%matplotlib inline
import d2lzh as d2l
from mxnet import autograd,gluon,nd
from mxnet.gluon import data as gdata,loss as gloss,nn#y=1.2x-3.4x²+5.6x³+5+ε，其中ε是噪声
n_train,n_test,true_w,true_b=100,100,[1.2,-3,4,5.6],5
features=nd.random.normal(shape=(n_train+n_test,1))#(200,1)#线性
poly_features=nd.concat(features,nd.power(features,2),nd.power(features,3))#多项式形状(200,3)
labels=(true_w[0]*poly_features[:,0] + true_w[1]*poly_features[:,1]+true_w[2]*poly_features[:,2]+true_b)#参数增多了(权重与偏置)
labels+=nd.random.normal(scale=0.1,shape=labels.shape)#加个噪声
#print(features[:2],poly_features[:2],labels[:2])
'''
[[0.13271435][1.0078678 ]]
<NDArray 2x1 @cpu(0)>
[[0.13271435 0.0176131  0.00233751][1.0078678  1.0157975  1.0237896 ]]
<NDArray 2x3 @cpu(0)>
[5.049143 7.190733]
<NDArray 2 @cpu(0)>
'''#定义一个画图函数(y轴为对数尺度)[在d2l包中已存在]
def semilogy(x_vals,y_vals,x_label,y_label,x2_vals=None,y2_vals=None,legend=None,figsize=(5,4)):d2l.set_figsize(figsize)d2l.plt.xlabel(x_label)d2l.plt.ylabel(y_label)d2l.plt.semilogy(x_vals,y_vals)if x2_vals and y2_vals:d2l.plt.semilogy(x2_vals,y2_vals,linestyle='-.')d2l.plt.legend(legend)#拟合数据集，观察不同复杂度对模型的影响
num_epochs,loss=100,gloss.L2Loss()
def fit_and_plot(train_features,test_features,train_labels,test_labels):net=nn.Sequential()net.add(nn.Dense(1))net.initialize()batch_size=min(10,train_labels.shape[0])train_iter=gdata.DataLoader(gdata.ArrayDataset(train_features,train_labels),batch_size,shuffle=True)trainer=gluon.Trainer(net.collect_params(),'sgd',{'learning_rate':0.01})train_ls,test_ls=[],[]for _ in range(num_epochs):for X,y in train_iter:with autograd.record():l=loss(net(X),y)l.backward()trainer.step(batch_size)train_ls.append(loss(net(train_features),train_labels).mean().asscalar())test_ls.append(loss(net(test_features),test_labels).mean().asscalar())print('最后一次迭代结果：训练损失',train_ls[-1],'测试损失',test_ls[-1])semilogy(range(1,num_epochs+1),train_ls,'epochs','loss',range(1,num_epochs+1),test_ls,['train','test'])print('权重值:',net[0].weight.data().asnumpy(),'\n偏差值:',net[0].bias.data().asnumpy())

fit_and_plot(poly_features[:n_train,:],poly_features[n_train:,:],labels[:n_train],labels[n_train:])
最后一次迭代结果：训练损失 0.0055423467 测试损失 0.006460184
权重值: [[ 1.1825476 -2.9724765  3.9992456]]
偏差值: [4.9615808]可以看出和真实权重值：1.2,-3.4,5.6以及偏差值：5相比较还是很接近的

%matplotlib inline
import d2lzh as d2l
from mxnet import autograd,gluon,init,nd
from mxnet.gluon import data as gdata,loss as gloss,nn#使用高维线性回归来模拟过拟合，特意将训练样本数设得很小：20
n_train,n_test,num_inputs=20,100,200
true_w,true_b=nd.ones((num_inputs,1))*0.01,0.05
features=nd.random.normal(shape=(n_train+n_test,num_inputs))
labels=nd.dot(features,true_w)+true_b
labels+=nd.random.normal(scale=0.01,shape=labels.shape)
train_features,test_features=features[:n_train,:],features[n_train:,:]
train_labels,test_labels=labels[:n_train],labels[n_train:]#初始化模型参数，并附上梯度
def init_params():w=nd.random.normal(scale=1,shape=(num_inputs,1))b=nd.zeros(shape=(1,))w.attach_grad()b.attach_grad()return [w,b]#定义L2范数惩罚项
def l2_penalty(w):return (w**2).sum()/2batch_size,num_epochs,lr=1,100,0.003
net,loss=d2l.linreg,d2l.squared_loss#线性回归，平方损失
train_iter=gdata.DataLoader(gdata.ArrayDataset(train_features,train_labels),batch_size,shuffle=True)#λ为0不使用权重衰减，也就是模拟过拟合
def fit_and_plot(lambd):w,b=init_params()train_ls,test_ls=[],[]for _ in range(num_epochs):for X,y in train_iter:with autograd.record():l=loss(net(X,w,b),y) + lambd*l2_penalty(w)#添加惩罚项l.backward()d2l.sgd([w,b],lr,batch_size)train_ls.append(loss(net(train_features,w,b),train_labels).mean().asscalar())test_ls.append(loss(net(test_features,w,b),test_labels).mean().asscalar())d2l.semilogy(range(1,num_epochs+1),train_ls,'epochs','loss',range(1,num_epochs+1),test_ls,['train','test'])print('L2权重的范数：',w.norm().asscalar())

