pytorch:多项式回归

r囧r小猫 2022-01-31 01:53 394阅读 0赞 
  1. import numpy as np
  2. import torch
  3. from torch.autograd import Variable
  4. from torch import nn, optim
  5. import matplotlib.pyplot as plt
  7. # 设置字体为中文
  8. plt.rcParams['font.sans-serif'] = ['SimHei']
  9. plt.rcParams['axes.unicode_minus'] = False
  11. # 构造成次方矩阵
  12. def make_fertures(x):
  13.     x = x.unsqueeze(1)
  14.     return torch.cat([x ** i for i in range(1, 4)], 1)
  16. # y = 0.9+0.5*x+3*x*x+2.4x*x*x
  17. W_target = torch.FloatTensor([0.5, 3, 2.4]).unsqueeze(1)
  18. b_target = torch.FloatTensor([0.9])
  20. # 计算x*w+b
  21. def f(x):
  22.     return x.mm(W_target) + b_target.item()
  25. def get_batch(batch_size=32):
  26.     random = torch.randn(batch_size)
  27.     random = np.sort(random)
  28.     random = torch.Tensor(random)
  29.     x = make_fertures(random)
  30.     y = f(x)
  31.     if (torch.cuda.is_available()):
  32.         return Variable(x).cuda(), Variable(y).cuda()
  33.     else:
  34.         return Variable(x), Variable(y)
  36. # 多项式模型
  37. class poly_model(nn.Module):
  38.     def __init__(self):
  39.         super(poly_model, self).__init__()
  40.         self.poly = nn.Linear(3, 1)  # 输入时3维，输出是1维
  42.     def forward(self, x):
  43.         out = self.poly(x)
  44.         return out
  46. if torch.cuda.is_available():
  47.     model = poly_model().cuda()
  48. else:
  49.     model = poly_model()
  50. # 均方误差，随机梯度下降
  51. criterion = nn.MSELoss()
  52. optimizer = optim.SGD(model.parameters(), lr=1e-3)
  54. epoch = 0  # 统计训练次数
  55. ctn = []
  56. lo = []
  57. while True:
  58.     batch_x, batch_y = get_batch()
  59.     output = model(batch_x)
  60.     loss = criterion(output, batch_y)
  61.     print_loss = loss.item()
  62.     optimizer.zero_grad()
  63.     loss.backward()
  64.     optimizer.step()
  65.     ctn.append(epoch)
  66.     lo.append(print_loss)
  67.     epoch += 1
  68.     if (print_loss < 1e-3):
  69.         break
  71. print("Loss: {:.6f}  after {} batches".format(loss.item(), epoch))
  72. print(
  73.     "==> Learned function: y = {:.2f} + {:.2f}*x + {:.2f}*x^2 + {:.2f}*x^3".format(model.poly.bias[0], model.poly.weight[0][0],
  74.                                                                                    model.poly.weight[0][1],
  75.                                                                                    model.poly.weight[0][2]))
  76. print("==> Actual function: y = {:.2f} + {:.2f}*x + {:.2f}*x^2 + {:.2f}*x^3".format(b_target[0], W_target[0][0],
  77.                                                                                     W_target[1][0], W_target[2][0]))
  78. # 1.可视化真实数据
  79. predict = model(batch_x)
  80. x = batch_x.numpy()[:, 0]  # x~1 x~2 x~3
  81. plt.plot(x, batch_y.numpy(), 'ro')
  82. plt.title(label='可视化真实数据')
  83. plt.show()
  84. # 2.可视化拟合函数
  85. predict = predict.data.numpy()
  86. plt.plot(x, predict, 'b')
  87. plt.plot(x, batch_y.numpy(), 'ro')
  88. plt.title(label='可视化拟合函数')
  89. plt.show()
  90. # 3.可视化训练次数和损失
  91. plt.plot(ctn,lo)
  92. plt.xlabel('训练次数')
  93. plt.ylabel('损失值')
  94. plt.title(label='训练次数与损失关系')
  95. plt.show()

实验结果：

watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3Nvbmd4aWFvbGluZ2Jhb2Jhbw_size_16_color_FFFFFF_t_70

watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3Nvbmd4aWFvbGluZ2Jhb2Jhbw_size_16_color_FFFFFF_t_70 1

watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3Nvbmd4aWFvbGluZ2Jhb2Jhbw_size_16_color_FFFFFF_t_70 2

注意：批量产生数据后，进行一个排序，否则可视化时，不是按照x轴从小到大绘制，出现很多折线。对应代码：

  1. random = np.sort(random)
  2.  random = torch.Tensor(random)

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