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 positive (increasing) or negative (decreasing) constraint 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.

from sklearn.ensemble import HistGradientBoostingRegressor
from sklearn.inspection import PartialDependenceDisplay
import numpy as np
import matplotlib.pyplot as plt


rng = np.random.RandomState(0)

n_samples = 5000
f_0 = rng.rand(n_samples)  # positive correlation with y
f_1 = rng.rand(n_samples)  # negative correlation with y
X = np.c_[f_0, f_1]
noise = rng.normal(loc=0.0, scale=0.01, size=n_samples)
y = 5 * f_0 + np.sin(10 * np.pi * f_0) - 5 * f_1 - np.cos(10 * np.pi * f_1) + noise

fig, ax = plt.subplots()


# Without any constraint
gbdt = HistGradientBoostingRegressor()
gbdt.fit(X, y)
disp = PartialDependenceDisplay.from_estimator(
    gbdt,
    X,
    features=[0, 1],
    line_kw={"linewidth": 4, "label": "unconstrained", "color": "tab:blue"},
    ax=ax,
)

# With positive and negative constraints
gbdt = HistGradientBoostingRegressor(monotonic_cst=[1, -1])
gbdt.fit(X, y)

PartialDependenceDisplay.from_estimator(
    gbdt,
    X,
    features=[0, 1],
    feature_names=(
        "First feature\nPositive constraint",
        "Second feature\nNegtive constraint",
    ),
    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 illustration")

plt.show()