[MxNet]正则化——惩罚较大参数（从零开始与gluon实现）

本文链接：https://blog.youkuaiyun.com/hello_SW/article/details/79049551

本文通过手写代码实现正则化过程，并利用MXNet的高级API进行对比，详细介绍了如何在深度学习中应用L2正则化来防止过拟合。包括数据生成、模型训练及评估等步骤。

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手动实现方式：在计算loss时加上lambd*L2

rom mxnet import ndarray as nd
from mxnet import autograd
from mxnet import gluon
import random
import matplotlib as mpl
mpl.rcParams['figure.dpi']=120

import mxnet as mx

num_train=20
num_test=100
num_inputs=200

true_w=nd.ones((num_inputs,1))*0.01
true_b=0.05

X=nd.random.normal(shape=(num_train+num_test,num_inputs))
y=nd.dot(X,true_w)
y+=.01*nd.random_normal(shape=y.shape)

X_train,X_test=X[:num_train],X[num_train:]
Y_train,Y_test=y[:num_train],y[num_train:]

batch_size=1
def data_iter(num_examples):
	idx=list(range(num_examples))
	random.shuffle(idx)
	for i in range(0,num_examples,batch_size):
		j=nd.array(idx[i:min(i+batch_size,num_examples)])
		yield X.take(j),y.take(j)
	
def init_params():
	w=nd.random_normal(scale=1,shape=(num_inputs,1))
	b=nd.zeros(shape=(1,))
	params=[w,b]
	for param in params:
		param.attach_grad()
	return params

def net(X,w,b):
	return nd.dot(X,w)+b

def L2_penalty(w,b):
	return ((w**2).sum+b**2)/2#L2_penalty是个标量，要加载Loss的每个值上

def square_loss(output,label):
	return (yhat-y.reshape(yhat.shape))**2/2

def sgd(params,lr,batch_size):
	for param in params:
		param[:]=param-lr*param/batch_size

def test(net,params,X,y):
	output=net(X,*params)#星号的意思是，本来net有三个参数，这里的params需要拆解成两个参数。
	return square_loss(output,y).mean().asscalar()

def train(lambd):
	epochs=10
	learning_rate=0.05
	w,b=params=init_params()
	for e in range(epoch):
		for data,label in data_iter(num_train):
			with autograd.record():
				output=net(data,*params)
				loss=square_loss(output,label)+lambd*L2_penalty(*params)
			loss.backward()
			sgd(params,learning_rate,batch_size)
		train_loss.append(test(net,params,X_train,y_train))
		test_loss.append(test(net,params,X_test,y_test))

使用gluon实现正则化时，lambd并不是在计算loss的环节出现的，体现在trainer的参数里，weight_decay

trainer = gluon.Trainer(net.collect_params(), 'sgd', {
                'learning_rate': learning_rate, 'wd': weight_decay})