第一：学习曲线
学习曲线是一种用来判断训练模型的一种方法，它会自动 把训练样本的数量按照预定的规则逐渐增加，然后画出不同训练样本数量时的模型准确度。
我们可以把Jtrain(theta) and Jtest(theta)作为纵坐标，画出与训练集数据集m的大小关系，这就是学习曲线。通过学习曲线，可以直观地观察到模型的准确性和训练数据大小的关系。 我们可以比较直观的了解到我们的模型处于一个什么样的状态，如：过拟合（overfitting）或欠拟合（underfitting）
如果数据集的大小为m，则通过下面的流程即可画出学习曲线：
1.把数据集分成训练数据集和交叉验证数据集（可以看作测试机）
2.取训练数据及的20%作为训练样本，训练出模型参数。
3.使用交叉验证数据集来计算训练出来的模型的准确性。
4.以续联数据及的准确性和交叉验证的准确性为纵坐标，训练数据集个数作为横坐标，在坐标轴上画出上述步骤计算出来的模型准确性。
5.训练数据集增加10%，调到步骤2，继续执行，知道训练数据集大小为100%。
第二：比较
参考链接：https://blog.csdn.net/u012328159/article/details/79255433
- learning_curve()：这个函数主要是用来判断（可视化）模型是否过拟合的，关于过拟合，就不多说了，具体可以看以前的博客：模型选择和改进
(X,y) = datasets.load_digits(return_X_y=True)
train_sizes,train_score,test_score = learning_curve(RandomForestClassifier(),X,y,train_sizes=[0.1,0.2,0.4,0.6,0.8,1],cv=10,scoring='accuracy')
train_error = 1- np.mean(train_score,axis=1)
test_error = 1- np.mean(test_score,axis=1)
plt.plot(train_sizes,train_error,'o-',color = 'r',label = 'training')
plt.plot(train_sizes,test_error,'o-',color = 'g',label = 'testing')
plt.legend(loc='best')
plt.xlabel('traing examples')
plt.ylabel('error')
plt.show()
- validation_curve()：这个函数主要是用来查看在参数不同的取值下模型的性能
(X,y) = datasets.load_digits(return_X_y=True)
# print(X[:2,:])
param_range = [10,20,40,80,160,250]
train_score,test_score = validation_curve(RandomForestClassifier(),X,y,param_name='n_estimators',param_range=param_range,cv=10,scoring='accuracy')
train_score = np.mean(train_score,axis=1)
test_score = np.mean(test_score,axis=1)
plt.plot(param_range,train_score,'o-',color = 'r',label = 'training')
plt.plot(param_range,test_score,'o-',color = 'g',label = 'testing')
plt.legend(loc='best')
plt.xlabel('number of tree')
plt.ylabel('accuracy')
plt.show()
第三：参数解释
from sklearn.model_selection import learning_curve
参数解释：参考：https://blog.csdn.net/gracejpw/article/details/102370364
image
X : array-like, shape (n_samples, n_features) Training vector, where n_samples is the number of samples and n_features is the number of features.
是一个m*n的矩阵，m:样品数量，n:特征数量
y : array-like, shape (n_samples) or (n_samples, n_features), optional Target relative to X for classification or regression; None for unsupervised learning.
是一个m*1的矩阵，m:样品数量，相对于X的目标进行分类或回归
groups : array-like, with shape (n_samples,), optional Group labels for the samples used while splitting the dataset into train/test set.
将数据集拆分为训练/测试集时使用的样本的标签分组。**[可选]**
**train_sizes **: array-like, shape (n_ticks,), dtype float or int Relative or absolute numbers of training examples that will be used to generate the learning curve. If the dtype is float, it is regarded as a fraction of the maximum size of the training set (that is determined by the selected validation method), i.e. it has to be within (0, 1]. Otherwise it is interpreted as absolute sizes of the training sets. Note that for classification the number of samples usually have to be big enough to contain at least one sample from each class. (default: np.linspace(0.1, 1.0, 5))
指定训练样品数量的变化规则。比如：np.linspace(0.1, 1.0, 5)表示把训练样品数量从0.1-1分成5等分，生成[0.1, 0.325,0.55,0.75,1]的序列，从序列中取出训练样品数量百分比，逐个计算在当前训练样本数量情况下训练出来的模型准确性。
