学习曲线

import matplotlib.pyplot as plt
import numpy as np
import statsmodels.api as sm
from sklearn.linear_model import LogisticRegression
from sklearn.model_selection import RepeatedStratifiedKFold, learning_curve
from sklearn.pipeline import make_pipeline
from sklearn.preprocessing import StandardScaler
from sklearn.tree import DecisionTreeClassifier

# Data: 6,366 married women (1974 survey); 1 = reports any extramarital affair
d = sm.datasets.fair.load_pandas().data
X = d.drop(columns="affairs")
y = (d["affairs"] > 0).astype(int)
cv = RepeatedStratifiedKFold(n_splits=5, n_repeats=2, random_state=0)
sizes = np.linspace(0.08, 1.0, 10)
models = {"Decision tree": DecisionTreeClassifier(random_state=0),
          "Logistic regression": make_pipeline(StandardScaler(), LogisticRegression(max_iter=1000))}

plt.rcParams["figure.constrained_layout.use"] = False   # manual margins leave room for the subtitle
fig, axes = plt.subplots(1, 2, figsize=(10, 5), sharey=True)
fig.subplots_adjust(left=0.08, right=0.97, top=0.80, bottom=0.12, wspace=0.12)
for ax, (name, model) in zip(axes, models.items()):
    n, train, valid = learning_curve(model, X, y, cv=cv, train_sizes=sizes, n_jobs=-1,
                                    shuffle=True, random_state=0)   # rows are sorted by outcome
    for scores, c, lab in [(train, "#8E8E93", "Training"), (valid, "#007AFF", "Cross-validated")]:
        m, s = scores.mean(axis=1), scores.std(axis=1)
        ax.fill_between(n, m - s, m + s, color=c, alpha=0.18, lw=0)
        ax.plot(n, m, color=c, lw=2.2, marker="o", ms=4)
        dy = 0.012 if lab == "Training" else -0.012
        ax.text(n[-1] + 80, m[-1] + dy, lab, va="center", fontsize=9.5, color=c, fontweight="semibold")
    gap = train.mean(axis=1)[-1] - valid.mean(axis=1)[-1]
    ax.annotate("", xy=(n[-1], valid.mean(axis=1)[-1]), xytext=(n[-1], train.mean(axis=1)[-1]),
                arrowprops=dict(arrowstyle="<->", color="#FF3B30", lw=1.2))
    ax.text(n[-1] - 100, valid.mean(axis=1)[-1] + (gap / 2 if gap > 0.05 else -0.04), f"gap {gap:.2f}",
            ha="right", va="center", fontsize=9.5, color="#FF3B30", fontweight="semibold")
    ax.set_title(name)
    ax.set_xlabel("Training observations")
    ax.set_xlim(0, n[-1] * 1.32)
axes[0].set_ylabel("Accuracy")
axes[0].set_ylim(0.5, 1.03)

fig.suptitle("The tree memorises its training set; the logistic regression plateaus with no gap",
             x=0.02, y=0.97, ha="left")
fig.text(0.02, 0.885, f"n = {len(y):,} women · majority-class baseline = {1 - y.mean():.2f} · "
         "5-fold × 2 repeats · lines = mean, bands = ±1 SD across folds",
         fontsize=9.5, color="#6E6E73")
plt.show()