一、手动实现softmax回归
# 手动实现softmax回归
# %matplotlib inline
import torch
from d2l import torch as d2l
import matplotlib.pyplot as plt
from IPython import display
# 参数初始化：
batch_size = 256
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)
# 将28*28的图片展开成一维的784长度的向量
num_inputs = 784
num_outputs = 10
# 初始化参数w的一个784*10的矩阵，偏置项b是一个长度为10的向量
W = torch.normal(0,0.1,size=(num_inputs, num_outputs), requires_grad = True)
b = torch.zeros(num_outputs, requires_grad = True)
lr = 0.1
# 累加器
class Accumulator():
def __init__(self, n):
self.data = [0.0] * n
def add(self, *args):
# 以n=2为例，每次add(arg1, arg2),则data[0]+=arg1, data[1]+=arg2
self.data = [a + float(b) for a, b in zip(self.data, args)]
def reset(self):
self.data = [0.0] * len(self.data)
def __getitem__(self, idx):
return self.data[idx]
# 定义一个动画类
class Animator:
def __init__(self, xlabel=None, ylabel=None, legend=None,
xlim=None, ylim=None, xscale='linear', yscale='linear',
fmts=('-', 'm', 'g--', 'r:'), nrows=1, ncols=1, figsize=(3.5, 3.5)):
if legend is None:
legend = []
self.fig, self.axes = plt.subplots(nrows, ncols, figsize = figsize)
if nrows * ncols == 1: # 如果只有一个子图
self.axes = [self.axes, ] # 也处理成list，为和多子图的情况统一处理
# 设置第一个子图的参数
self.xlabel = xlabel
self.ylabel = ylabel
self.xlim = xlim
self.ylim = ylim
self.xscale = xscale
self.yscale = yscale
self.legend = legend
self.X, self.Y, self.fmts = None, None, fmts
def config_axes(self):
"""设置坐标轴"""
self.axes[0].set_xlabel(self.xlabel)
self.axes[0].set_ylabel(self.ylabel)
if self.xlim is not None:
self.axes[0].set_xlim(self.xlim)
if self.ylim is not None:
self.axes[0].set_ylim(self.ylim)
self.axes[0].set_xscale(self.xscale)
self.axes[0].set_yscale(self.yscale)
if self.legend:
self.axes[0].legend(self.legend)
# 添加数据点,x=epoch+1, y=metric[0]~~metric[n]
def add(self, x, y):
if not hasattr(y, '__len__'): # 如果y不可迭代
y = [y]
n = len(y)
if not hasattr(x, '__len__'):
x = [x] * n
if not self.Y: # self.Y维度是n(代表n种需要图示的y值)，每一个元素都是一个列表[第1次train的值,第2次...]
self.Y = [ [] for _ in range(n) ]
if not self.X:
self.X = [ [] for _ in range(n) ]
for i, (a, b) in enumerate(zip(x, y)):
if a is not None and b is not None:
self.X[i].append(a)
self.Y[i].append(b)
self.axes[0].cla() # 清除axes[0]的参数设置
for x, y, fmt in zip(self.X, self.Y, self.fmts):
self.axes[0].plot(x, y, fmt)
self.config_axes()
display.display(self.fig)
display.clear_output(wait=True)
# softmax函数，传入的是已经计算完的W*X(n*10)+b(10*1) = n*10的矩阵
# n代表样本的个数，10列对应着是10个种类的线性值
def softmax(X):
X_exp = torch.exp(X)
partition = X_exp.sum(1, keepdim=True) # 对每一行求和得到一个n*1的向量
return X_exp / partition # 利用广播机制对每行的10个元素除以该行的sum
# 模型函数,输入为训练数据(n*784)
def net(X):
# 先把训练数据X的列变为784，行数自动计算，这样保证了X为n*784的矩阵
# 再将X与W做点积得到n*10的矩阵传入给softmax
# 这样就返回了经过softmax化的n*10的矩阵
# 每一行的每个列就代表在这列种类下的概率
return softmax(torch.matmul(X.reshape((-1, W.shape[0])), W) + b)
# 交叉损失函数,输入y_hat是net得到的n*10的矩阵，y是n维度向量
# 通过遍历y_hat的1到n行，列=y[当前行号]来得到y_hat预测的概率(因为y是类别的idx)
def cross_entropy(y_hat, y):
