Pytorch实现线性回归Linear Regression

借助 PyTorch 实现深度神经网络 - 线性回归 - 第 2 周 | Coursera

线性回归预测

用PyTorch实现线性回归模块

创建自定义模块（内含一个线性回归）

训练线性回归模型

对于线性回归，特定类型的噪声是高斯噪声

平均损失均方误差函数：

loss求解（导数=0）：

梯度下降

表示学习率

学习率过高，可能错过参数的最佳值

学习率过低，需要大量的迭代才能获得最小值

Batch Gradient Descent：使用整个训练集来更新模型的参数

用Pytorch实现线性回归--梯度

每个epoch就是一个iteration：

画图版：

python 复制代码

import torch
w=torch.tensor(-10.0,requires_grad=True)
X=torch.arange(-3,3,0.1).view(-1,1)
f=-3*X

python 复制代码

# The class for plotting

class plot_diagram():
    
    # Constructor
    def __init__(self, X, Y, w, stop, go = False):
        start = w.data
        self.error = []
        self.parameter = []
        print(type(X.numpy()))
        self.X = X.numpy()
       
        self.Y = Y.numpy()
        self.parameter_values = torch.arange(start, stop)
        self.Loss_function = [criterion(forward(X), Y) for w.data in self.parameter_values] 
        w.data = start
        
    # Executor
    def __call__(self, Yhat, w, error, n):
        self.error.append(error)
        self.parameter.append(w.data)
        plt.subplot(212)
        plt.plot(self.X, Yhat.detach().numpy())
        plt.plot(self.X, self.Y,'ro')
        plt.xlabel("A")
        plt.ylim(-20, 20)
        plt.subplot(211)
        plt.title("Data Space (top) Estimated Line (bottom) Iteration " + str(n))
        # Convert lists to PyTorch tensors
        parameter_values_tensor = torch.tensor(self.parameter_values)
        loss_function_tensor = torch.tensor(self.Loss_function)

        # Plot using the tensors
        plt.plot(parameter_values_tensor.numpy(), loss_function_tensor.numpy())
  
        plt.plot(self.parameter, self.error, 'ro')
        plt.xlabel("B")
        plt.figure()
    
    # Destructor
    def __del__(self):
        plt.close('all')

python 复制代码

gradient_plot = plot_diagram(X, Y, w, stop = 5)

python 复制代码

# Define a function for train the model

def train_model(iter):
    LOSS=[]
    for epoch in range (iter):
        
        # make the prediction as we learned in the last lab
        Yhat = forward(X)
        
        # calculate the iteration
        loss = criterion(Yhat,Y)
        
        # plot the diagram for us to have a better idea
        gradient_plot(Yhat, w, loss.item(), epoch)
        
        # store the loss into list
        LOSS.append(loss.item())
        
        # backward pass: compute gradient of the loss with respect to all the learnable parameters
        loss.backward()
        
        # updata parameters
        w.data = w.data - lr * w.grad.data
        
        # zero the gradients before running the backward pass
        w.grad.data.zero_()

python 复制代码

train_model(4)

用Pytorch实现线性回归--训练

与上文类似，只是多加了个b

梯度

画函数图：

python 复制代码

# The class for plot the diagram

class plot_error_surfaces(object):
    
    # Constructor
    def __init__(self, w_range, b_range, X, Y, n_samples = 30, go = True):
        W = np.linspace(-w_range, w_range, n_samples)
        B = np.linspace(-b_range, b_range, n_samples)
        w, b = np.meshgrid(W, B)    
        Z = np.zeros((30,30))
        count1 = 0
        self.y = Y.numpy()
        self.x = X.numpy()
        for w1, b1 in zip(w, b):
            count2 = 0
            for w2, b2 in zip(w1, b1):
                Z[count1, count2] = np.mean((self.y - w2 * self.x + b2) ** 2)
                count2 += 1
            count1 += 1
        self.Z = Z
        self.w = w
        self.b = b
        self.W = []
        self.B = []
        self.LOSS = []
        self.n = 0
        if go == True:
            plt.figure()
            plt.figure(figsize = (7.5, 5))
            plt.axes(projection='3d').plot_surface(self.w, self.b, self.Z, rstride = 1, cstride = 1,cmap = 'viridis', edgecolor = 'none')
            plt.title('Cost/Total Loss Surface')
            plt.xlabel('w')
            plt.ylabel('b')
            plt.show()
            plt.figure()
            plt.title('Cost/Total Loss Surface Contour')
            plt.xlabel('w')
            plt.ylabel('b')
            plt.contour(self.w, self.b, self.Z)
            plt.show()
    
    # Setter
    def set_para_loss(self, W, B, loss):
        self.n = self.n + 1
        self.W.append(W)
        self.B.append(B)
        self.LOSS.append(loss)
    
    # Plot diagram
    def final_plot(self): 
        ax = plt.axes(projection = '3d')
        ax.plot_wireframe(self.w, self.b, self.Z)
        ax.scatter(self.W,self.B, self.LOSS, c = 'r', marker = 'x', s = 200, alpha = 1)
        plt.figure()
        plt.contour(self.w,self.b, self.Z)
        plt.scatter(self.W, self.B, c = 'r', marker = 'x')
        plt.xlabel('w')
        plt.ylabel('b')
        plt.show()
    
    # Plot diagram
    def plot_ps(self):
        plt.subplot(121)
        plt.ylim
        plt.plot(self.x, self.y, 'ro', label="training points")
        plt.plot(self.x, self.W[-1] * self.x + self.B[-1], label = "estimated line")
        plt.xlabel('x')
        plt.ylabel('y')
        plt.ylim((-10, 15))
        plt.title('Data Space Iteration: ' + str(self.n))

        plt.subplot(122)
        plt.contour(self.w, self.b, self.Z)
        plt.scatter(self.W, self.B, c = 'r', marker = 'x')
        plt.title('Total Loss Surface Contour Iteration' + str(self.n))
        plt.xlabel('w')
        plt.ylabel('b')
        plt.show()