Python Logistic回归实战:正则化、概率评估与阈值选择

# 把标准化和Logistic回归封装在同一流水线中，防止信息泄漏pipe = Pipeline([    (”scale”, StandardScaler()),    (”model”, LogisticRegression(        solver=”liblinear”, max_iter=5000, random_state=SEED    ))])# C越小代表L2正则化越强，在对数尺度上设置候选值param_grid = {    ”model__C”: [0.01, 0.03, 0.1, 0.3, 1, 3, 10, 30, 100]}# 分层五折保持每折类别比例接近，并以ROC AUC选择参数cv = StratifiedKFold(n_splits=5, shuffle=True, random_state=SEED)search = GridSearchCV(    pipe, param_grid=param_grid, scoring=”roc_auc”,    cv=cv, n_jobs=1, return_train_score=True)search.fit(X_train, y_train)# 整理每个C的平均验证AUC和折间标准差results = pd.DataFrame(search.cv_results_)cv_summary = pd.DataFrame({    ”C”: results[”param_model__C”].astype(float),    ”mean_auc”: results[”mean_test_score”],    ”sd_auc”: results[”std_test_score”]}).sort_values(”C”)# 误差线展示五折之间的波动，虚线标出最终选择fig, ax = plt.subplots(figsize=(8.5, 5.3), dpi=160)ax.errorbar(    cv_summary[”C”], cv_summary[”mean_auc”],    yerr=cv_summary[”sd_auc”], marker=”o”,    linewidth=2, capsize=4, color=”#2468a2”)ax.axvline(    search.best_params_[”model__C”], linestyle=”--”, color=”#d95f02”,    label=f”Best C = {search.best_params_['model__C']}”)ax.set_xscale(”log”)ax.set_xlabel(”Inverse regularization strength (C)”)ax.set_ylabel(”5-fold validation ROC AUC”)ax.set_title(”Cross-validated regularization strength”)ax.legend(frameon=False)fig.tight_layout()plt.savefig(”logistic_cv.png”, bbox_inches=”tight”)plt.close()print(f”最佳C：{search.best_params_['model__C']}”)print(f”最佳五折AUC：{search.best_score_:.4f}”)print(cv_summary.sort_values(”mean_auc”, ascending=False).head(3).to_string(    index=False, float_format=lambda x: f”{x:.4f}”))

最佳C：3最佳五折AUC：0.9978      C  mean_auc  sd_auc 3.0000    0.9978  0.0025 1.0000    0.9978  0.002310.0000    0.9976  0.0027

# 对训练集生成折外概率，每个样本都由未见过它的模型预测oof_prob = cross_val_predict(    search.best_estimator_, X_train, y_train,    cv=cv, method=”predict_proba”, n_jobs=1)[:, 1]# 在训练集折外ROC上最大化Youden指数，测试集不参与选择fpr_oof, tpr_oof, thresholds = roc_curve(y_train, oof_prob)finite = np.isfinite(thresholds)youden = tpr_oof[finite] - fpr_oof[finite]best_threshold = thresholds[finite][np.argmax(youden)]# 网格搜索对象已经用最佳参数在完整训练集上重新拟合test_prob = search.best_estimator_.predict_proba(X_test)[:, 1]# 同一函数统一计算默认阈值与候选阈值下的分类指标def score_at(threshold):    pred = (test_prob >= threshold).astype(int)    tn, fp, fn, tp = confusion_matrix(y_test, pred).ravel()    return {        ”accuracy”: accuracy_score(y_test, pred),        ”precision”: precision_score(y_test, pred),        ”sensitivity”: recall_score(y_test, pred),        ”specificity”: tn / (tn + fp),        ”f1”: f1_score(y_test, pred),        ”tn”: tn, ”fp”: fp, ”fn”: fn, ”tp”: tp    }default_score = score_at(0.5)tuned_score = score_at(best_threshold)roc_auc = roc_auc_score(y_test, test_prob)ap = average_precision_score(y_test, test_prob)brier = brier_score_loss(y_test, test_prob)print(f”折外候选阈值：{best_threshold:.4f}”)print(f”测试集 ROC AUC：{roc_auc:.4f}”)print(f”测试集 AP：{ap:.4f}，Brier：{brier:.4f}”)print(f”阈值0.5：灵敏度={default_score['sensitivity']:.4f}，特异度={default_score['specificity']:.4f}”)print(f”候选阈值：灵敏度={tuned_score['sensitivity']:.4f}，特异度={tuned_score['specificity']:.4f}”)print(f”混淆矩阵 TN/FP/FN/TP：{tuned_score['tn']}/{tuned_score['fp']}/{tuned_score['fn']}/{tuned_score['tp']}”)

