简 介： 这是利用线性回归模型来 处理波士顿房价的预测。通过随机梯度下降完成模型的训练。对于最终的结果来看，预测的误差还是非常大的。
关键词： 波士顿房价，NN，AI
创建项目
文章目录
创建带有
housing.data的项目
housing.data的项目
读取数据库
总 结
程序
?
§01 创建项目
一、创建带有housing.data的项目
??进入AI Studio用户的主页，打开“项目”中的“创建和Fork项目”，点击“创建”，进行项目的创建。
▲ 图1.1.1 AI Studio下的项目管理界面
??选择创先Notebook类型的项目，可以加快交互过程。
▲ 图1.1.2 选择Notebook类型的项目
??在配置环境中选择BML CodeLab。 对于项目框架选择：PaddlePaddle 2.2.0, 项目环境选择 Python3.7。
▲ 图1.1.4 选择BML CodeLab进行配置环境
▲ 图1.1.3 选择波士顿房价数据集合
??然后最终在建立的项目中，存在data目录中，就自动带有housing.data。
1、housing.data结构
??下面是housing.data前几行的内容。
0.00632 18.00 2.310 0 0.5380 6.5750 65.20 4.0900 1 296.0 15.30 396.90 4.98 24.00
0.02731 0.00 7.070 0 0.4690 6.4210 78.90 4.9671 2 242.0 17.80 396.90 9.14 21.60
0.02729 0.00 7.070 0 0.4690 7.1850 61.10 4.9671 2 242.0 17.80 392.83 4.03 34.70
0.03237 0.00 2.180 0 0.4580 6.9980 45.80 6.0622 3 222.0 18.70 394.63 2.94 33.40
0.06905 0.00 2.180 0 0.4580 7.1470 54.20 6.0622 3 222.0 18.70 396.90 5.33 36.20
0.02985 0.00 2.180 0 0.4580 6.4300 58.70 6.0622 3 222.0 18.70 394.12 5.21 28.70
0.08829 12.50 7.870 0 0.5240 6.0120 66.60 5.5605 5 311.0 15.20 395.60 12.43 22.90
0.14455 12.50 7.870 0 0.5240 6.1720 96.10 5.9505 5 311.0 15.20 396.90 19.15 27.10
0.21124 12.50 7.870 0 0.5240 5.6310 100.00 6.0821 5 311.0 15.20 386.63 29.93 16.50
0.17004 12.50 7.870 0 0.5240 6.0040 85.90 6.5921 5 311.0 15.20 386.71 17.10 18.90
0.22489 12.50 7.870 0 0.5240 6.3770 94.30 6.3467 5 311.0 15.20 392.52 20.45 15.00
0.11747 12.50 7.870 0 0.5240 6.0090 82.90 6.2267 5 311.0 15.20 396.90 13.27 18.90
0.09378 12.50 7.870 0 0.5240 5.8890 39.00 5.4509 5 311.0 15.20 390.50 15.71 21.70
▲ 图1.1.5 数据各段的含义
2、预测模型
线性预测模型来描述影响放假和各种影响因素之间的关系。
y = ∑ j = 1 M x j w j + b y = \sum\limits_{j = 1}^M {x_j w_j } + b y=j=1∑M?xj?wj?+b
-
其中：
-
wj：模型权重
b：偏置
M S E = 1 n ∑ i = 1 n ( Y ^ i ? Y i ) 2 MSE = {1 \over n}\sum\limits_{i = 1}^n {\left( {\hat Y_i - Y_i } \right)^2 } MSE=n1?i=1∑n?(Y^i??Yi?)2
▲ 图1.1.6 线性回归单个神经网络模型
二、读取数据库
1、读取数据
（1）数据调入data
??利用numpy 读取数据。
data = fromfile(datafile, sep=' ')
printf(data)
printf(len(data))
??可以看到读取的数据为一列数据。
[6.320e-03 1.800e+01 2.310e+00 ... 3.969e+02 7.880e+00 1.190e+01]
7084
（2）数据转换成二维矩阵
feature_names = ['CRIM', 'ZN', 'INDUS', 'CHAS', 'NOX', 'RM', 'AGE', 'DIS',
'RAD', 'TAX', 'PTRATIO', 'B', 'LSTA', 'MEDV']
feature_num = len(feature_names)
data = data.reshape([data.shape[0]//feature_num, feature_num])
printf(data)
#------------------------------------------------------------
data_file = 'data/data58711/housing.data'
