一 评价尺度
sklearn包含四种评价尺度
1 均方差（mean-squared-error）
2 平均绝对值误差（mean_absolute_error）
3 **可释方差得分（explained_variance_score） **
4 中值绝对误差（Median absolute error）
5 R2 决定系数（拟合优度）
- 模型越好：r2→1
- 模型越差：r2→0
二 逻辑斯蒂回归
1 概述
在逻辑斯蒂回归中，我们将会采用sigmoid函数作为激励函数，所以它被称为sigmoid回归或对数几率回归（logistic regression），需要注意的是，虽然带有回归，但事实上它并不是一种回归算法，而是一种分类算法。
优点:
1 它是直接对分类的可能性进行建模的，无需事先假设数据分布，这样就避免了假设分布不准确所带来的问题
2 其针对于分类的可能性进行建模的，所以它不仅能预测出类别，还可以得到属于该类别的概率
3 实现简单，易于理解和实现；计算代价不高，速度很快，存储资源低
4 数据量大就用逻辑斯蒂 数据量小，特征多，用SVM knn
缺点:
容易欠拟合，分类精度可能不高
线性回归与逻辑回归的区别
线性回归: 线性回归用来做回归预测,解决回归问题
根据几组已知数据和拟合函数训练其中未知参数，使得拟合损失达到最小。然后用所得拟合函数进行预测。
逻辑回归: 逻辑回归用于做二分类 , 解决分类问题
和拟合函数训练其中未知参数 , 使得对数似然函数最大。然后用所得的拟合函数进行二分类。
| 线性回归 | 逻辑回归 | |
|---|---|---|
| 目的 | 预测 | 分类 |
| 未知 | {0,1} | |
| 函数 | 拟合函数 | 预测函数 |
| 参数计算方式 | 最小二乘 | 最大似然估计 |
注意:
1 预测函数其实就是拟合函数做了一个逻辑函数的转换
2 最大似然估计是计算使得数据出现的可能性最大的参数，依仗的自然是Probability。而最小二乘是计算误差损失。因此两者不可混淆
(2) 本质的区分
逻辑回归就是对线性回归做了一个压缩，将y 的值从y∈(+∞,−∞)压缩到(0,1)。为什么简单的压缩就能将回归问题变成分类问题?
从数据说起，线性回归的样本的输出，都是连续值，y∈(+∞,−∞)而，逻辑回归中y∈{0,1}，只能取0和1。对于拟合函数也有本质上的差别：
\]
\]
线性回归拟合函数，的确是对f(x)的输出变量y的拟合，而逻辑回归的拟合函数是对为1类的样本概率拟合。
-
为什么采用1类的样本概率进行拟合,这里就要谈到logstic函数的本质
若要直接通过回归的方法去预测二分类问题， y 到底是0类还是1类，最好的函数是单位阶跃函数。然而单位阶跃函数不连续（GLM 的必要条件），而 logsitic 函数恰好接近于单位阶跃函数，且单调可微。于是希望通过该复合函数去拟合分类问题,产生：
于是，θTX=0就相当于是1类和0类的决策边界：
- \[当θTX>0，则有y>0.5；若θTX→+∞ ,则y→1 ，即y 为1类;
\] -
\[当θTX<0，则有y<0.5 ; 若θTX→−∞，则y→0，即 y 为0类。
\]这个时候就能看出区别来了，在线性回归中θTXθTX为预测值的拟合函数；而在逻辑回归中θTX=0为决策边界
因此利用Logistics回归进行分类的主要思想是：根据现有数据对分类边界线建立回归公式，以此进行分类。
三 Logistic Regression实战练习
实例: 手写数字分类
import numpy as np
import pandas as pd
from pandas import Series,DataFrame
import matplotlib.pyplot as plt
%matplotlib inline
# LogisticRegression虽然是线性回归模型，但是只能处理分类问题
# 概率模型，使用概率进行分类
from sklearn.linear_model import LogisticRegression
from sklearn.neighbors import KNeighborsClassifier
# 加载手写数字集
from sklearn import datasets
digits = datasets.load_digits() #
#输出 {'data': array([[ 0., 0., 5., ..., 0., 0., 0.],
[ 0., 0., 0., ..., 10., 0., 0.],
[ 0., 0., 0., ..., 16., 9., 0.],
...,
[ 0., 0., 1., ..., 6., 0., 0.],
[ 0., 0., 2., ..., 12., 0., 0.],
[ 0., 0., 10., ..., 12., 1., 0.]]),
'target': array([0, 1, 2, ..., 8, 9, 8]),
'target_names': array([0, 1, 2, 3, 4, 5, 6, 7, 8, 9]),
'images': array([[[ 0., 0., 5., ..., 1., 0., 0.],
[ 0., 0., 13., ..., 15., 5., 0.],
....