batch_size,num_epochs,lr=1,100,0.003
def fit_and_plot_gluon(wd):net=nn.Sequential()net.add(nn.Dense(1))net.initialize(init.Normal(sigma=1))#对权重做衰减，权重名称一般以weight结尾train_w=gluon.Trainer(net.collect_params('.*weight'),'sgd',{'learning_rate':lr,'wd':wd})#对偏差不做衰减train_b=gluon.Trainer(net.collect_params('.*bias'),'sgd',{'learning_rate':lr})train_ls,test_ls=[],[]for _ in range(num_epochs):for X,y in train_iter:with autograd.record():l=loss(net(X),y)l.backward()train_w.step(batch_size)train_b.step(batch_size)train_ls.append(loss(net(train_features),train_labels).mean().asscalar())test_ls.append(loss(net(test_features),test_labels).mean().asscalar())d2l.semilogy(range(1,num_epochs+1),train_ls,'epochs','loss',range(1,num_epochs+1),test_ls,['train','test'])print('L2范数的权重值:',net[0].weight.data().norm().asscalar())

import d2lzh as d2l
from mxnet import autograd,gluon,init,nd
from mxnet.gluon import loss as gloss,nn#drop_prob丢弃的概率
def dropout(X,drop_prob):keep_prob=1-drop_probif keep_prob==0:return X.zeros_like()mask=nd.random.uniform(0,1,X.shape)<keep_probreturn mask*X/keep_probnum_inputs,num_outputs,num_hidden1,num_hidden2=784,10,256,256
W1=nd.random.normal(scale=0.01,shape=(num_inputs,num_hidden1))
b1=nd.zeros(num_hidden1)
W2=nd.random.normal(scale=0.01,shape=(num_hidden1,num_hidden2))
b2=nd.zeros(num_hidden2)
W3=nd.random.normal(scale=0.01,shape=(num_hidden2,num_outputs))
b3=nd.zeros(num_outputs)
params=[W1,b1,W2,b2,W3,b3]
for param in params:param.attach_grad()#每个层的丢弃概率的设置：靠近输入层的一般设置小一点，另外测试的时候不需要使用丢弃法
drop_prob1,drop_prob2=0.2,0.5
def net(X):X=X.reshape((-1,num_inputs))H1=(nd.dot(X,W1)+b1).relu()if autograd.is_training():H1=dropout(H1,drop_prob1)#在第一层全连接后添加丢弃层H2=(nd.dot(H1,W2)+b2).relu()if autograd.is_training():H2=dropout(H2,drop_prob2)#在第二层全连接后添加丢弃层return nd.dot(H2,W3)+b3#训练Fashion-MNIST数据集来测试丢弃法
num_epochs,lr,batch_size=5,0.5,256
loss=gloss.SoftmaxCrossEntropyLoss()
train_iter,test_iter=d2l.load_data_fashion_mnist(batch_size)
d2l.train_ch3(net,train_iter,test_iter,loss,num_epochs,batch_size,params,lr)

net=nn.Sequential()
net.add(nn.Dense(256,activation='relu'),nn.Dropout(drop_prob1),nn.Dense(256,activation='relu'),nn.Dropout(drop_prob2),nn.Dense(10))
net.initialize(init.Normal(sigma=0.01))
trainer=gluon.Trainer(net.collect_params(),'sgd',{'learning_rate':lr})
d2l.train_ch3(net,train_iter,test_iter,loss,num_epochs,batch_size,None,None,trainer)

import matplotlib.pyplot as plt
plt.rcParams['font.sans-serif'] = ['SimHei']#界面可带中文
plt.rcParams['axes.unicode_minus'] = False#正常显示负号