**cv **: int, cross-validation generator or an iterable, optional Determines the cross-validation splitting strategy.
交叉验证拆分策略，可以使用sklearn.model_selection.ShuffleSplit
None，要使用默认的三折交叉验证（v0.22版本中将改为五折）
整数，用于指定（分层）KFold中的折叠数，
CV splitter
可迭代的集（训练，测试）拆分为索引数组。
对于整数/无输入，如果估计器是分类器，y是二进制或多类，则使用StratifiedKFold。在所有其他情况下，都使用KFold。
scoring：字符串，可调用或无，可选，默认：None，模型性能的评价指标，如（‘accuracy’、‘f1’、”mean_squared_error”等）
exploit_incremental_learning：布尔值，可选，默认值：False
如果估算器支持增量学习，此参数将用于加快拟合不同训练集大小的速度。
n_jobs：int或None，可选（默认=None）
要并行运行的作业数。None表示1。 -1表示使用所有处理器。
pre_dispatch：整数或字符串，可选
并行执行的预调度作业数（默认为全部）。该选项可以减少分配的内存。该字符串可以是“ 2 * n_jobs”之类的表达式。
shuffle：布尔值，可选
是否在基于``train_sizes’'为前缀之前对训练数据进行洗牌。
random_state：int，RandomState实例或无，可选（默认=None）
如果为int，则random_state是随机数生成器使用的种子；否则为false。如果是RandomState实例，则random_state是随机数生成器；如果为None，则随机数生成器是np.random使用的RandomState实例。在shuffle为True时使用。
error_score：‘raise’ | ‘raise-deprecating’ 或数字
如果估算器拟合中出现错误，则分配给分数的值。如果设置为“ raise”，则会引发错误。如果设置为“raise-deprecating”，则会在出现错误之前打印FutureWarning。如果给出数值，则引发FitFailedWarning。此参数不会影响重新安装步骤，这将始终引发错误。默认值为“不赞成使用”，但从0.22版开始，它将更改为np.nan。
返回值：
image
第四：使用
from sklearn.linear_model import LogisticRegression
from sklearn.model_selection import ShuffleSplit
from sklearn.model_selection import train_test_split
from sklearn.model_selection import learning_curve
from sklearn.preprocessing import PolynomialFeatures
from sklearn.pipeline import Pipeline
from sklearn.datasets import load_breast_cancer
import matplotlib.pyplot as plt
import numpy as np
import time
cancer = load_breast_cancer()
X = cancer.data
y = cancer.target
def polynomial_model(degree = 1, **kargs):
polynomial_features = PolynomialFeatures(degree = degree, include_bias = False)
logistic_regression = LogisticRegression(**kargs)
pipeline = Pipeline([("pf", polynomial_features),
("lr", logistic_regression)])
return pipeline
def plot_learning_curve(plt, estimator, title, X, y, ylim = None, cv = None, n_jobs = 1, train_size = np.linspace(0.1,1,5)):
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_size)
print("train_sizes:\n",train_sizes, "\ntrain_scores:\n",train_scores, "\ntest_scores:\n",test_scores)
train_scores_mean = np.mean(train_scores, axis = 1)
test_scores_mean = np.mean(test_scores, axis = 1)
train_scores_std = np.std(train_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")
return plt
cv = ShuffleSplit(n_splits = 10, test_size = 0.2, random_state = 0)
title = "Learning Curves (degreee={0}, penalty={1})"
degrees = [1,2]
penalty = ["l1", "l2"]
start = time.clock()
plt.figure(figsize = (12,4), dpi = 144)
j = 0
for p in penalty:
for i in range(len(degrees)):
plt.subplot(len(penalty), len(degrees), j + 1)
plot_learning_curve(plt, polynomial_model(degree = degrees[i], penalty = p), title.format(degrees[i], p), X, y, ylim = (0.8,1.01), cv = cv)
j += 1
plt.tight_layout()
plt.savefig("1.png")
learning_curve的返回值结果如下：
learning_curve返回结果展示
共选择了5组数据且选择了10折交叉验证，所以,train_sizes 为5个元素的narray,train_scores 和 test_scores为5*10的矩阵，每一行，为一次数据的每一折的结果，对其求平均值，作为最终的准确性。
第五：性能评估
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