•  目的：判断学习算法是否过拟合（高方差）或者欠拟合（高偏差）；

• 过拟合：模型中有太多自由度或参数，对未知数据泛化能力差；解决办法：增加训练样本或降低自由度或参数；

• 欠拟合：训练和预测精度都很差；解决办法：增加模型参数；

  
  

• learing curve:描述样本大小与测试精度和训练精度之间的关系；
  

training accuracy和validation accuracy 都随着training size而变化，但是在training accuracy 和 validation accuracy之间存在差值，所以模型具有轻微的过拟合；

import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
from sklearn.learning_curve import learning_curve
from sklearn.preprocessing import StandardScaler
from sklearn.decomposition import PCA
from sklearn.linear_model import LogisticRegression
from sklearn.pipeline import Pipeline
###############################################################################
df = pd.read_csv('http://archive.ics.uci.edu/ml/machine-learning-databases/breast-cancer-wisconsin/wdbc.data', header=None)
#将数据分成训练集和测试集
from sklearn.preprocessing import LabelEncoder
X = df.loc[:, 2:].values
y = df.loc[:, 1].values
le = LabelEncoder()
y = le.fit_transform(y)
#print(le.transform(['M', 'B']))
#将数据分成训练集和测试集
from sklearn.cross_validation import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2,random_state=1)
pipe_lr = Pipeline([
        ('scl', StandardScaler()),
        ('clf', LogisticRegression(penalty='l2', random_state=0))])
        
train_sizes, train_scores, test_scores = learning_curve(estimator=pipe_lr,
                              X=X_train,
                              y=y_train,
                              train_sizes=np.linspace(0.1,1.0,10),
                              cv=10,
                              n_jobs=1)
train_mean = np.mean(train_scores, axis=1)
train_std = np.std(train_scores, axis=1)
test_mean = np.mean(test_scores, axis=1)
test_std = np.std(test_scores, axis=1)
plt.plot(train_sizes, train_mean, color='blue', marker='o', markersize=5, label='training accuracy')
plt.fill_between(train_sizes, train_mean+train_std, train_mean-train_std,alpha=0.15,color='blue')
plt.plot(train_sizes, test_mean, color='green', linestyle='--',marker='s', markersize=5, label='validation accuracy')
plt.fill_between(train_sizes, test_mean+test_std, test_mean-test_std,alpha=0.15,color='green')
plt.grid()
plt.xlabel('Number of training samples')
plt.ylabel('Accuracy')
plt.legend(loc='lower right')
plt.ylim([0.9, 1.0])
plt.show()

• validation curve：描述准确率与模型参数之间的关系；

随着LogisticRegession正则化参数C的变化，training accuracy和validtion accuracy都发生变化；但最佳C值在0.1左右；

import matplotlib.pyplot as plt
import numpy as np
import pandas as pd
from sklearn.learning_curve import learning_curve
from sklearn.preprocessing import StandardScaler
from sklearn.decomposition import PCA
from sklearn.linear_model import LogisticRegression
from sklearn.pipeline import Pipeline
from sklearn.learning_curve import validation_curve
###############################################################################
df = pd.read_csv('http://archive.ics.uci.edu/ml/machine-learning-databases/breast-cancer-wisconsin/wdbc.data', header=None)
#将数据分成训练集和测试集
from sklearn.preprocessing import LabelEncoder
X = df.loc[:, 2:].values
y = df.loc[:, 1].values
le = LabelEncoder()
y = le.fit_transform(y)
#print(le.transform(['M', 'B']))
#将数据分成训练集和测试集
from sklearn.cross_validation import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.2,random_state=1)
###############################################################################
param_range = [0.001, 0.01, 0.1, 1.0, 10.0, 100.0]
pipe_lr = Pipeline([
        ('scl', StandardScaler()),
        ('clf', LogisticRegression(penalty='l2', random_state=0))])
train_scores, test_scores = validation_curve(estimator=pipe_lr,
                              X=X_train,
                              y=y_train,
                              param_name='clf__C',
                              param_range=param_range,
                              cv=10)
train_mean = np.mean(train_scores, axis=1)
train_std = np.std(train_scores, axis=1)
test_mean = np.mean(test_scores, axis=1)
test_std = np.std(test_scores, axis=1)
plt.plot(param_range, train_mean, color='blue', marker='o', markersize=5, label='training accuracy')
plt.fill_between(param_range, train_mean+train_std, train_mean-train_std,alpha=0.15,color='blue')
plt.plot(param_range, test_mean, color='green', linestyle='--',marker='s', markersize=5, label='validation accuracy')
plt.fill_between(param_range, test_mean+test_std, test_mean-test_std,alpha=0.15,color='green')
plt.grid()
plt.xscale('log')
plt.xlabel('Parameter C')
plt.ylabel('Accuracy')
plt.legend(loc='lower right')
plt.ylim([0.92, 1.0])
plt.show()

#参考《Python 机器学习》，作者：Sebastian Raschaka， 机械工业出版社；