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Pytorch入门

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环境

Anaconda

Jupyter

优势在于可以即时运行，随时观察结果

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import torch
import numpy as np

基础知识

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# Vector
t1 = torch.tensor([1., 2, 3, 4])
t2 = torch.tensor([[11., 12], [21, 22], [31, 32]])

tensor([1., 2., 3., 4.])
tensor([[11., 12.],
[21., 22.],
[31., 32.]])

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# Matrix
x = np.array([[1, 2], [3, 4]])
y = torch.from_numpy(x)

线性回归

先看案例中的线性回归

Region Temp.(F) Rainfall(mm) Humidity(%) Apples(ton) Oranges(ton)
Kanto 73 67 43 56 70
Johto 91 88 64 81 101
Hoenn 87 134 58 119 133
Sinnoh 102 43 37 22 37
Unova 69 96 70 103 119

各地区因环境因素差异而造成苹果和橙子的产量差异

于是有以下线性回归方程用以预测水果产量，相对于不同水果，温度、降水、湿度分别予以不同的权重，外加一个偏差

$$yieldApple = w11 * temp + w12 * rainfall + w13 * humidity + b1$$
$$yieldOrange = w21 * temp + w22 * rainfall + w23 * humidity + b2$$

此刻，我们得到了

  1. 长度为5，宽度为3的输入
  2. 长度为5，宽度为2的输出
  3. 长度为3，宽度为2的权重
  4. 宽度为2的偏差
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# Input (temp, rainfall, humidity)
inputs = np.array([[73, 67, 43],
                   [91, 88, 64],
                   [87, 134, 58],
                   [102, 43, 37],
                   [69, 96, 70]], dtype='float32')

# Targets (apple, oranges)
inputs = np.array([[56, 70],
                   [81, 101],
                   [119, 133],
                   [22, 37],
                   [103, 119]], dtype='float32')

# Convert inputs and targets to tensors
inputs = torch.from_numpy(inputs)
targets = torch.from_numpy(targets)

# 权重和偏差从随机数开始
# Weights 
w = torch.randn(2, 3, requires_grad=True)
# Biases
b = torch.randn(2, requires_grad=True)

\begin {pmatrix}
1 & a_1 & a_1^2 & \cdots & a_1^n \
1 & a_2 & a_2^2 & \cdots & a_2^n \
\vdots & \vdots& \vdots & \ddots & \vdots \
1 & a_m & a_m^2 & \cdots & a_m^n
\end {pmatrix}

所以我们定义模型

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def model(input):
    return input @ w.t() + b

预测即为

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preds = model(inputs)

这里的权重和偏移是随机生成的，所以预测结果合不上很正常

损失函数

1.计算preds和targets之间的差异
2.平方差矩阵所有元素以消除负值
3.计算结果矩阵中元素的平均值
最终结果为均方误差MSE
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# MSE loss
def mse(t1, t2):
    diff = t1 - t2
    return torch.sum(diff * diff) / diff.numel()

# Compute loss
loss = mse(preds, targets)

计算梯度

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# Compute gradients
loss.backward()

计算权重梯度

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# Gradients for weights
w.grad

重置梯度

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# Reset the gradients
w.grad.zero_()
b.grad.zero_()
  1. 生成预测
  2. 计算损失
  3. 计算梯度w.r.t权重和偏差
  4. 通过减去与梯度成比例的小量来调整权重
  5. 将渐变重置为零
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# Train for 100 epochs
for _ in range(100):
    preds = model(inputs)
    loss = mse(preds, targets)
    loss.backward()
    with torch.no_grad():
        w -= w.grad * 1e-5
        b -= b.grad * 1e-5
        w.grad.zero_()
        b.grad.zero_()

总结

创建TensorDataset和DataLoader

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from torch.utils.data import TensorDataset
from torch.utils.data import DataLoader

batch_size = 5

train_ds = TensorDataset(inputs, targets)
train_dl = DataLoader(train_ds, batch_size, shuffle=True)
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class Net(nn.Module):
    def __init__(self):
        super(Net, self).__init__()
        self.linear = nn.Linear(1,1)

    def forward(self, x):
        out = self.linear(x)
        return out