折外候选阈值：0.5228测试集 ROC AUC：0.9841测试集 AP：0.9830，Brier：0.0227阈值0.5：灵敏度=0.9623，特异度=0.9889候选阈值：灵敏度=0.9623，特异度=0.9889混淆矩阵 TN/FP/FN/TP：89/1/2/51

# 提取标准化后的模型系数，绝对值反映线性预测中的相对贡献coef = pd.Series(    search.best_estimator_.named_steps[”model”].coef_[0],    index=X.columns)top_coef = coef.reindex(coef.abs().sort_values(ascending=False).index).head(6)# 分别计算ROC、PR和分位数分箱校准曲线fpr, tpr, _ = roc_curve(y_test, test_prob)precision, recall, _ = precision_recall_curve(y_test, test_prob)prob_true, prob_pred = calibration_curve(    y_test, test_prob, n_bins=8, strategy=”quantile”)# 扫描一组阈值，观察灵敏度、特异度和F1的取舍threshold_grid = np.linspace(0.05, 0.95, 91)threshold_df = pd.DataFrame([    {”threshold”: t, **score_at(t)} for t in threshold_grid])# 四个子图分别回答排序、阳性预测、校准和阈值问题fig, axes = plt.subplots(2, 2, figsize=(10.4, 8.2), dpi=160)axes[0, 0].plot(fpr, tpr, color=”#2468a2”, linewidth=2,                label=f”AUC = {roc_auc:.3f}”)axes[0, 0].plot([0, 1], [0, 1], ”--”, color=”0.6”)axes[0, 0].set(xlabel=”False positive rate”, ylabel=”True positive rate”,               title=”ROC curve”)axes[0, 0].legend(frameon=False)axes[0, 1].plot(recall, precision, color=”#1b9e77”, linewidth=2,                label=f”AP = {ap:.3f}”)axes[0, 1].axhline(y_test.mean(), linestyle=”--”, color=”0.6”,                   label=f”Prevalence = {y_test.mean():.3f}”)axes[0, 1].set(xlabel=”Recall”, ylabel=”Precision”,               title=”Precision-recall curve”)axes[0, 1].legend(frameon=False)axes[1, 0].plot(prob_pred, prob_true, marker=”o”,                color=”#7570b3”, linewidth=2)axes[1, 0].plot([0, 1], [0, 1], ”--”, color=”0.6”)axes[1, 0].set(xlabel=”Mean predicted probability”,               ylabel=”Observed fraction”, title=”Calibration curve”)axes[1, 1].plot(threshold_df[”threshold”], threshold_df[”sensitivity”],                label=”Sensitivity”, color=”#d95f02”)axes[1, 1].plot(threshold_df[”threshold”], threshold_df[”specificity”],                label=”Specificity”, color=”#1b9e77”)axes[1, 1].plot(threshold_df[”threshold”], threshold_df[”f1”],                label=”F1”, color=”#2468a2”)axes[1, 1].axvline(best_threshold, linestyle=”--”, color=”0.25”,                   label=f”OOF threshold = {best_threshold:.2f}”)axes[1, 1].set(xlabel=”Decision threshold”, ylabel=”Metric”,               title=”Threshold trade-offs”)axes[1, 1].legend(frameon=False, fontsize=8)for ax in axes.ravel():    ax.set_xlim(left=0)fig.suptitle(”Independent test-set evaluation”, fontsize=14, y=1.01)fig.tight_layout()plt.savefig(”logistic_evaluation.png”, bbox_inches=”tight”)plt.close()print(”绝对系数最大的6个特征：”)for name, value in top_coef.items():    print(f”{name}: {value:.4f}”)

绝对系数最大的6个特征：worst texture: 2.4218worst radius: 1.7390worst area: 1.7367fractal dimension error: -1.5588worst perimeter: 1.3821area error: 1.3008