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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：

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

# The class for plottingclass plot_diagram():# Constructordef __init__(self, X, Y, w, stop, go = False):start = w.dataself.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# Executordef __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 tensorsparameter_values_tensor = torch.tensor(self.parameter_values)loss_function_tensor = torch.tensor(self.Loss_function)# Plot using the tensorsplt.plot(parameter_values_tensor.numpy(), loss_function_tensor.numpy())plt.plot(self.parameter, self.error, 'ro')plt.xlabel("B")plt.figure()# Destructordef __del__(self):plt.close('all')

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

# Define a function for train the modeldef train_model(iter):LOSS=[]for epoch in range (iter):# make the prediction as we learned in the last labYhat = forward(X)# calculate the iterationloss = criterion(Yhat,Y)# plot the diagram for us to have a better ideagradient_plot(Yhat, w, loss.item(), epoch)# store the loss into listLOSS.append(loss.item())# backward pass: compute gradient of the loss with respect to all the learnable parametersloss.backward()# updata parametersw.data = w.data - lr * w.grad.data# zero the gradients before running the backward passw.grad.data.zero_()

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：

# The class for plot the diagramclass plot_error_surfaces(object):# Constructordef __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 = 0self.y = Y.numpy()self.x = X.numpy()for w1, b1 in zip(w, b):count2 = 0for w2, b2 in zip(w1, b1):Z[count1, count2] = np.mean((self.y - w2 * self.x + b2) ** 2)count2 += 1count1 += 1self.Z = Zself.w = wself.b = bself.W = []self.B = []self.LOSS = []self.n = 0if 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()# Setterdef set_para_loss(self, W, B, loss):self.n = self.n + 1self.W.append(W)self.B.append(B)self.LOSS.append(loss)# Plot diagramdef 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 diagramdef plot_ps(self):plt.subplot(121)plt.ylimplt.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()