回顾

逻辑回归

数据

data

行为样本，列为feature。

Multiple Dimension Logistic Regression Model

简单的逻辑回归模型中一个样本为一个feature对应一个y hat，这里有8个feature，对应的也是一个y hat。所以每一个feature与权重w相乘加上偏置得到的结果才是我们想要的。这里使用了矩阵的乘法和python中的广播机制。

Mini-Batch (N samples)

Mini-Batch

根据矩阵乘法的对应关系，当输出为N×1维，输入为N×8维时，权重w的为8×1维。上面的Linear(8,1)的8和1分别对应着输入和输出的维数。

Linear Layer

Example: Artificial Neural Network

Artificial Neural Network

该神经网络共3层；第一层是8维到6维的非线性空间变换，第二层是6维到4维的非线性空间变换，第三层是4维到1维的非线性空间变换。

计算图

Example: Diabetes Prediction

Diabetes Prediction

Prepare Dataset

import numpy as np
import torch
import matplotlib.pyplot as plt
 
# prepare dataset
xy = np.loadtxt('diabetes.csv', delimiter=',', dtype=np.float32)
x_data = torch.from_numpy(xy[:, :-1]) # 第一个‘：’是指读取所有行，第二个‘：’是指从第一列开始，最后一列不要
y_data = torch.from_numpy(xy[:, [-1]]) # [-1] 最后得到的是个矩阵

Define Model

class Model(torch.nn.Module):
    def __init__(self):
        super(Model, self).__init__()
        self.linear1 = torch.nn.Linear(8, 6) # 第一层输入8维到6维
        self.linear2 = torch.nn.Linear(6, 4) # 第二层输入6维到4维
        self.linear3 = torch.nn.Linear(4, 1) # 第三层输入4维到1维
        self.sigmoid = torch.nn.Sigmoid() # 将其看作是网络的一层，而不是简单的函数使用
 
    def forward(self, x):
        x = self.sigmoid(self.linear1(x))
        x = self.sigmoid(self.linear2(x))
        x = self.sigmoid(self.linear3(x)) # y hat
        return x
  
model = Model()

Construct Loss and Optimizer

# construct loss and optimizer
# criterion = torch.nn.BCELoss(size_average = True)
criterion = torch.nn.BCELoss(reduction='mean')  
optimizer = torch.optim.SGD(model.parameters(), lr=0.1)

Training Cycle

epoch_list = []
loss_list = []
# training cycle forward, backward, update
for epoch in range(100):
    y_pred = model(x_data)
    loss = criterion(y_pred, y_data)
    print(epoch, loss.item())
    epoch_list.append(epoch)
    loss_list.append(loss.item())
 
    optimizer.zero_grad()
    loss.backward()
 
    optimizer.step()

代码

import numpy as np
import torch
import matplotlib.pyplot as plt
 
# prepare dataset
xy = np.loadtxt('diabetes.csv', delimiter=',', dtype=np.float32)
x_data = torch.from_numpy(xy[:, :-1]) # 第一个‘：’是指读取所有行，第二个‘：’是指从第一列开始，最后一列不要
y_data = torch.from_numpy(xy[:, [-1]]) # [-1] 最后得到的是个矩阵
 
# design model using class
 
 
class Model(torch.nn.Module):
    def __init__(self):
        super(Model, self).__init__()
        self.linear1 = torch.nn.Linear(8, 6) # 输入数据x的特征是8维，x有8个特征
        self.linear2 = torch.nn.Linear(6, 4)
        self.linear3 = torch.nn.Linear(4, 1)
        self.sigmoid = torch.nn.Sigmoid() # 将其看作是网络的一层，而不是简单的函数使用
 
    def forward(self, x):
        x = self.sigmoid(self.linear1(x))
        x = self.sigmoid(self.linear2(x))
        x = self.sigmoid(self.linear3(x)) # y hat
        return x
 
 
model = Model()
 
# construct loss and optimizer
# criterion = torch.nn.BCELoss(size_average = True)
criterion = torch.nn.BCELoss(reduction='mean')  
optimizer = torch.optim.SGD(model.parameters(), lr=0.1)
 
epoch_list = []
loss_list = []
# training cycle forward, backward, update
for epoch in range(100):
    y_pred = model(x_data)
    loss = criterion(y_pred, y_data)
    print(epoch, loss.item())
    epoch_list.append(epoch)
    loss_list.append(loss.item())
 
    optimizer.zero_grad()
    loss.backward()
 
    optimizer.step()
 
 
plt.plot(epoch_list, loss_list)
plt.ylabel('loss')
plt.xlabel('epoch')
plt.show()

结果

# 参数说明
# 第一层的参数：
layer1_weight = model.linear1.weight.data
layer1_bias = model.linear1.bias.data
print("layer1_weight", layer1_weight)
print("layer1_weight.shape", layer1_weight.shape)
print("layer1_bias", layer1_bias)
print("layer1_bias.shape", layer1_bias.shape)

作业-Try different activate function

import numpy as np
import torch
import matplotlib.pyplot as plt
 
# prepare dataset
xy = np.loadtxt('diabetes.csv', delimiter=',', dtype=np.float32)
x_data = torch.from_numpy(xy[:, :-1]) # 第一个‘：’是指读取所有行，第二个‘：’是指从第一列开始，最后一列不要
y_data = torch.from_numpy(xy[:, [-1]]) # [-1] 最后得到的是个矩阵
 
# design model using class
 
class Model(torch.nn.Module):
    def __init__(self):
        super(Model, self).__init__()
        self.linear1 = torch.nn.Linear(8, 6) # 输入数据x的特征是8维，x有8个特征
        self.linear2 = torch.nn.Linear(6, 4)
        self.linear3 = torch.nn.Linear(4, 1)
        self.activate = torch.nn.Hardsigmoid() # 将其看作是网络的一层，而不是简单的函数使用
 
    def forward(self, x):
        x = self.activate(self.linear1(x))
        x = self.activate(self.linear2(x))
        x = self.activate(self.linear3(x)) # y hat
        return x
 
 
model = Model()
 
# construct loss and optimizer
# criterion = torch.nn.BCELoss(size_average = True)
criterion = torch.nn.BCELoss(reduction='mean')  
optimizer = torch.optim.SGD(model.parameters(), lr=0.1)
 
epoch_list = []
loss_list = []
# training cycle forward, backward, update
for epoch in range(100):
    y_pred = model(x_data)
    loss = criterion(y_pred, y_data)
    print(epoch, loss.item())
    epoch_list.append(epoch)
    loss_list.append(loss.item())
 
    optimizer.zero_grad()
    loss.backward()
 
    optimizer.step()
 
 
plt.plot(epoch_list, loss_list)
plt.ylabel('loss')
plt.xlabel('epoch')
plt.title('Hardsigmoid')
plt.show()