深度学习之逻辑回归的实现--sigmoid
1 什么是逻辑回归
1.1逻辑回归与线性回归的区别：
线性回归预测的是⼀个连续的值，不论是单变量还是多变量（⽐如多层感知器），他都返回的是⼀个连续的值，放在图中就是条连续的曲线，他常⽤来表⽰的数学⽅法是Y=aX+b；
与之相对的，逻辑回归给出的值并不是连续的，⽽是类似于“是” 和 “否” 的回答，这就类似于⼆元分类的问题。
1.2逻辑回归实现（sigmoid）：
在逻辑回归算法中，我们常使⽤的激活函数是Sigmoid函数，他能够将数据映射到 0 到 1 之间，并且通过映射判断，如果映射到的值在1 ，就返回出⼀个正⾯的结果，与之相反，当映射的值为0时就返回⼀个负⾯的结果，这就是我们上⾯所提到的回答： “是”或“否”。那么，什么是Sigmoid函数呢？
Sigmoid函数是⼀种在⽣物学中常见的S型函数，也称为S型⽣长曲线，他的值我们可以看做是恒在 0 到 1 之间的（因为这段区间使我
们真正所关⼼的）。sigmoid的形式如下图所⽰：
深度学习⽹络本质上来说也是⼀种多层映射⽹络，当我们输⼊特征后，在通过如多层感知器的映射后，会⼀层层的映射到⼀个最终的形式。使⽤Sigmoid函数的意义就在于，他会在最后的映射中将结果映射成为0 到 1 之间的值，这时候我们就可以将映射后的值看做是神经⽹络给出的概率的结果。
1.3逻辑回归的常⽤损失函数（交叉熵）：
在线性回归中，我们常⽤ “m” （平⽅差）来进⾏损失的刻画，但是“m”⼀般来进⾏惩罚的是损失与原有的数据集在同⼀个数量级的情况，假如说数量级特别的庞⼤，但是损失值⽐较⼩，那么所得到的损失就会很⼩，不利于我们的训练。针对这种情形，我们在逻辑回归中（同时在⼤多数的⼆分类问题中）使⽤更有效的⽅法————交叉熵，他会给我们展现出⼀种更⼤的损失。下⾯这个图就直观的显⽰出了
L2（均⽅差）与logistic（交叉熵）之间关于在处理损失的差别。
在keras中，我们使⽤的函数是binary_crosntropy，下⾯会以⼀个例⼦的形式来使⽤交叉熵实现逻辑回归。
2逻辑回归的简单实现
这是⼀个关于信⽤卡是否存在欺诈⾏为的预测。
我们给出部分数据集，并查看是否为⼀个⼆分类问题
data = pd.read_csv('tensorflow_study\datat\credit-a.csv')
# 查看数据
print(data.head())
# 查看数据是否为⼆分类问题
print(data.iloc[:,-1].value_counts())
然后，我们取出数据，并建⽴⼀个神经⽹络模型，这⾥采⽤两个隐藏层，使得训练时拟合程度更⾼⼀些。
# 取出除了最后⼀列的所有数据
x = data.iloc[:, :-1]
# 取出数据并进⾏替换
y = data.iloc[:, -1].replace(-1,0)
# 模拟神经⽹络创建顺序模型，添加两个隐藏层
# 第⼀层是获取到的4个单元的隐藏层，数据集是15个数据的元组，使⽤relu激活
小小少年# 第⼆层是⼀个简单的数据处理层
# 第三层是输出层，使⽤Sigmoid进⾏激活，完成映射
model = tf.keras.Sequential(
[tf.keras.layers.Den(4,input_shape=(15,),activation='relu'),
tf.keras.layers.Den(4,activation='relu'),
tf.keras.layers.Den(1,activation='sigmoid')]
)天气冷图片
model.summary()
查看⼀下我们创建的模型是否符合我们的需求
再配置⼀个优化器，采⽤TensorFlow的梯度下降算法进⾏优化，使⽤交叉熵作为损失函数，并计算其正确率，开始训练我们的模型，再调⽤原始数据集中的前三个数据进⾏预测测试。
model.summary()
# 配置优化器
# 使⽤梯度下降算法进⾏优化，使⽤交叉熵作为损失函数，并计算其正确率
optimizer='adam',
loss='binary_crosntropy',
metrics=['acc']
)
# 训练模型
history = model.fit(x,y,epochs=100)
t_data = data.iloc[:3,:-1]
print(model.predict(t_data))
结果显⽽易见
这时候，我们也可以通过pandas进⾏对我们模型的训练过程进⾏可视化查看，⽅便我们能够更加准确的针对我们的模型训练做⼀些改进。
