深度学习之线性回归

#!/usr/bin/env python
# -*- coding: utf-8 -*-
# @Time    : 2019/1/15 23:04
# @Author  : Cunyu
# @Site    : cunyu1943.github.io
# @File    : linearRegression.py
# @Software: PyCharm


from IPython import display
from matplotlib import pyplot as plt
from mxnet import autograd, nd
import random

""""
线性回归的从零实现
"""

# 生成人工数据集

num_input = 2
num_examples = 1000
true_w = [2, -3.4]
true_b = 4.2

features = nd.random.normal(scale=1, shape=(num_examples, num_input))
labels = true_w[0] * features[:,0] + true_w[1] * features[:,1] + true_b
labels += nd.random.normal(scale=0.01, shape=labels.shape)

print(features[0], labels[0])

def use_svg_display():
	# 用矢量图显示
	display.set_matplotlib_formats('svg')

def set_figsize(figsize = (3.5, 2.5)):
	use_svg_display()
	# 设置图的尺寸
	plt.rcParams['figure.figsize'] = figsize

set_figsize()
plt.scatter(features[:,1].asnumpy(), labels.asnumpy(), 1)
plt.show()

# 读取数据
def data_iter(batch_size, features, labels):
	num_examples = len(features)
	indices = list(range(num_examples))
	random.shuffle(indices)
	for i in range(0, num_examples, batch_size):
		j = nd.array(indices[i:min(i+batch_size, num_examples)])
		yield features.take(j), labels.take(j) # take函数根据索引返回对应元素

batch_size = 10
for X, y in data_iter(batch_size, features, labels):
	print(X, y)
	break


# 初始化模型参数
w = nd.random.normal(scale=0.01, shape=(num_input, 1))
b = nd.zeros(shape=(1,))

w.attach_grad()
b.attach_grad()

# 定义模型
def linreg(X, w, b):
	return nd.dot(X, w) + b

# 定义损失函数
def squared_loss(y_hat, y):
	return (y_hat-y.reshape(y_hat.shape)) ** 2 / 2

# 定义优化算法
def sgd(params, lr, batch_size):
	for param in params:
		param[:] = param - lr * param.grad / batch_size

# 训练模型
lr = 0.03
num_epochs = 3
net = linreg
loss = squared_loss

print('批量样本求平均:')
for epoch in range(num_epochs): # 训练模型一共需num_epochs个迭代周期
	# 每个迭代周期中，会使用训练数据集中所有样本一次（假设样本数据能够被批量大小整除），X和y分别是小批量样本的特征和标签
    for X, y in data_iter(batch_size, features, labels):
        with autograd.record():
            l = loss(net(X, w, b), y) # l是有关小批量X和y的损失
        l.backward() # 小批量的损失对模型参数求梯度
        sgd([w, b], lr, batch_size) # 使用小批量随机梯度下降迭代模型参数
    train_l = loss(net(features, w, b), labels)
    print('epoch %d, loss: %f' % (epoch + 1, train_l.mean().asnumpy()))
print('权重：\n', true_w, w)
print('偏差：\n', true_b, b)

#!/usr/bin/env python
# -*- coding: utf-8 -*-
# @Time    : 2019/4/10 10:34
# @Author  : cunyu
# @Site    : cunyu1943.github.io
# @File    : linearRegressionSimple.py
# @Software: PyCharm

from mxnet import autograd, nd

# 生成数据集
num_inputs = 2
num_examples = 1000
true_w = [2, -3.4]
true_b = 4.2
features = nd.random.normal(scale=1, shape=(num_examples, num_inputs))
labels = true_w[0] * features[:, 0] + true_w[1] * features[:, 1] + true_b
labels += nd.random.normal(scale=0.01, shape=labels.shape)

# 读取数据
from mxnet.gluon import data as gdata

batch_size = 10
# 将训练数据的特征和标签组合
dataset = gdata.ArrayDataset(features, labels)
# 随机读取小批量
data_iter = gdata.DataLoader(dataset, batch_size, shuffle=True)
# 读取并打印第一个小批量数据样本
for X, y in data_iter:
	print(X, y)
	break

# 定义模型
from mxnet.gluon import nn

net = nn.Sequential()
net.add(nn.Dense(1))

# 初始化模型参数
from mxnet import init

net.initialize(init.Normal(sigma=0.01))

# 定义损失函数
from mxnet.gluon import loss as gloss

loss = gloss.L2Loss()  # 平方损失又称为L2范数损失

# 定义优化函数
from mxnet import gluon

trainer = gluon.Trainer(net.collect_params(), 'sgd', {'learning_rate': 0.03})

# 训练模型
num_epochs = 3
for epoch in range(1, num_epochs + 1):
	for X, y in data_iter:
		with autograd.record():
			l = loss(net(X), y)
		l.backward()
		trainer.step(batch_size)
	l = loss(net(features), labels)
	print('epoch: %d, loss: %f' % (epoch, l.mean().asnumpy()))

dense = net[0]
print(true_w, dense.weight.data())
print(true_b, dense.bias.data())