feature_names = ['CRIM', 'ZN', 'INDUS', 'CHAS', 'NOX', 'RM', 'AGE', 'DIS',
'RAD', 'TAX', 'PTRATIO', 'B', 'LSTA', 'MEDV']
def load_file(filename, ratio):
data = fromfile(filename, sep = ' ')
feature_num = len(feature_names)
data = data.reshape([data.shape[0]//feature_num, feature_num])
train_num = int(data.shape[0]*ratio)
train_data = data[:train_num]
maximums, minimums, averages = (train_data.max(axis=0),
train_data.min(axis=0),
train_data.sum(axis=0)/train_data.shape[0])
for i in range(feature_num):
data[:,i] = (data[:,i] - minimums[i]) / (maximums[i] - minimums[i])
train_data = data[:train_num]
test_data = data[train_num:]
return train_data, test_data
#------------------------------------------------------------
training_data, testing_data = load_file(data_file, 0.8)
x = training_data[:,:-1]
y = training_data[:,-1:]
2、数据预处理
（1）分割训练与测试集合
train_data_ratio = 0.8
train_data_offset = int(data.shape[0]*train_data_ratio)
train_data = data[:train_data_offset]
（2）数据归一化
maximum, minimum, averages = (train_data.max(axis=0),
train_data.min(axis=0),
train_data.sum(axis=0)/train_data.shape[0])
printf(maximum, minimum, averages)
[ 88.9762 100. 25.65 1. 0.871 8.78 100. 12.1265
24. 666. 22. 396.9 37.97 50. ] [6.3200e-03 0.0000e+00 4.6000e-01 0.0000e+00 3.8500e-01 3.5610e+00
2.9000e+00 1.1296e+00 1.0000e+00 1.8700e+02 1.2600e+01 7.0800e+01
1.7300e+00 5.0000e+00] [1.91589931e+00 1.42326733e+01 9.50232673e+00 8.66336634e-02
5.31731931e-01 6.33310891e+00 6.44274752e+01 4.17421361e+00
6.78960396e+00 3.52910891e+02 1.80262376e+01 3.79971757e+02
1.13549505e+01 2.41757426e+01]
（3）绘制数据曲线
def plotx_y(x, y, features=''):
xy = sorted(zip(x.flatten(),y.flatten()), key=lambda x:x[0])
x = [s[0] for s in xy]
y = [s[1] for s in xy]
plt.plot(x,y)
plt.xlabel(features)
plt.ylabel(feature_names[-1])
plt.title(features)
plt.grid(True)
plt.tight_layout()
# plt.savefig('plot.png')
plt.show()
#------------------------------------------------------------
id = 11
plotx_y(x[:,id], y, feature_names[id])
▲ 图1.2.1 数据曲线
3、模型设计
??设计Network的类，来计算对应的 预测输出。
（1）网络设计
class Network(object):
def __init__(self, num_of_weights):
random.seed(0)
self.w = random.randn(num_of_weights, 1)
self.b = 0
def forward(self, x):
z = dot(x, self.w) + self.b
return z
def loss(self, x, y):
error = z - y
cost = error * error
cost = mean(cost)
return cost
#------------------------------------------------------------
net = Network(13)
x1 = x[:3]
y1 = y[:3]
z = net.forward(x1)