# 得到对每个数据的真实类别的预测概率p(n*1)，再返回-log(p)
# 因为此时我们希望每个p都越大越好，因此p越大-logp越小，反之越大
return -torch.log(y_hat[range(len(y)), y])
# 计算y_hat中概率最大的类别预测正确的个数
def accuracy(y_hat, y):
# 如果y_hat是矩阵
if len(y_hat.shape) > 1 and y_hat.shape[1] > 1:
y_hat = y_hat.argmax(axis=1)
cmp = y_hat.type(y.dtype) == y
return float(cmp.type(y.dtype).sum())
# 评估一个数据迭代器的精度
def evaluate_iter(net, data_iter):
if isinstance(net, torch.nn.Module):
net.eval() # 如果net是nn中的模型，我就把net设置为评估模式，防止额外构建计算图
metric = Accumulator(2) # 创建存储2个data的累加器
with torch.no_grad():
for X, y in data_iter:
metric.add(accuracy(net(X), y), y.numel())
return metric[0] / metric[1]
# 自定义优化器
def updater(batch_size):
return d2l.sgd([W,b], lr, batch_size)
# 一个训练迭代周期
def train_epoch_ch3(net, train_iter, loss, updater): # updater是更新用的优化器
# 如果net是nn中的神经网络就开启训练模式
if isinstance(net, torch.nn.Module):
net.train()
# metric[0]:训练损失和, metric[1]:预测正确数量, metric[2]:样本总数
metric = Accumulator(3)
for X, y in train_iter:
y_hat = net(X) # 先取第一批data和label，得到预测的y_hat
l = loss(y_hat, y)
if isinstance(updater, torch.optim.Optimizer): # 如果优化器是torch框架的
updater.zero_grad()
l.mean().backward() # l.mean()等价于sum(l)/len(y) 牛的
updater.step()
else:
l.sum().backward()
updater(len(y))
metric.add(float(l.sum()), accuracy(y_hat, y), y.numel())
#返回平均训练损失和精度
return metric[0]/metric[2], metric[1]/metric[2]
def train_ch3(net, train_iter, test_iter, loss, num_epochs, updater):
animator = Animator(xlabel='epoch', xlim=[1, num_epochs], ylim=[0.3, 0.9],
legend=['train loss', 'train acc', 'test acc'])
for epoch in range(num_epochs):
train_metrics = train_epoch_ch3(net, train_iter, loss, updater)
test_acc = evaluate_iter(net, test_iter)
# 利用元组的拼接y=(train_tetrics, test_acc)
animator.add(epoch+1, train_metrics + (test_acc, )) # 这让调用add的时候保证了y是个元组，这样add会把这个元组转换成为list
train_loss, train_acc = train_metrics
assert train_loss < 0.9, train_loss
assert train_acc > 0.7 and train_acc <= 1, train_acc
assert test_acc > 0.7 and test_acc <= 1, train_acc
def predict_ch3(net, test_iter, n=6):
for X, y in test_iter:
break
trues = d2l.get_fashion_mnist_labels(y)
preds = d2l.get_fashion_mnist_labels(net(X).argmax(axis=1))
titles = [true +'\n' + pred for true, pred in zip(trues, preds)]
d2l.show_images(
X[0:n].reshape((n, 28, 28)), 1, n, titles=titles[0:n])
num_epochs = 10
train_ch3(net, train_iter, test_iter, cross_entropy, num_epochs, updater)训练过程：
二、利用pytorch框架实现softmax回归
# 利用pytorch框架实现softmax回归
import torch
from torch import nn
from d2l import torch as d2l
batch_size = 256
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)
def init_weights(m):
if type(m) == nn.Linear:
nn.init.normal_(m.weight, std=0.01)
# net构建了两个layer，第一层把输入的一个样本(1,28,28)展开成 (1,784)
# 第二层是一个接受(1,784)并且输出(1,10)的线性激活函数
net = nn.Sequential(nn.Flatten(), nn.Linear(784, 10))
net.apply(init_weights)
loss = nn.CrossEntropyLoss(reduction='none')
trainer = torch.optim.SGD(net.parameters(), lr=0.1)
num_epochs = 10
d2l.train_ch3(net, train_iter, test_iter, loss, num_epochs, trainer)训练过程：
