pytorch:多项式回归

r囧r小猫 2022-01-31 01:53 368阅读 0赞

import numpy as np
    import torch
    from torch.autograd import Variable
    from torch import nn, optim
    import matplotlib.pyplot as plt
    
    # 设置字体为中文
    plt.rcParams['font.sans-serif'] = ['SimHei']
    plt.rcParams['axes.unicode_minus'] = False
    
    # 构造成次方矩阵
    def make_fertures(x):
        x = x.unsqueeze(1)
        return torch.cat([x ** i for i in range(1, 4)], 1)
    
    # y = 0.9+0.5*x+3*x*x+2.4x*x*x
    W_target = torch.FloatTensor([0.5, 3, 2.4]).unsqueeze(1)
    b_target = torch.FloatTensor([0.9])
    
    # 计算x*w+b
    def f(x):
        return x.mm(W_target) + b_target.item()
    
    
    def get_batch(batch_size=32):
        random = torch.randn(batch_size)
        random = np.sort(random)
        random = torch.Tensor(random)
        x = make_fertures(random)
        y = f(x)
        if (torch.cuda.is_available()):
            return Variable(x).cuda(), Variable(y).cuda()
        else:
            return Variable(x), Variable(y)
    
    # 多项式模型
    class poly_model(nn.Module):
        def __init__(self):
            super(poly_model, self).__init__()
            self.poly = nn.Linear(3, 1)  # 输入时3维，输出是1维
    
        def forward(self, x):
            out = self.poly(x)
            return out
    
    if torch.cuda.is_available():
        model = poly_model().cuda()
    else:
        model = poly_model()
    # 均方误差，随机梯度下降
    criterion = nn.MSELoss()
    optimizer = optim.SGD(model.parameters(), lr=1e-3)
    
    epoch = 0  # 统计训练次数
    ctn = []
    lo = []
    while True:
        batch_x, batch_y = get_batch()
        output = model(batch_x)
        loss = criterion(output, batch_y)
        print_loss = loss.item()
        optimizer.zero_grad()
        loss.backward()
        optimizer.step()
        ctn.append(epoch)
        lo.append(print_loss)
        epoch += 1
        if (print_loss < 1e-3):
            break
    
    print("Loss: {:.6f}  after {} batches".format(loss.item(), epoch))
    print(
        "==> Learned function: y = {:.2f} + {:.2f}*x + {:.2f}*x^2 + {:.2f}*x^3".format(model.poly.bias[0], model.poly.weight[0][0],
                                                                                       model.poly.weight[0][1],
                                                                                       model.poly.weight[0][2]))
    print("==> Actual function: y = {:.2f} + {:.2f}*x + {:.2f}*x^2 + {:.2f}*x^3".format(b_target[0], W_target[0][0],
                                                                                        W_target[1][0], W_target[2][0]))
    # 1.可视化真实数据
    predict = model(batch_x)
    x = batch_x.numpy()[:, 0]  # x~1 x~2 x~3
    plt.plot(x, batch_y.numpy(), 'ro')
    plt.title(label='可视化真实数据')
    plt.show()
    # 2.可视化拟合函数
    predict = predict.data.numpy()
    plt.plot(x, predict, 'b')
    plt.plot(x, batch_y.numpy(), 'ro')
    plt.title(label='可视化拟合函数')
    plt.show()
    # 3.可视化训练次数和损失
    plt.plot(ctn,lo)
    plt.xlabel('训练次数')
    plt.ylabel('损失值')
    plt.title(label='训练次数与损失关系')
    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：

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

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[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3Nvbmd4aWFvbGluZ2Jhb2Jhbw_size_16_color_FFFFFF_t_70 1]: /images/20220131/e923d7fcd36a44f787ef45a341eed264.png
[watermark_type_ZmFuZ3poZW5naGVpdGk_shadow_10_text_aHR0cHM6Ly9ibG9nLmNzZG4ubmV0L3Nvbmd4aWFvbGluZ2Jhb2Jhbw_size_16_color_FFFFFF_t_70 2]: /images/20220131/e06c1766ca0b4b3ab0409605421b7507.png