波士顿房价预测——线性模型（numpy实现）
数据准备
下载数据集：https://archive.ics.uci.edu/ml/machine-learning-databases/housing/housing.data
代码实现参考百度 AI Studio实现
github地址:（内包含数据集）
https://github.com/Classmate-Huang/Boston-Housing-Forecast
代码1
梯度下降
import numpy as np
import matplotlib.pyplot as plt
def load_data():
# 导入房价数据
datafile = 'housing.data'
data = np.fromfile(datafile, sep=' ')
# 将原始数据Reshape 并且拆分成训练集和测试集
data = data.reshape([-1, 14])
offset = int(data.shape[0]*0.8)
train_data = data[:offset]
# 归一化处理
maximums, minimums, avgs = train_data.max(axis=0), train_data.min(axis=0), train_data.sum(axis=0) / train_data.shape[0]
for i in range(14):
data[:, i] = (data[:, i] - avgs[i]) / (maximums[i] - minimums[i])
train_data = data[:offset]
test_data = data[offset:]
return train_data, test_data
class Network(object):
def __init__(self, num_of_weight):
# 随机产生w初始值
np.random.seed(0)
# randn函数返回一组样本，具有标准正态分布，维度为[num_of_weight, 1]
self.w = np.random.randn(num_of_weight, 1)
self.b = 0.
def forword(self, x): # 前向计算
z = np.dot(x, self.w) + self.b
return z
def loss(self, z, y): # loss计算
error = z - y
cost = error * error
cost = np.mean(cost)
return cost
def gradient(self, x, y): # 计算梯度
z = self.forword(x)
gradient_w = np.mean((z - y)*x, axis=0)
gradient_w = gradient_w[:, np.newaxis] # [13,] -> [13, 1]
gradient_b = np.mean((z - y), axis=0)
return gradient_w, gradient_b
def update(self, gradient_w, gradient_b, eta=0.01): # 更新参数
self.w = self.w - eta*gradient_w
self.b = self.b - eta*gradient_b
def train(self, x, y, iterations=100, eta=0.01): # 训练代码
losses = []
for i in range(iterations): # 训练多少轮
z = self.forword(x) # 前向计算
loss = self.loss(z, y) # 得到loss
gradient_w, gradient_b = self.gradient(x, y) # 计算梯度
self.update(gradient_w, gradient_b, eta) # 更新参数
losses.append(loss)
if (i+1) % 10 == 0:
print('iter {}, loss {}'.format(i, loss))
return losses
train_data, test_data = load_data()
x = train_data[:, :-1]
y = train_data[:, -1:]
net = Network(13)
# 开始训练
losses = net.train(x, y, iterations=1000, eta=0.01)
# 画出损失函数变化趋势
plot_x = np.arange(1000)
plot_y = np.array(losses)
plt.plot(plot_x, plot_y)
plt.show()
代码2
Mini-Batch Stochastic Gradient Descent 小批量随机梯度下降
import numpy as np
import matplotlib.pyplot as plt
def load_data():
# 导入房价数据
datafile = 'housing.data'
data = np.fromfile(datafile, sep=' ')
# 将原始数据Reshape 并且拆分成训练集和测试集
data = data.reshape([-1, 14])
offset = int(data.shape[0]*0.8)
train_data = data[:offset]
# 归一化处理
maximums, minimums, avgs = train_data.max(axis=0), train_data.min(axis=0), train_data.sum(axis=0) / train_data.shape[0]
for i in range(14):
data[:, i] = (data[:, i] - avgs[i]) / (maximums[i] - minimums[i])
train_data = data[:offset]
test_data = data[offset:]
return train_data, test_data
class Network(object):
def __init__(self, num_of_weight):
# 随机产生w初始值
# np.random.seed(0)
# randn函数返回一组样本，具有标准正态分布，维度为[num_of_weight, 1]
self.w = np.random.randn(num_of_weight, 1)
self.b = 0.
def forword(self, x): # 前向计算
z = np.dot(x, self.w) + self.b
return z
def loss(self, z, y): # loss计算
error = z - y
cost = error * error
cost = np.mean(cost)
return cost
def gradient(self, x, y): # 计算梯度
z = self.forword(x)
gradient_w = np.mean((z - y)*x, axis=0)
gradient_w = gradient_w[:, np.newaxis] # [13,] -> [13, 1]
gradient_b = np.mean((z - y), axis=0)
return gradient_w, gradient_b
def update(self, gradient_w, gradient_b, eta=0.01): # 更新参数
self.w = self.w - eta*gradient_w
self.b = self.b - eta*gradient_b
def train(self, train_data, num_epcches, batch_size=10, eta=0.01): # 训练代码
n = len(train_data)
print(n)
losses = []
for epoch_id in range(num_epcches):
# 在每轮迭代之前，将训练数据的顺序随机打乱
np.random.shuffle(train_data)
# 将数据拆分，每个mini_batch包含batch_size条数据
mini_batches = [train_data[k:k+batch_size] for k in range(0, n, batch_size)]
# enumerate()函数将一个可遍历的数据对象组合为一个索引列表，同时列出数据下标和数据
for iter_id, mini_batch in enumerate(mini_batches):
x = mini_batch[:, :-1]
y = mini_batch[:, -1:]
z = self.forword(x)
loss = self.loss(z, y)
gradient_w, gradient_b = self.gradient(x, y)
self.update(gradient_w, gradient_b, eta)
losses.append(loss)
print('Epoch{:3d} / iter {:3d}, loss = {:.4f}'.format(epoch_id, iter_id, loss))
return losses
train_data, test_data = load_data()
net = Network(13)
# 开始训练
losses = net.train(train_data, batch_size=50, num_epcches=100, eta=0.01)
# 画出损失函数变化趋势
plot_x = np.arange(len(losses))
plot_y = np.array(losses)
plt.plot(plot_x, plot_y)
plt.show()