softmax回归的从零实现（附代码）

softmax回归是一个多分类模型，但是他跟线性回归一样将输入特征与权重做线性叠加，与线性不同的是他有多个输出，输出的个数对应分类标签的个数，比如四个特征和三种输出动物类别，则权重包含12个标量（带下标的w），偏差包含三个标量（带下标的b），且对每个输入计算o1,o2,o3

然后再对这些输出值进行softmax‘运算，softmax也是单层模型

import torch
from IPython import display
from d2l import torch as d2l


batch_size=256
train_iter, test_iter = d2l.load_data_fashion_mnist(batch_size)




#初始化模型参数
num_inputs = 784
num_outputs = 10
w = torch.normal(0,0.01,size=(num_inputs,num_outputs),requires_grad=True)
b = torch.zeros(num_outputs,requires_grad=True)




X = torch.tensor([[1.,2.,3.],[4.,5.,6.]])
X.sum(0,keepdim=True),X.sum(1,keepdim=True)





   Output:  (tensor([[5., 7., 9.]]),
             tensor([[ 6.],
                    [15.]]))





#定义softmax回归
def softmax(X):
    X_exp = torch.exp(X)
    partition = X_exp.sum(1,keepdim=True)
    return X_exp/partition#这里应用了广播机制


x= torch.normal(0,1,(2,5))
x_prob= softmax(x)
x_prob,x_prob.sum(1)





 Output:   (tensor([[0.0902, 0.0850, 0.2683, 0.1946, 0.3619],
             [0.0551, 0.4104, 0.2667, 0.1486, 0.1192]]),
            tensor([1., 1.]))



#实现softmax回归
def net(X):
    return softmax(torch.matmul(X.reshape((-1,w.shape[0])),w)+b)




y = torch.tensor([0,2])
y_hat= torch.tensor([[0.1,0.3,0.6],[0.3,0.3,0.5]])
y_hat[[0,1],y]





 Output:   tensor([0.1000, 0.5000])





#定义损失函数
def cross_entropy(y_hat,y):
    return -torch.log(y_hat[range(len(y_hat)),y])
cross_entropy(y_hat,y)





  Output:  tensor([2.3026, 0.6931])





#分类精度
def accuracy(y_hat,y):
    if(len(y_hat.shape)>1 and y_hat.shape[0]>1):
        y_hat=y_hat.argmax(axis=1)
    cmp = y_hat.type(y.dtype) ==y
    return float(cmp.type(y.dtype).sum())
accuracy(y_hat,y)/len(y)




  Output:  0.5





#我们可以评估任意模型的net的准确率
def evaluate_accuracy(net,data_iter):
    if isinstance(net,torch.nn.Module):
        net.eval()#将模型设置为评估模式
    metric = Accumulator(2)#正确预测数，预测总数，是一个累加的迭代器
    for X,y in data_iter:
        metric.add(accuracy(net(X),y),y.numel())
    return metric[0]/metric[1]




class Accumulator:
    def __init__(self,n):
        self.data=[0.0]*n
    def add(self,*args):
        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]
evaluate_accuracy(net,test_iter)





  Output:  0.1196





def train_epoch_ch3(net, train_iter, loss, updater):  #@save
    """训练模型一个迭代周期（定义见第3章）"""
    # 将模型设置为训练模式
    if isinstance(net, torch.nn.Module):
        net.train()
    # 训练损失总和、训练准确度总和、样本数
    metric = Accumulator(3)
    for X, y in train_iter:
        # 计算梯度并更新参数
        y_hat = net(X)
        l = loss(y_hat, y)
        if isinstance(updater, torch.optim.Optimizer):
            # 使用PyTorch内置的优化器和损失函数
            updater.zero_grad()
            l.mean().backward()
            updater.step()
        else:
            # 使用定制的优化器和损失函数
            l.sum().backward()
            updater(X.shape[0])
        metric.add(float(l.sum()), accuracy(y_hat, y), y.numel())
    # 返回训练损失和训练精度
    return metric[0] / metric[2], metric[1] / metric[2]



class Animator:  #@save
    """在动画中绘制数据"""
    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, 2.5)):
        # 增量地绘制多条线
        if legend is None:
            legend = []
        d2l.use_svg_display()
        self.fig, self.axes = d2l.plt.subplots(nrows, ncols, figsize=figsize)
        if nrows * ncols == 1:
            self.axes = [self.axes, ]
        # 使用lambda函数捕获参数
        self.config_axes = lambda: d2l.set_axes(
            self.axes[0], xlabel, ylabel, xlim, ylim, xscale, yscale, legend)
        self.X, self.Y, self.fmts = None, None, fmts

    def add(self, x, y):
        # 向图表中添加多个数据点
        if not hasattr(y, "__len__"):
            y = [y]
        n = len(y)
        if not hasattr(x, "__len__"):
            x = [x] * n
        if not self.X:
            self.X = [[] for _ in range(n)]
        if not self.Y:
            self.Y = [[] 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()
        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)




#训练函数
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_accuracy(net,test_iter)
        animator.add(epoch+1,train_metrics+(test_acc,))
    train_loss,train_acc = train_metrics
#     assert train_loss<0.5,train_loss
#     assert train_acc <=1 and train_acc>0.7,train_acc
#     assert test_acc <=1 and test_acc>0.7,test_acc




lr = 0.1
#设置优化函数
def updater(batch_size):
    return d2l.sgd([w,b],lr,batch_size)



num_epochs =10
train_ch3(net,train_iter,test_iter,cross_entropy,num_epochs,updater)

Output:

#预测
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])
predict_ch3(net,test_iter)

output: