学习曲线(learning curve)来判断模型状态：过拟合欠拟合

学习曲线(learning curve)来判断模型状态：过拟合欠拟合

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学习曲线是什么

学习曲线是不同训练集大小，模型在训练集和验证集上的得分变化曲线。也就是以样本数为横坐标，训练和交叉验证集上的得分（如准确率）为纵坐标。learning curve可以帮助我们判断模型现在所处的状态：过拟合（overfiting / high variance） or 欠拟合（underfitting / high bias）
模型欠拟合、过拟合、偏差和方差平衡 时对应的学习曲线如下图所示：

怎么看学习曲线

左上角的图中训练集和验证集上的曲线能够收敛。在训练集合验证集上准确率相差不大，却都很差。这说明模拟对已知数据和未知都不能进行准确的预测，属于高偏差。这种情况模型很可能是欠拟合。可以针对欠拟合采取对应的措施。

右上角的图中模型在训练集上和验证集上的准确率差距很大。说明模型能够很好的拟合已知数据，但是泛化能力很差，属于高方差。模拟很可能过拟合，要采取过拟合对应的措施

怎么画学习曲线

官方学习曲线例子

import numpy as np
import matplotlib.pyplot as plt
from sklearn.naive_bayes import GaussianNB
from sklearn.svm import SVC
from sklearn.datasets import load_digits
from sklearn.model_selection import learning_curve
from sklearn.model_selection import ShuffleSplit


def plot_learning_curve(estimator, title, X, y, ylim=None, cv=None,
                        n_jobs=1, train_sizes=np.linspace(.1, 1.0, 5)):
    """
    画出data在某模型上的learning curve.
    参数解释
    ----------
    estimator : 你用的分类器。
    title : 表格的标题。
    X : 输入的feature，numpy类型
    y : 输入的target vector
    ylim : tuple格式的(ymin, ymax), 设定图像中纵坐标的最低点和最高点
    cv : 做cross-validation的时候，数据分成的份数，其中一份作为cv集，其余n-1份作为training(默认为3份)
    n_jobs : 并行的的任务数(默认1)
    """
    plt.figure()
    plt.title(title)
    if ylim is not None:
        plt.ylim(*ylim)
    plt.xlabel("Training examples")
    plt.ylabel("Score")
    train_sizes, train_scores, test_scores = learning_curve(
        estimator, X, y, cv=cv, n_jobs=n_jobs, train_sizes=train_sizes)
    train_scores_mean = np.mean(train_scores, axis=1)
    train_scores_std = np.std(train_scores, axis=1)
    test_scores_mean = np.mean(test_scores, axis=1)
    test_scores_std = np.std(test_scores, axis=1)
    plt.grid()

    plt.fill_between(train_sizes, train_scores_mean - train_scores_std,
                     train_scores_mean + train_scores_std, alpha=0.1,
                     color="r")
    plt.fill_between(train_sizes, test_scores_mean - test_scores_std,
                     test_scores_mean + test_scores_std, alpha=0.1, color="g")
    plt.plot(train_sizes, train_scores_mean, 'o-', color="r",
             label="Training score")
    plt.plot(train_sizes, test_scores_mean, 'o-', color="g",
             label="Cross-validation score")

    plt.legend(loc="best")
    plt.draw()
    plt.show()

    midpoint = ((train_scores_mean[-1] + train_scores_std[-1]) + (test_scores_mean[-1] - test_scores_std[-1])) / 2
    diff = (train_scores_mean[-1] + train_scores_std[-1]) - (test_scores_mean[-1] - test_scores_std[-1])
    return midpoint, diff


digits = load_digits()
X, y = digits.data, digits.target


title = "Learning Curves (Naive Bayes)"
# Cross validation with 100 iterations to get smoother mean test and train
# score curves, each time with 20% data randomly selected as a validation set.
cv = ShuffleSplit(n_splits=100, test_size=0.2, random_state=0)

estimator = GaussianNB()
plot_learning_curve(estimator, title, X, y, ylim=(0.7, 1.01), cv=cv, n_jobs=4)

title = "Learning Curves (SVM, RBF kernel, $\gamma=0.001$)"
# SVC is more expensive so we do a lower number of CV iterations:
cv = ShuffleSplit(n_splits=10, test_size=0.2, random_state=0)
estimator = SVC(gamma=0.001)
plot_learning_curve(estimator, title, X, y, (0.7, 1.01), cv=cv, n_jobs=4)

参考文献

用学习曲线 learning curve 来判别过拟合问题
机器学习系统模型调优实战–所有调优技术都附相应的scikit-learn实现
官方文档