Pytorch:多项式回归

1.目标

拟合函数 $ f(x)=2x_{1}^{3}+3x_2^2+4x_3+0.5 $

2.理论

原理和一维线性回归以及多维线性回归差不多，只不过次数更高。

3.实现

3.1 环境

python == 3.6
torch == 1.4

3.2 构造数据

# 这个是目标权重和偏置
w = torch.FloatTensor([2.0, 3.0, 4.0]).unsqueeze(1)
b = torch.FloatTensor([0.5])

def create_data(batch_size=32):
    random = torch.randn(batch_size)
    random = random.unsqueeze(1)  # 添加一个维度
    # 纵向连接tensor
    x = torch.cat([random**i for i in range(1,4)], 1)
    # 矩阵乘法
    y = x.mm(w) + b[0]
    if torch.cuda.is_available():
        return x.cuda(), y.cuda()
    return x, y

3.3 构造模型并创建对象

class PloyRegression(nn.Module):
    def __init__(self):
        super(PloyRegression, self).__init__()
        self.ploy = nn.Linear(3,1)
        
    def forward(self, x):
        out = self.ploy(x)
        return out

model = PloyRegression()
if torch.cuda.is_available():
    model = model.cuda()

3.4 选择优化器

criterion = nn.MSELoss()
optimizer = optim.SGD(model.parameters(), lr=1e-3)

这里使用的是均方误差，使用随机梯度下降，学习率为0.001.

3.5 开始训练

epoch = 0
while True:
    # 创建数据
    batch_x, batch_y = create_data()
    # 前向传播
    output = model(batch_x)
    # 损失计算
    loss = criterion(output, batch_y)
    # 获取损失值
    loss_value = loss.data.cpu().numpy()
    # 梯度置零
    optimizer.zero_grad()
    # 反向传播
    loss.backward()
    # 更新参数
    optimizer.step()
    
    epoch += 1
    if loss_value < 1e-3:
        break
    # 每100步打印一次损失
    if (epoch+1)%100==0:
        print("Epoch{}, loss:{:.6f}".format(epoch+1, loss_value))

3.6 验证结果

model.eval()  # 开启验证模式

# 构造数据
x_train = np.array([[2.167],[3.1],[3.3],[4.168],[4.4],[5.313],[5.5],[6.182],[6.7],[6.9],[7.042],[7.59],[7.997],[9.779],[10.791]], dtype=np.float32)
x_train = torch.from_numpy(x_train)

x = torch.cat([x_train**i for i in range(1,4)], 1)
y = x.mm(w) + b
# 绘制数据点
plt.plot(x_train.numpy(),y.numpy(),'ro') 
# 提取拟合参数
w_get = model.ploy.weight.data.T
b_get = model.ploy.bias.data
print('w:{},b:{}'.format(w_get.cpu().numpy(), b_get.cpu().numpy()))
# 计算预测值
Y_get = x.mm(w_get.cpu())  + b_get.cpu()
plt.plot(x_train.numpy(), Y_get.numpy(), '-')
plt.show()

# print:w:[[1.9365442],[2.9985998],[4.012949 ]],b:[0.5068841]

4.意见建议欢迎留言