pytorch實(shí)現(xiàn)多項(xiàng)式回歸

# 相較于一元線性回歸模型，多項(xiàng)式回歸可以很好的提高擬合精度，但要注意過(guò)擬合風(fēng)險(xiǎn)
# 多項(xiàng)式回歸方程 f(x) = -1.13x-2.14x^2+3.12x^3-0.01x^4+0.512
import torch
import matplotlib.pyplot as plt
import numpy as np
# 數(shù)據(jù)準(zhǔn)備(測(cè)試數(shù)據(jù))
x = torch.linspace(-2,2,50)
print(x.shape)
y = -1.13*x - 2.14*torch.pow(x,2) + 3.15*torch.pow(x,3) - 0.01*torch.pow(x,4) + 0.512
plt.scatter(x.data.numpy(),y.data.numpy())
plt.show()

# 此時(shí)輸入維度為4維
# 為了拼接輸入數(shù)據(jù)，需要編寫輔助數(shù)據(jù)，輸入標(biāo)量x,使其變?yōu)榫仃?，使用torch.cat拼接
def features(x): # 生成矩陣
    # [x,x^2,x^3,x^4]
    x = x.unsqueeze(1)
    print(x.shape)
    return torch.cat([x ** i for i in range(1,5)], 1)
result = features(x)
print(result.shape)
# 目標(biāo)公式用于計(jì)算輸入特征對(duì)應(yīng)的標(biāo)準(zhǔn)輸出
# 目標(biāo)公式的權(quán)重如下
x_weight = torch.Tensor([-1.13,-2.14,3.15,-0.01]).unsqueeze(1)
b = torch.Tensor([0.512])
# 得到x數(shù)據(jù)對(duì)應(yīng)的標(biāo)準(zhǔn)輸出
def target(x):
    return x.mm(x_weight) + b.item()

# 新建一個(gè)隨機(jī)生成輸入數(shù)據(jù)和輸出數(shù)據(jù)的函數(shù)，用于生成訓(xùn)練數(shù)據(jù)

def get_batch_data(batch_size):
    # 生成batch_size個(gè)隨機(jī)的x
    batch_x = torch.randn(batch_size)
    # 對(duì)于每個(gè)x要生成一個(gè)矩陣
    features_x = features(batch_x)
    target_y = target(features_x)
    return features_x,target_y

# 創(chuàng)建模型
class PolynomialRegression(torch.nn.Module):
    def __init__(self):
        super(PolynomialRegression, self).__init__()
        # 輸入四維度 輸出一維度
        self.poly = torch.nn.Linear(4,1)

    def forward(self, x):
        return self.poly(x)

# 開始訓(xùn)練模型
epochs = 10000
batch_size = 32
model = PolynomialRegression()
criterion = torch.nn.MSELoss()
optimizer = torch.optim.SGD(model.parameters(),0.001)

for epoch in range(epochs):
    print("{}/{}".format(epoch+1,epochs))
    batch_x,batch_y = get_batch_data(batch_size)
    out = model(batch_x)
    loss = criterion(out,batch_y)
    optimizer.zero_grad()
    loss.backward()
    # 更新梯度
    optimizer.step()
    if (epoch % 100 == 0):
        print("Epoch:[{}/{}]，loss:{:.6f}".format(epoch,epochs,loss.item()))
    if (epoch % 1000 == 0):
        predict = model(features(x))
        print(x.shape)
        print(predict.shape)
        print(predict.squeeze(1).shape)
        plt.plot(x.data.numpy(),predict.squeeze(1).data.numpy(),"r")
        loss = criterion(predict,y)
        plt.title("Loss:{:.4f}".format(loss.item()))
        plt.xlabel("X")
        plt.ylabel("Y")
        plt.scatter(x,y)
        plt.show()