1.从零开始实现线性回归
下面是用pytorch从零开始实现一个线性回归
import torch
from IPython import display
from matplotlib import pyplot as plt
import numpy as np
import random
# 生成数据集
# set input feature number
num_inputs = 2
# set example number
num_examples = 1000
# set true weight and bias in order to generate corresponded label
true_w = [2, -3.4]
true_b = 4.2
features = torch.randn(num_examples, num_inputs,
dtype=torch.float32)
labels = true_w[0] * features[:, 0] + true_w[1] * features[:, 1] + true_b
labels += torch.tensor(np.random.normal(0, 0.01, size=labels.size()),
dtype=torch.float32)
# 读取数据集
def data_iter(batch_size, features, labels):
num_examples = len(features)
indices = list(range(num_examples))
random.shuffle(indices) # random read 10 samples
for i in range(0, num_examples, batch_size):
j = torch.LongTensor(indices[i: min(i + batch_size, num_examples)]) # the last time may be not enough for a whole batch
yield features.index_select(0, j), labels.index_select(0, j)
# 模型参数初始化
w = torch.tensor(np.random.normal(0, 0.01, (num_inputs, 1)), dtype=torch.float32)
b = torch.zeros(1, dtype=torch.float32)
w.requires_grad_(requires_grad=True)
b.requires_grad_(requires_grad=True)
# 定义模型
def linreg(X, w, b):
return torch.mm(X, w) + b
# 定义损失函数
def squared_loss(y_hat, y):
return (y_hat - y.view(y_hat.size())) ** 2 / 2
# 定义优化函数
def sgd(params, lr, batch_size):
for param in params:
param.data -= lr * param.grad / batch_size # ues .data to operate param without gradient track
# 训练
# super parameters init
lr = 0.03
num_epochs = 5
net = linreg
loss = squared_loss
# training
for epoch in range(num_epochs): # training repeats num_epochs times
# in each epoch, all the samples in dataset will be used once
# X is the feature and y is the label of a batch sample
for X, y in data_iter(batch_size, features, labels):
l = loss(net(X, w, b), y).sum()
# calculate the gradient of batch sample loss
l.backward()
# using small batch random gradient descent to iter model parameters
sgd([w, b], lr, batch_size)
# reset parameter gradient
w.grad.data.zero_()
b.grad.data.zero_()
train_l = loss(net(features, w, b), labels)
print('epoch %d, loss %f' % (epoch + 1, train_l.mean().item()))
2.SoftMax相关知识
softmax是一种用来对于离散输出的衡量函数
softmax函数的不变性:
这是由于softmax函数的常数不变性,即,推导如下:
用这个性质可以处理一些梯度爆炸的问题
3.从零开始实现softmax
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import torch
import torchvision
import numpy as np
import sys
batch_size = 256
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)
num_inputs = 784
print(28*28)
num_outputs = 10
W = torch.tensor(np.random.normal(0, 0.01, (num_inputs, num_outputs)), dtype=torch.float)
b = torch.zeros(num_outputs, dtype=torch.float)
def softmax(X):
X_exp = X.exp()
partition = X_exp.sum(dim=1, keepdim=True)
# print("X size is ", X_exp.size())
# print("partition size is ", partition, partition.size())
return X_exp / partition # 这里应用了广播机制
def net(X):
return softmax(torch.mm(X.view((-1, num_inputs)), W) + b)
def cross_entropy(y_hat, y):
return - torch.log(y_hat.gather(1, y.view(-1, 1)))
def accuracy(y_hat, y):
return (y_hat.argmax(dim=1) == y).float().mean().item()
num_epochs, lr = 5, 0.1
# 本函数已保存在d2lzh_pytorch包中方便以后使用
def train_ch3(net, train_iter, test_iter, loss, num_epochs, batch_size,
params=None, lr=None, optimizer=None):
for epoch in range(num_epochs):
train_l_sum, train_acc_sum, n = 0.0, 0.0, 0
for X, y in train_iter:
y_hat = net(X)
l = loss(y_hat, y).sum()
# 梯度清零
if optimizer is not None:
optimizer.zero_grad()
elif params is not None and params[0].grad is not None:
for param in params:
param.grad.data.zero_()
l.backward()
if optimizer is None:
d2l.sgd(params, lr, batch_size)
else:
optimizer.step()
train_l_sum += l.item()
train_acc_sum += (y_hat.argmax(dim=1) == y).sum().item()
n += y.shape[0]
test_acc = evaluate_accuracy(test_iter, net)
print('epoch %d, loss %.4f, train acc %.3f, test acc %.3f'
% (epoch + 1, train_l_sum / n, train_acc_sum / n, test_acc))
train_ch3(net, train_iter, test_iter, cross_entropy, num_epochs, batch_size, [W, b], lr)