Plot Monotonic Constraints¶
===================== Monotonic Constraints¶
This example illustrates the effect of monotonic constraints on a gradient boosting estimator.
We build an artificial dataset where the target value is in general positively correlated with the first feature (with some random and non-random variations), and in general negatively correlated with the second feature.
By imposing a monotonic increase or a monotonic decrease constraint, respectively, on the features during the learning process, the estimator is able to properly follow the general trend instead of being subject to the variations.
This example was inspired by the XGBoost documentation <https://xgboost.readthedocs.io/en/latest/tutorials/monotonic.html>_.
Imports for Monotonic Constraints in Gradient Boosting¶
Monotonic constraints enforce that the model’s prediction must be non-decreasing (constraint=1) or non-decreasing (constraint=-1) with respect to a specified feature, regardless of what patterns exist in the training data. The monotonic_cst parameter in HistGradientBoostingRegressor accepts a list (one constraint per feature) or a dictionary mapping feature names to constraints. During tree construction, each split is checked to ensure it does not violate the monotonicity requirement, effectively pruning the search space of valid splits.
When to use monotonic constraints: In many domains, prior knowledge dictates the direction of a feature’s effect – for example, house price should increase with square footage, or default risk should decrease with income. Without constraints, gradient boosting can fit spurious non-monotonic patterns caused by noise, confounders, or insufficient data in certain feature ranges. The PartialDependenceDisplay visualization clearly shows the difference: the unconstrained model captures both the true linear trend and the oscillatory noise (sin/cos components), while the constrained model smoothly follows only the monotonic trend. This produces more interpretable and trustworthy predictions, which is essential in regulated industries like finance and healthcare.
# Authors: The scikit-learn developers
# SPDX-License-Identifier: BSD-3-Clause
# %%
import matplotlib.pyplot as plt
import numpy as np
from sklearn.ensemble import HistGradientBoostingRegressor
from sklearn.inspection import PartialDependenceDisplay
rng = np.random.RandomState(0)
n_samples = 1000
f_0 = rng.rand(n_samples)
f_1 = rng.rand(n_samples)
X = np.c_[f_0, f_1]
noise = rng.normal(loc=0.0, scale=0.01, size=n_samples)
# y is positively correlated with f_0, and negatively correlated with f_1
y = 5 * f_0 + np.sin(10 * np.pi * f_0) - 5 * f_1 - np.cos(10 * np.pi * f_1) + noise
# %%
# Fit a first model on this dataset without any constraints.
gbdt_no_cst = HistGradientBoostingRegressor()
gbdt_no_cst.fit(X, y)
# %%
# Fit a second model on this dataset with monotonic increase (1)
# and a monotonic decrease (-1) constraints, respectively.
gbdt_with_monotonic_cst = HistGradientBoostingRegressor(monotonic_cst=[1, -1])
gbdt_with_monotonic_cst.fit(X, y)
# %%
# Let's display the partial dependence of the predictions on the two features.
fig, ax = plt.subplots()
disp = PartialDependenceDisplay.from_estimator(
gbdt_no_cst,
X,
features=[0, 1],
feature_names=(
"First feature",
"Second feature",
),
line_kw={"linewidth": 4, "label": "unconstrained", "color": "tab:blue"},
ax=ax,
)
PartialDependenceDisplay.from_estimator(
gbdt_with_monotonic_cst,
X,
features=[0, 1],
line_kw={"linewidth": 4, "label": "constrained", "color": "tab:orange"},
ax=disp.axes_,
)
for f_idx in (0, 1):
disp.axes_[0, f_idx].plot(
X[:, f_idx], y, "o", alpha=0.3, zorder=-1, color="tab:green"
)
disp.axes_[0, f_idx].set_ylim(-6, 6)
plt.legend()
fig.suptitle("Monotonic constraints effect on partial dependences")
plt.show()
# %%
# We can see that the predictions of the unconstrained model capture the
# oscillations of the data while the constrained model follows the general
# trend and ignores the local variations.
# %%
# .. _monotonic_cst_features_names:
#
# Using feature names to specify monotonic constraints
# ----------------------------------------------------
#
# Note that if the training data has feature names, it's possible to specify the
# monotonic constraints by passing a dictionary:
import pandas as pd
X_df = pd.DataFrame(X, columns=["f_0", "f_1"])
gbdt_with_monotonic_cst_df = HistGradientBoostingRegressor(
monotonic_cst={"f_0": 1, "f_1": -1}
).fit(X_df, y)
np.allclose(
gbdt_with_monotonic_cst_df.predict(X_df), gbdt_with_monotonic_cst.predict(X)
)