多项式回归
import torch import numpy def make_features(x): '''获取 [x, x^2, x^3]...的矩阵''' x = x.unsqueeze(1) #将一维数据变为（n，1）二维矩阵形式 return torch.cat([x ** i for i in range(1, 4)], 1) #按列拼接 def f(x): W_target = torch.Tensor([0.5, 3., 2.4]).unsqueeze(1) b_target = torch.Tensor([0.9]) return x.mm(W_target) + b_target # 表达式：f(x) = X * W_target + b_target batch_size=32 random = torch.randn(batch_size) def get_batch(batch_size=32): ''' 获取32个数据对:(x, f(x)) ''' # random = torch.randn(batch_size) x = make_features(random) y = f(x) return torch.autograd.Variable(x), torch.autograd.Variable(y) class poly_model(torch.nn.Module): ''' 定义多项式模型 ''' def __init__(self): super(poly_model, self).__init__() self.poly = torch.nn.Linear(3,1) #输入3维[x, x^2, x^3]，输出1维y def forward(self, x): out = self.poly(x) return out model = poly_model() criterion = torch.nn.MSELoss() optimizer = torch.optim.SGD(model.parameters(), lr=1e-3) epoch = 0 #get data batch_x, batch_y = get_batch() while True: #forward out = model(batch_x) loss = criterion(out, batch_y) print_loss = loss.data optimizer.zero_grad() loss.backward() optimizer.step() epoch += 1 if print_loss < 1e-2: print('epoch:',epoch) break print(list(model.parameters())) #打印最后学习到的参数w, b学习结果如下：
epoch: 1179 [Parameter containing: tensor([[0.5059, 3.0444, 2.3960]], requires_grad=True), Parameter containing: tensor([0.7748], requires_grad=True)]绘制曲线：
import matplotlib.pyplot as plt model.eval() predict = model(torch.autograd.Variable(batch_x)) predict = predict.data.numpy() plt.plot(sorted(random), sorted(batch_y.numpy()), 'ro', label='real curve') plt.plot(sorted(random), sorted(predict.flatten()), label= 'Fitting curve') plt.legend() plt.show()