print('Predict:\n', z)
loss = net.loss(z, y1)
print('Loss:', loss)
Predict:
[[2.39362982]
[2.46752393]
[2.02483479]]
Loss: 3.384496992612791
（2）网络性能分析
w5 = arange(-160.0, 160.0, 1.0)
w9 = arange(-160.0, 160.0, 1.0)
losses = zeros([len(w5), len(w9)])
for i in range(len(w5)):
net.w[5] = w5[i]
for j in range(len(w9)):
net.w[9] = w9[j]
z = net.forward(x)
loss = net.loss(z,y)
losses[i, j] = loss
fig = plt.figure()
ax = Axes3D(fig)
w5, w9 = meshgrid(w5, w9)
ax.plot_surface(w5, w9, losses, rstride=1, cstride=1, cmap='rainbow')
plt.show()
▲ 图1.2.2 w5，w9性能分析
▲ w0,w1的性能分析
▲ w2,w3的性能分析
4、网络训练
#------------------------------------------------------------
class Network(object):
def __init__(self, num_of_weights):
random.seed(0)
self.w = random.randn(num_of_weights, 1)
self.b = 0
def forward(self, x):
z = dot(x, self.w) + self.b
return z
def loss(self, z, y):
error = z - y
cost = error * error
cost = mean(cost)
return cost
def gradient(self, x, y):
z = self.forward(x)
gradient_w = (z-y)*x
gradient_w = mean(gradient_w, axis=0)
gradient_w = gradient_w[:,newaxis]
gradient_b = z - y
gradient_b = mean(gradient_b)
return gradient_w, gradient_b
def update(self, gradient_w, gradient_b, eta=0.01):
self.w = self.w - eta * gradient_w
self.b = self.b - eta * gradient_b
def train(self, x, y, iterations=100, eta=0.01):
losses = []
for i in range(iterations):
z = self.forward(x)
L = self.loss(z, y)
gradient_w, gradient_b = self.gradient(x, y)
self.update(gradient_w, gradient_b, eta)
losses.append(L)
if (i+1) % 10 == 0:
print('iter {}, loss {}'.format(i, L))
return losses
#------------------------------------------------------------
net = Network(13)
num_iterations = 1000
losses = net.train(x, y, iterations = num_iterations, eta=0.01)
#------------------------------------------------------------
savefile = 'housenet.txt'
with open(savefile, 'w') as f:
f.write(str(net.w))
f.write(str(net.b))
plot_x = arange(num_iterations)
plot_y = array(losses)
plt.plot(plot_x, plot_y)
plt.xlabel("Iteration")
plt.ylabel("Losses")
plt.grid(True)
plt.tight_layout()
plt.show()
（1）eta=0.01
▲ 图1.2.5 训练过程误差变化
（2）eta=0.1
▲ 图1.2.6 训练过程误差变化
（3）eta=0.5
▲ 图1.2.7 训练过程误差变化
（4）eta=0.6
??在学习速率在0.6，训练过程发散了。
▲ 图1.2.8 训练过程误差变化
5、网络参数
??训练完网络参数为：
[[ 0.23852968]
[ 0.08666859]
[ 0.02218764]
[ 0.05609168]
[-0.08528696]
[ 0.52452387]
[ 0.02993498]
[-0.2387991 ]
[ 0.1138169 ]
[-0.15394358]
[-0.14860527]
[ 0.05872705]
[-0.51617963]]
0.3815643929638751
▲ 图1.2.9 模型误差
?
