`sphx_glr_auto_examples_model_selection_plot_cost_sensitive_learning.py`,
# for more details.