为什么数据集的 SGD 损失与线性回归的 pytorch 代码与临时 python 代码不匹配？

Question

我正在尝试对葡萄酒数据集实施多元线性回归。但是当我将 Pytorch 的结果与 Python 的临时代码进行比较时，损失并不相同。

我的暂存代码：

功能：

def yinfer(X, beta):
  return beta[0] + np.dot(X,beta[1:]) 

def cost(X, Y, beta):
  sum = 0
  m = len(Y)
  for i in range(m): 
    sum = sum + ( yinfer(X[i],beta) - Y[i])*(yinfer(X[i],beta) - Y[i])
  return  sum/(1.0*m)

主要代码：

alpha = 0.005
b=[0,0.04086357 ,-0.02831656  ,0.09622949 ,-0.15162516  ,0.60188454  ,0.47528714,
  -0.6066466  ,-0.22995654 ,-0.58388734  ,0.20954669 ,-0.67851365]
beta = np.array(b)
print(beta)
iterations = 1000
arr_cost = np.zeros((iterations,2))
m = len(Y)
temp_beta = np.zeros(12)
for i in range(iterations):
  for k in range(m): 
        temp_beta[0] =  yinfer(X[k,:], beta) - Y[k]
        temp_beta[1:] = (yinfer(X[k,:], beta) - Y[k])*X[k,:]
        beta = beta - alpha*temp_beta/(1.0*m)    #(m*np.linalg.norm(temp_beta))
  arr_cost[i] = [i,cost(X,Y,beta)]
  #print(cost(X,Y,beta))
plt.scatter(arr_cost[0:iterations,0], arr_cost[0:iterations,1])

我使用了与 Pytorch 代码中使用的相同的权重

我的 Pytorch 代码：

class LinearRegression(nn.Module):
  def __init__(self,n_input_features):
    super(LinearRegression,self).__init__()
    self.linear=nn.Linear(n_input_features,1)
    # self.linear.weight.data=b.view(1,-1)
    self.linear.bias.data.fill_(0.0)
    nn.init.xavier_uniform_(self.linear.weight)
    # nn.init.xavier_normal_(self.linear.bias)
  def forward(self,x):
    y_predicted=self.linear(x)
    return y_predicted
model=LinearRegression(11)

criterion = nn.MSELoss()
num_epochs=1000
for epoch in range(num_epochs):
  for x,y in train_data:
    y_pred=model(x)
    loss=criterion(y,y_pred)
    # print(loss)
    loss.backward()
    optimizer.step()
    optimizer.zero_grad()

我的数据加载器：

class Data(Dataset):
    def __init__(self):
        self.x=x_train
        self.y=y_train
        self.len=self.x.shape[0]
    def __getitem__(self,index):
      return self.x[index],self.y[index]
    def __len__(self):
        return self.len
dataset=Data()
train_data=DataLoader(dataset=dataset,batch_size=1,shuffle=False)

有人可以告诉我为什么会发生这种情况或者我的代码中有任何错误吗？

Answer 1

代码需要进行一些调整。我还必须创建数据和优化器，而您没有提供这些。通过以下更改，两种方法都会产生学习函数。当然，两种方法之间的最佳超参数（例如alpha或 ）iterations可能有所不同，您可能需要单独找到它们。

# Create data:
import sklearn
X, Y = sklearn.datasets.load_diabetes(return_X_y=True)
# Adding a random column to match your data shape:
X = np.hstack((X, np.random.randn(X.shape[0], 1)))

iterations = 500

################
# Python version
def yinfer(X, beta):
    return beta[0] + np.dot(X,beta[1:]) 

def cost(X, Y, beta):
    sum = 0
    m = len(Y)
    for i in range(m): 
        sum = sum + ( yinfer(X[i], beta) - Y[i])*(yinfer(X[i], beta) - Y[i])
    return  sum/(1.0*m)

beta = np.array([0,0.04086357 ,-0.02831656  ,0.09622949 ,-0.15162516  ,0.60188454  ,0.47528714,
  -0.6066466  ,-0.22995654 ,-0.58388734  ,0.20954669 ,-0.67851365])
arr_cost = []
m = len(Y)
alpha = 0.1
temp_beta = np.zeros(12)
for i in range(iterations):
    for k in range(m): 
        temp_beta[0] =  yinfer(X[k,:], beta) - Y[k]
        temp_beta[1:] = (yinfer(X[k,:], beta) - Y[k])*X[k,:]
        beta = beta - alpha*temp_beta/(1.0*m)
    arr_cost.append(cost(X,Y,beta))

#################
# Pytorch version
from torch import nn
from torch import optim

class LinearRegression(nn.Module):
    def __init__(self,n_input_features):
        super(LinearRegression,self).__init__()
        self.linear=nn.Linear(n_input_features,1)
        self.linear.bias.data.fill_(0.0)
        nn.init.xavier_uniform_(self.linear.weight)
    def forward(self,x):
        y_predicted=self.linear(x)
        return y_predicted

class Data(Dataset):
    def __init__(self, x_train, y_train):
        self.x=x_train
        self.y=y_train
        self.len=self.x.shape[0]
    def __getitem__(self,index):
        return self.x[index],self.y[index]
    def __len__(self):
        return self.len
train_data=DataLoader(dataset=Data(X, Y),batch_size=1,shuffle=False)

criterion = nn.MSELoss()
model=LinearRegression(11)
optimizer = optim.SGD(model.parameters(), lr=0.01)

loss_vals = []  # store results
for epoch in range(iterations):
    for x, y in train_data:
        x, y = x.float(), y.float()
        y_pred=model.forward(x)
        loss=criterion(y, y_pred)
        loss.backward()
        optimizer.step()
        optimizer.zero_grad()
    loss_vals.append(float(loss))
    
##############
# Plot results
f, ax = plt.subplots(1,1, figsize=(20,5))
ax.plot(range(1, iterations+1), arr_cost, label='python')
ax.plot(range(1, iterations+1), loss_vals, label='torch')
ax.legend(); ax.set_xlabel('epochs'); ax.set_xlabel('loss');