data = digits.data #(1797, 64) 表示1797条,一维64的矩阵
images = digits.images #(1797, 8, 8) 表示1797条,8*8的二维矩阵
display(data.shape,images.shape)
plt.imshow(images[0],cmap='gray')
plt.imshow(data[0].reshape((8,8)),cmap='gray') #将64一维转成8*8的二维矩阵实际都是表示一组数据
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# 对数据集进行拆分，得到训练集和测试集
from sklearn.model_selection import train_test_split
X_train,X_test,y_train,y_test = train_test_split(data,target,test_size=0.2,random_state=1)
#采用逻辑斯蒂回归模型与KNN
logistic = LogisticRegression()
knn = KNeighborsClassifier(n_neighbors=5)
#对knn与逻辑斯蒂进行训练
logistic.fit(X_train,y_train)
y1_ = logistic.predict(X_test)
knn.fit(X_train,y_train)
y2_ = knn.predict(X_test)
查看模型评分
# 分类模型可以查看准确率来对模型进行评价
# 直接用算法模型调用score方法来实现
logistic.score(X_test,y_test)
knn.score(X_test,y_test)
#输出 0.9694444444444444
0.9944444444444445
# 模型在测试集上评分特别高，但是在真实环境下准确率却很低，这叫病态
# 引起这种现象的原因，主要是算法训练的过度拟合
分类展示
# 展示分类的成果
# 取测试集的前100个数据
plt.figure(figsize=(12,16))
for i in range(100):
axes = plt.subplot(10,10,i+1)
img = X_test[i].reshape((8,8))
axes.imshow(img,cmap='gray')
axes.axis('off')
true = y_test[i]
knn_r = y2_[i]
logistic_r = y1_[i]
title = 'T:'+str(true)+'\nK:'+str(knn_r) + ' L:'+str(logistic_r)
axes.set_title(title)
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" 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# 对logistic函数进行调参，查看参数对结果的影响
# 超参 函数级别 knn n_neibors logistic pentily C
# 模型参数 f(x) = wx+b
logistic = LogisticRegression(C=0.5,penalty='l1')
logistic.fit(X_train,y_train)
logistic.score(X_test,y_test)
#0.975
人脸的自动补全
导包
import numpy as np
import pandas as pd
from pandas import Series,DataFrame
from sklearn.datasets import fetch_olivetti_faces
import matplotlib.pyplot as plt
%matplotlib inline
提取数据
faces = fetch_olivetti_faces()
data = faces.data
images = faces.images
target = faces.target
拆分测试训练集
from sklearn.linear_model import LinearRegression,Ridge,Lasso
from sklearn.neighbors import KNeighborsRegressor
# 拆分训练集和测试集
from sklearn.model_selection import train_test_split
# 每个人拿出9张照片做训练数据，拿出1张照片做测试数据
# 样本特征采用上半边脸，样本标签采用下半边脸
def train_test_split_face(data,test_size):
X_train = []
X_test = []
y_train = []
y_test = []
for i in range(40):
for j in range(10):
face = data[i*10+j]
up_face = face[:2048]
bottom_face = face[2048:]
if j < (1-test_size)*10:
# 保存为训练数据
X_train.append(up_face)
y_train.append(bottom_face)
else:
# 保存为测试数据
X_test.append(up_face)
y_test.append(bottom_face)
return np.array(X_train),np.array(X_test),np.array(y_train),np.array(y_test)
#训练集与测试集
X_train,X_test,y_train,y_test = train_test_split_face(data,test_size=0.1)
#拆分出的上下半边脸
plt.imshow(X_train[0].reshape((32,64)),cmap='gray')
plt.imshow(y_train[0].reshape((32,64)),cmap='gray')
训练模型
knn = KNeighborsRegressor()
linear = LinearRegression()
ridge = Ridge()
lasso = Lasso()
knn.fit(X_train,y_train)
linear.fit(X_train,y_train)
ridge.fit(X_train,y_train)
lasso.fit(X_train,y_train)
预测数据
# 预测所有数据
knn_y_ = knn.predict(X_test)
linear_y_ = linear.predict(X_test)
ridge_y_ = ridge.predict(X_test)
lasso_y_ = lasso.predict(X_test)
plt.figure(figsize=(10,4))
true_up_face = X_test[0]
true_bottom_face = y_test[0]
pre_bottom_face = knn_y_[0]
axes1 = plt.subplot(1,2,1)
true_face = np.concatenate((true_up_face,true_bottom_face))
axes1.imshow(true_face.reshape((64,64)),cmap='gray')
axes1.set_title('True')
axes2 = plt.subplot(1,2,2)
pre_face = np.concatenate((true_up_face,pre_bottom_face))
axes2.imshow(pre_face.reshape((64,64)),cmap='gray')
axes2.set_title('Predict')
results = np.array([knn_y_,ridge_y_,lasso_y_,linear_y_])
titles = np.array(['KNN','RIDGE','LASSO','LINEAR'])
plt.figure(figsize=(16,18))
for i in range(5):
true_up_face = X_test[i]
true_bottom_face = y_test[i]
true_face = np.concatenate((true_up_face,true_bottom_face)).reshape((64,64))
axes = plt.subplot(5,5,i*5+1)
axes.imshow(true_face,cmap='gray')
axes.set_title('True')
for index,y_ in enumerate(results):
axes = plt.subplot(5,5,i*5+1+index+1)
pre_bottom_face = y_[index]
pre_face = np.concatenate((true_up_face,pre_bottom_face)).reshape((64,64))
axes.imshow(pre_face,cmap='gray')
axes.set_title(titles[index])
数据量较少,仅为测试使用