比较在scikit-learn中调整超参数的方法

这篇文章是关于LogisticRegressionCV，GridSearchCV和cross_val_score之间的区别。请考虑以下设置：

import numpy as np
from sklearn.datasets import load_digits
from sklearn.linear_model import LogisticRegression, LogisticRegressionCV
from sklearn.model_selection import train_test_split, GridSearchCV, \
     StratifiedKFold, cross_val_score
from sklearn.metrics import confusion_matrix

read = load_digits()
X, y = read.data, read.target
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size = 0.3)

在惩罚逻辑回归中，我们需要设置控制正则化的参数C。scikit-learn中有3种通过交叉验证找到最佳C的方法。

Logistic回归

clf = LogisticRegressionCV (Cs = 10, penalty = "l1",
    solver = "saga", scoring = "f1_macro")
clf.fit(X_train, y_train)
confusion_matrix(y_test, clf.predict(X_test))

旁注：文档指出，SAGA和LIBLINEAR是L1惩罚的唯一优化器，而SAGA对于大型数据集则更快。不幸的是，热启动仅适用于Newton-CG和LBFGS。

GridSearchCV

clf = LogisticRegression (penalty = "l1", solver = "saga", warm_start = True)
clf = GridSearchCV (clf, param_grid = {"C": np.logspace(-4, 4, 10)}, scoring = "f1_macro")
clf.fit(X_train, y_train)
confusion_matrix(y_test, clf.predict(X_test))
result = clf.cv_results_

cross_val_score

cv_scores = {}
for val in np.logspace(-4, 4, 10):
    clf = LogisticRegression (C = val, penalty = "l1",
        solver = "saga", warm_start = True)
    cv_scores[val] = cross_val_score (clf, X_train, y_train,
        cv = StratifiedKFold(), scoring = "f1_macro").mean()

clf = LogisticRegression (C = max(cv_scores, key = cv_scores.get),
        penalty = "l1", solver = "saga", warm_start = True)
clf.fit(X_train, y_train)
confusion_matrix(y_test, clf.predict(X_test))

问题

我是否以3种方式正确执行了交叉验证？

这三种方式都等效吗？如果不是，是否可以通过更改代码使其等效？

就优雅，速度或任何标准而言，哪种方法最好？（换句话说，为什么在scikit-learn中有3种交叉验证方式？）

欢迎对任何一个问题提供简单的答案；我意识到它们有些长，但是希望它们是scikit-learn中超参数选择的一个很好的总结。