1.模型误差产生的原因
（1）模型无法表示基本数据的复杂度，而造成偏差。
（2）因模型对训练它所用到的数据过度敏感造成的方差。
2.由偏差造成的误差——准确率和欠拟合
有足够数据表示模型，但是由于模型不够复杂，不能捕捉基本关系，因而造成误差。
这样一来模型会系统的错误表示数据，从而导致准确率降低，这种现象叫做欠拟合。
简单说来就是模型不合适就会造成偏差。
3.方差造成的误差——精度和过拟合
在训练模型时，通常使用较大量数据的有限数据集，如果选择随机选择的数据子集不断对模型进行训练，可以预料它的预测结果会因提供给它的不同训练子集而不同。方差是用来衡量预测结果和所给的测试样本之间的差距。出现方差是正常的，但是方差过高说明该模型无法将预测结果泛化到更多数据。对训练集过渡敏感，称之为过拟合。高方差会导致训练集上效果很好，测试集上效果很差。
通常可以用更多数据来训练降低模型预测的方差，提高模型预测的准确率。如果没有很多数据，可以降低模型的复杂度来减小方差。
# In this exercise we'll examine a learner which has high variance, and tries to learn
# nonexistant patterns in the data.
# Use the learning curve function from sklearn.learning_curve to plot learning curves
# of both training and testing error.
# CODE YOU HAVE TO TYPE IN IS IN LINE 35
from sklearn.tree import DecisionTreeRegressor
import matplotlib.pyplot as plt
# PLEASE NOTE:
# In sklearn 0.18, the import would be from sklearn.model_selection import learning_curve
from sklearn.learning_curve import learning_curve # sklearn version 0.17
from sklearn.cross_validation import KFold
from sklearn.metrics import explained_variance_score, make_scorer
import numpy as np
# Set the learning curve parameters; you'll need this for learning_curves
size = 1000
cv = KFold(size,shuffle=True)
score = make_scorer(explained_variance_score)
# Create a series of data that forces a learner to have high variance
X = np.round(np.reshape(np.random.normal(scale=5,size=2*size),(-1,2)),2)
y = np.array([[np.sin(x[0]+np.sin(x[1]))] for x in X])
def plot_curve():
# Defining our regression algorithm
reg = DecisionTreeRegressor()
# Fit our model using X and y
reg.fit(X,y)
print "Regressor score: {:.4f}".format(reg.score(X,y))
# TODO: Use learning_curve imported above to create learning curves for both the
# training data and testing data. You'll need reg, X, y, cv and score from above.
train_sizes, train_scores, test_scores = learning_curve(reg,X,y,cv=cv,scoring=score)
# Taking the mean of the test and training scores
train_scores_mean = np.mean(train_scores,axis=1)
test_scores_mean = np.mean(test_scores,axis=1)
# Plotting the training curves and the testing curves using train_scores_mean and test_scores_mean
plt.plot(train_sizes ,train_scores_mean,'-o',color='b',label="train_scores_mean")
plt.plot(train_sizes,test_scores_mean ,'-o',color='r',label="test_scores_mean")
# Plot aesthetics
plt.ylim(-0.1, 1.1)
plt.ylabel("Curve Score")
plt.xlabel("Training Points")
plt.legend(bbox_to_anchor=(1.1, 1.1))
plt.show()
