我是否在 pytorch 中使用多项式回归?

Question

我正在尝试通过pytorch进行多项式回归。首先，我只尝试线性回归(b + wx(。

model_1 = RegressionModel()
W = torch.zeros(1, requires_grad=True)
b = torch.zeros(1, requires_grad = True)
optimizer_1 = torch.optim.SGD([W, b], lr = 0.001)
x_train = torch.FloatTensor(dataset.x_data['LSTAT'])
y_train = torch.FloatTensor(dataset.data['target'])
nb_epochs = 10000
for epoch in range(nb_epochs + 1):
hypothesis = x_train * W + b
cost = torch.nn.functional.mse_loss(hypothesis, y_train.float())
optimizer_1.zero_grad()
cost.backward()
optimizer_1.step()
print('Epoch {:4d}/{} W: {:.3f}, b: {:.3f}, Cost: {:.6f}'.format(epoch, 
nb_epochs, W.item(), b.item(), cost.item()))

然后我更改并添加了一些变量来做多项式回归(b + w1x + w2x^2(

model_2 = RegressionModel()
W1 = torch.zeros(1, requires_grad=True) 
W2 = torch.zeros(1, requires_grad=True) 
b = torch.zeros(1, requires_grad = True)
optimizer_2 = torch.optim.SGD([W2, W1, b], lr = 0.0000099)
x_train = torch.FloatTensor(dataset.x_data['LSTAT'])
y_train = torch.FloatTensor(dataset.data['target'])
nb_epochs = 10000
for epoch in range(nb_epochs + 1):
hypothesis = b + x_train * W1 + x_train * x_train * W2
cost = torch.nn.functional.mse_loss(hypothesis, y_train.float())
optimizer_2.zero_grad()
cost.backward()
optimizer_2.step()
print('Epoch {:4d}/{} W1: {:.3f}, W2: {:.3f}, b: {:.3f}, Cost: 
{:.6f}'.format(epoch, nb_epochs, W1.item(), W2.item(), b.item(), 
cost.item()))

我可以尝试这样的多项式回归吗？如果没有，如果您让我知道，我将不胜感激。我真的是菜鸟...

Answer 1

你的代码应该可以工作了。处理较大的数据时，如果在单个矩阵运算中进行回归会更有效。为此，您需要首先预先计算输入要素的多项式：

x_train_polynomial = torch.stack([x_train, x_train ** 2], dim=1)

要保存某些线条，可以将投影重写为线性图层：

import torch.nn as nn
projection = nn.Linear(2, 1, bias=True)

在训练循环中，您可以调用：

hypothesis = projection(x_train_polynomial)