莫烦PYTHON 关系拟合（回归）

pytorch中默认的数据输入格式：行是样本，列是特征/属性
autograd directly supports tensors
自动微分可以直接在tensor中进行，不需要将x，y转为variable
但是loss依旧是variable，打印其值为loss.data.numpy()

要点

我会这次会来见证神经网络是如何通过简单的形式将一群数据用一条线条来表示. 或者说, 是如何在数据当中找到他们的关系, 然后用神经网络模型来建立一个可以代表他们关系的线条.
回归训练的动态过程

建立伪数据集

我们创建一些假数据来模拟真实的情况. 比如一个一元二次函数: y = a * x^2 + b, 我们给 y 数据加上一点噪声来更加真实的展示它.

import torch
import matplotlib.pyplot as plt

x = torch.unsqueeze(torch.linspace(-1, 1, 100), dim=1)  # x data (tensor), shape=(100, 1)
y = x.pow(2) + 0.2*torch.rand(x.size())                 # noisy y data (tensor), shape=(100, 1)

# 画图
plt.scatter(x.data.numpy(), y.data.numpy())
plt.show()

训练网络

训练的步骤很简单, 如下:

# optimizer 是训练的工具
optimizer = torch.optim.SGD(net.parameters(), lr=0.2)  # 传入 net 的所有参数, 学习率
loss_func = torch.nn.MSELoss()      # 预测值和真实值的误差计算公式 (均方差)

for t in range(100):
    prediction = net(x)     # 喂给 net 训练数据 x, 输出预测值

    loss = loss_func(prediction, y)     # 计算两者的误差

    optimizer.zero_grad()   # 清空上一步的残余更新参数值
    loss.backward()         # 误差反向传播, 计算参数更新值
    optimizer.step()        # 将参数更新值施加到 net 的 parameters 上

可视化训练过程

为了可视化整个训练的过程, 更好的理解是如何训练, 我们如下操作:

import matplotlib.pyplot as plt

plt.ion()   # 画图
plt.show()

for t in range(200):

    ...
    loss.backward()
    optimizer.step()

    # 接着上面来
    if t % 5 == 0:
        # plot and show learning process
        plt.cla()
        plt.scatter(x.data.numpy(), y.data.numpy())
        plt.plot(x.data.numpy(), prediction.data.numpy(), 'r-', lw=5)
        plt.text(0.5, 0, 'Loss=%.4f' % loss.data.numpy(), fontdict={'size': 20, 'color':  'red'})
        plt.pause(0.1)

完整代码

"""
View more, visit my tutorial page: https://morvanzhou.github.io/tutorials/
My Youtube Channel: https://www.youtube.com/user/MorvanZhou
Dependencies:
torch: 0.4
matplotlib
"""
import torch
import torch.nn.functional as F
import matplotlib.pyplot as plt

# torch.manual_seed(1)    # reproducible

x = torch.unsqueeze(torch.linspace(-1, 1, 100), dim=1)  # x data (tensor), shape=(100, 1)
print(x)
print(type(x))
print(x.size())
y = x.pow(2) + 0.2*torch.rand(x.size())                 # noisy y data (tensor), shape=(100, 1)

# torch can only train on Variable, so convert them to Variable
# The code below is deprecated in Pytorch 0.4. Now, autograd directly supports tensors
# x, y = Variable(x), Variable(y)

# plt.scatter(x.data.numpy(), y.data.numpy())
# plt.show()


class Net(torch.nn.Module):
    def __init__(self, n_feature, n_hidden, n_output):
        super(Net, self).__init__()
        self.hidden = torch.nn.Linear(n_feature, n_hidden)   # hidden layer
        self.predict = torch.nn.Linear(n_hidden, n_output)   # output layer

    def forward(self, x):
        x = F.relu(self.hidden(x))      # activation function for hidden layer
        x = self.predict(x)             # linear output
        return x

net = Net(n_feature=1, n_hidden=10, n_output=1)     # define the network
print(net)  # net architecture

optimizer = torch.optim.SGD(net.parameters(), lr=0.2)
loss_func = torch.nn.MSELoss()  # this is for regression mean squared loss

plt.ion()   # something about plotting

for t in range(200):
    prediction = net(x)     # input x and predict based on x

    loss = loss_func(prediction, y)     # must be (1. nn output, 2. target)
    print('第',t,'的LOSS is :', loss.data.numpy())

    optimizer.zero_grad()   # clear gradients for next train
    loss.backward()         # backpropagation, compute gradients
    optimizer.step()        # apply gradients

    if t % 5 == 0:
        # plot and show learning process
        plt.cla()
        plt.scatter(x.data.numpy(), y.data.numpy())
        plt.plot(x.data.numpy(), prediction.data.numpy(), 'r-', lw=5)
        plt.text(0.5, 0, 'Loss=%.4f' % loss.data.numpy(), fontdict={'size': 20, 'color':  'red'})
        plt.pause(0.1)

plt.ioff()
plt.show()