# 查看我们在训练过程中的loss和acc的变化情况
# 散点图展⽰数据
plt.figure(1)
ax1 = plt.subplot(2,1,1)
ax2 = plt.subplot(2,1,2)
plt.sca(ax1)
plt.title('loss ')
plt.plot(history.epoch,('loss'))
plt.sca(ax2)
plt.title('acc ')
plt.plot(history.epoch,('acc'))
plt.show()
在这⾥，我们就会明显的发现，当我们训练到18次的时候，loss的变化就趋于稳定状态了，⼆acc也是跟随着loss的稳定趋于更⼩的波动。
：：下⾯附上源码和数据
'''
@Author: mountain
@Date: 2020-03-30 16:11:00
@Description: 逻辑回归 --预测信⽤卡是否存在欺诈⾏为
'''
import pandas as pd
学习目标作文import matplotlib.pyplot as plt
import tensorflow as tf
data = pd.read_csv('tensorflow_study\datat\credit-a.csv')
# 查看数据
print(data.head())
# 查看数据是否为⼆分类问题
print(data.iloc[:,-1].value_counts())
# 取出除了最后⼀列的所有数据
x = data.iloc[:, :-1]
# 取出数据并进⾏替换
y = data.iloc[:, -1].replace(-1,0)
# 模拟神经⽹络创建顺序模型，添加两个隐藏层
# 第⼀层是获取到的4个单元的隐藏层，数据集是15个数据的元组，使⽤relu激活
# 第⼆层是⼀个简单的数据处理层
# 第三层是输出层，使⽤Sigmoid进⾏激活，完成映射
model = tf.keras.Sequential(
[tf.keras.layers.Den(4,input_shape=(15,),activation='relu'),
tf.keras.layers.Den(4,activation='relu'),
tf.keras.layers.Den(1,activation='sigmoid')]
)
model.summary()
# 配置优化器
# 使⽤梯度下降算法进⾏优化，使⽤交叉熵作为损失函数，并计算其正确率
optimizer='adam',
loss='binary_crosntropy',
metrics=['acc']
)
# 训练模型
history = model.fit(x,y,epochs=100)
t_data = data.iloc[:3,:-1]
print(model.predict(t_data))
# 查看我们在训练过程中的loss和acc的变化情况# 散点图展⽰数据
plt.figure(1)
ax1 = plt.subplot(2,1,1)
ax2 = plt.subplot(2,1,2)
plt.sca(ax1)
plt.title('loss ')
plt.plot(history.epoch,('loss')) plt.sca(ax2)
plt.title('acc ')
plt.plot(history.epoch,('acc')) plt.show()
ljhg
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三年级语文辅导
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1,18.83,9.5,0,0,9,0,1.625,0,0,6,0,0,40,600,-1
1,26.92,13.5,0,0,8,1,5,0,0,2,1,0,0,5000,-1
1,31.25,3.75,0,0,2,1,0.625,0,0,9,0,0,181,0,-1
1,56.5,16,0,0,4,7,0,0,0,15,1,0,0,247,-1
0,43,0.29,1,1,2,1,1.75,0,0,8,1,0,100,375,-1
0,22.33,11,0,0,9,0,2,0,0,1,1,0,80,278,-1
0,27.25,1.665,0,0,2,1,5.085,0,0,9,1,0,399,827,-1 0,32.83,2.5,0,0,2,1,2.75,0,0,6,1,0,160,2072,-1
