随机梯度下降的提前停止#

随机梯度下降是一种优化技术，它以随机方式最小化损失函数，并逐样本执行梯度下降步骤。特别是，它是一种非常有效的线性模型拟合方法。

作为一种随机方法，损失函数在每次迭代时不一定会减少，并且只能保证期望中的收敛。因此，监控损失函数的收敛可能很困难。

另一种方法是监控验证分数的收敛。在这种情况下，输入数据被分成训练集和验证集。然后在训练集上拟合模型，并根据在验证集上计算的预测分数来确定停止标准。这使我们能够找到足以构建模型的最小迭代次数，该模型可以很好地泛化到未见过的数据，并减少过度拟合训练数据的可能性。

如果 early_stopping=True，则会激活此提前停止策略；否则，停止标准仅使用整个输入数据的训练损失。为了更好地控制提前停止策略，我们可以指定一个参数 validation_fraction，它设置了我们留出来计算验证分数的输入数据集的比例。优化将继续进行，直到验证分数在最后 n_iter_no_change 次迭代中没有至少提高 tol。实际的迭代次数可在属性 n_iter_ 中找到。

此示例说明了如何在 SGDClassifier 模型中使用提前停止来实现与没有提前停止构建的模型几乎相同的精度。这可以显著减少训练时间。请注意，即使从早期迭代开始，不同停止标准之间的分数也会有所不同，因为某些训练数据会因验证停止标准而被排除在外。

No stopping criterion: .................................................
Training loss: .................................................
Validation score: .................................................

# Authors: Tom Dupre la Tour
#
# License: BSD 3 clause

import sys
import time

import matplotlib.pyplot as plt
import numpy as np
import pandas as pd

from sklearn import linear_model
from sklearn.datasets import fetch_openml
from sklearn.exceptions import ConvergenceWarning
from sklearn.model_selection import train_test_split
from sklearn.utils import shuffle
from sklearn.utils._testing import ignore_warnings


def load_mnist(n_samples=None, class_0="0", class_1="8"):
    """Load MNIST, select two classes, shuffle and return only n_samples."""
    # Load data from http://openml.org/d/554
    mnist = fetch_openml("mnist_784", version=1, as_frame=False)

    # take only two classes for binary classification
    mask = np.logical_or(mnist.target == class_0, mnist.target == class_1)

    X, y = shuffle(mnist.data[mask], mnist.target[mask], random_state=42)
    if n_samples is not None:
        X, y = X[:n_samples], y[:n_samples]
    return X, y


@ignore_warnings(category=ConvergenceWarning)
def fit_and_score(estimator, max_iter, X_train, X_test, y_train, y_test):
    """Fit the estimator on the train set and score it on both sets"""
    estimator.set_params(max_iter=max_iter)
    estimator.set_params(random_state=0)

    start = time.time()
    estimator.fit(X_train, y_train)

    fit_time = time.time() - start
    n_iter = estimator.n_iter_
    train_score = estimator.score(X_train, y_train)
    test_score = estimator.score(X_test, y_test)

    return fit_time, n_iter, train_score, test_score


# Define the estimators to compare
estimator_dict = {
    "No stopping criterion": linear_model.SGDClassifier(n_iter_no_change=3),
    "Training loss": linear_model.SGDClassifier(
        early_stopping=False, n_iter_no_change=3, tol=0.1
    ),
    "Validation score": linear_model.SGDClassifier(
        early_stopping=True, n_iter_no_change=3, tol=0.0001, validation_fraction=0.2
    ),
}

# Load the dataset
X, y = load_mnist(n_samples=10000)
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.5, random_state=0)

results = []
for estimator_name, estimator in estimator_dict.items():
    print(estimator_name + ": ", end="")
    for max_iter in range(1, 50):
        print(".", end="")
        sys.stdout.flush()

        fit_time, n_iter, train_score, test_score = fit_and_score(
            estimator, max_iter, X_train, X_test, y_train, y_test
        )

        results.append(
            (estimator_name, max_iter, fit_time, n_iter, train_score, test_score)
        )
    print("")

# Transform the results in a pandas dataframe for easy plotting
columns = [
    "Stopping criterion",
    "max_iter",
    "Fit time (sec)",
    "n_iter_",
    "Train score",
    "Test score",
]
results_df = pd.DataFrame(results, columns=columns)

# Define what to plot
lines = "Stopping criterion"
x_axis = "max_iter"
styles = ["-.", "--", "-"]

# First plot: train and test scores
fig, axes = plt.subplots(nrows=1, ncols=2, sharey=True, figsize=(12, 4))
for ax, y_axis in zip(axes, ["Train score", "Test score"]):
    for style, (criterion, group_df) in zip(styles, results_df.groupby(lines)):
        group_df.plot(x=x_axis, y=y_axis, label=criterion, ax=ax, style=style)
    ax.set_title(y_axis)
    ax.legend(title=lines)
fig.tight_layout()

# Second plot: n_iter and fit time
fig, axes = plt.subplots(nrows=1, ncols=2, figsize=(12, 4))
for ax, y_axis in zip(axes, ["n_iter_", "Fit time (sec)"]):
    for style, (criterion, group_df) in zip(styles, results_df.groupby(lines)):
        group_df.plot(x=x_axis, y=y_axis, label=criterion, ax=ax, style=style)
    ax.set_title(y_axis)
    ax.legend(title=lines)
fig.tight_layout()

plt.show()

脚本总运行时间：（0 分 33.878 秒）