§02 总??结
??这是利用线性回归模型来 处理波士顿房价的预测。通过随机梯度下降完成模型的训练。对于最终的结果来看，预测的误差还是非常大的。
◎ 程序
#!/usr/local/bin/python
# -*- coding: gbk -*-
#============================================================
# TESTHOUSE.PY -- by Dr. ZhuoQing 2021-12-09
#
# Note:
#============================================================
from headm import *
from mpl_toolkits.mplot3d import Axes3D
#------------------------------------------------------------
data_file = 'data/data58711/housing.data'
feature_names = ['CRIM', 'ZN', 'INDUS', 'CHAS', 'NOX', 'RM', 'AGE', 'DIS',
'RAD', 'TAX', 'PTRATIO', 'B', 'LSTA', 'MEDV']
def load_file(filename, ratio):
data = fromfile(filename, sep = ' ')
feature_num = len(feature_names)
data = data.reshape([data.shape[0]//feature_num, feature_num])
train_num = int(data.shape[0]*ratio)
train_data = data[:train_num]
maximums, minimums, averages = (train_data.max(axis=0),
train_data.min(axis=0),
train_data.sum(axis=0)/train_data.shape[0])
for i in range(feature_num):
data[:,i] = (data[:,i] - minimums[i]) / (maximums[i] - minimums[i])
train_data = data[:train_num]
test_data = data[train_num:]
return train_data, test_data
#------------------------------------------------------------
training_data, testing_data = load_file(data_file, 0.8)
x = training_data[:,:-1]
y = training_data[:,-1:]
#printf(x.shape, y.shape)
#------------------------------------------------------------
def plotx_y(x, y, features=''):
xy = sorted(zip(x.flatten(),y.flatten()), key=lambda x:x[0])
x = [s[0] for s in xy]
y = [s[1] for s in xy]
plt.plot(x,y)
plt.xlabel(features)
plt.ylabel(feature_names[-1])
plt.title(features)
plt.grid(True)
plt.tight_layout()
plt.show()
#------------------------------------------------------------
'''
id = 11
plotx_y(x[:,id], y, feature_names[id])
'''
#------------------------------------------------------------
class Network(object):
def __init__(self, num_of_weights):
random.seed(0)
self.w = random.randn(num_of_weights, 1)
self.b = 0
def forward(self, x):
z = dot(x, self.w) + self.b
return z
def loss(self, z, y):
error = z - y
cost = error * error
cost = mean(cost)
return cost
def gradient(self, x, y):
z = self.forward(x)
gradient_w = (z-y)*x
gradient_w = mean(gradient_w, axis=0)
gradient_w = gradient_w[:,newaxis]
gradient_b = z - y
gradient_b = mean(gradient_b)
return gradient_w, gradient_b
def update(self, gradient_w, gradient_b, eta=0.01):
self.w = self.w - eta * gradient_w
self.b = self.b - eta * gradient_b
def train(self, x, y, iterations=100, eta=0.01):
losses = []
for i in range(iterations):
z = self.forward(x)
L = self.loss(z, y)
gradient_w, gradient_b = self.gradient(x, y)
self.update(gradient_w, gradient_b, eta)
losses.append(L)
if (i+1) % 10 == 0:
print('iter {}, loss {}'.format(i, L))
return losses
#------------------------------------------------------------
net = Network(13)
num_iterations = 1000
losses = net.train(x, y, iterations = num_iterations, eta=0.5)
#------------------------------------------------------------
savefile = 'housenet.txt'
with open(savefile, 'w') as f:
f.write(str(net.w) +'\n')
f.write(str(net.b) + '\n')
#------------------------------------------------------------
z = net.forward(x)
plt.plot(z-y, label='Error')
plt.plot(y, label='Origin')
plt.plot(z, label='Prediction')
plt.xlabel("N")
plt.ylabel("Error")
plt.legend(loc='upper right')
plt.grid(True)
plt.tight_layout()
plt.show()
#------------------------------------------------------------
'''
plot_x = arange(num_iterations)
plot_y = array(losses)
plt.plot(plot_x, plot_y)
plt.xlabel("Iteration")
plt.ylabel("Losses")
plt.grid(True)
plt.tight_layout()
plt.show()
'''
#------------------------------------------------------------
'''
w5 = arange(-160.0, 160.0, 1.0)
w9 = arange(-160.0, 160.0, 1.0)
losses = zeros([len(w5), len(w9)])
for i in range(len(w5)):
net.w[2] = w5[i]
for j in range(len(w9)):
net.w[3] = w9[j]
z = net.forward(x)
loss = net.loss(z,y)
losses[i, j] = loss
fig = plt.figure()
ax = Axes3D(fig)
w5, w9 = meshgrid(w5, w9)
ax.plot_surface(w5, w9, losses, rstride=1, cstride=1, cmap='rainbow')
plt.show()
'''
#------------------------------------------------------------
# END OF FILE : TESTHOUSE.PY
#============================================================
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