手撸大模型-基础篇简单线性回归模型预测房价

# NumPy Pandas Matplotlib
import numpy as np
import matplotlib.pyplot as plt

'''
双特征，矩阵化
'''

1. Min-Max 归一化及其逆操作

1.1 输入数据归一化

def normalize1(sample, data):
max_value = np.max(data)
min_value = np.min(data)
return (sample - min_value) / (max_value - min_value)

1.2 预测结果去归一化

def d_normalize1(sample, data):
max_value = np.max(data)
min_value = np.min(data)
return sample * (max_value - min_value) + min_value

2. Z-score 标准化及其逆操作

2.1 输入数据归一化

def normalize2(sample, data):
mean = np.mean(data)
stds = np.std(data)
return (sample - mean) / stds

2.2 预测结果去归一化
def d_normalize2(sample, data):
mean = np.mean(data)
stds = np.std(data)
return sample * stds + mean

3. 模型定义

def model(X, W, b):
return X@W + b

4. 损失函数
使用均方误差（MSE）作为损失函数：
def loss_func(predict, label):
return (predict - label)**2

5. 主程序
if __name__ == "__main__":
np.random.seed(17)

prices_raw = np.arange(37294, 87294, 5000) + np.random.randn(10)*3000
years_raw = np.arange(2014, 2024)
areas_raw = np.arange(80, 140, 6) + np.random.randn(10)

# X = np.vstack((areas_raw, years_raw)).T

5.1 数据标准化
prices = normalize2(prices_raw, prices_raw)
years = normalize2(years_raw, years_raw)
areas = normalize2(areas_raw, areas_raw)

X = np.vstack((areas, years)).T

5.2 模型初始化与训练参数设置

设置训练周期（epoch）为 100。
模型输入特征维度为 2，输出特征维度为 1。
初始化权重矩阵 W 为全零矩阵，偏置 b 为 0。
设置学习率 lr 为 0.01。
设定批量大小 batch_size 为 3（小批量梯度下降）。

epoch = 100
in_features = 2
out_features = 1
W = np.zeros((in_features, out_features))
b = 0.

lr = 0.01

batch_size = 3
5.3 小批量梯度下降训练循环

for e in range(epoch):

cursor = 0
while cursor <= len(X):
actual_batchsize = min(len(X)-cursor, batch_size)
batch_inputs = X[cursor: cursor + actual_batchsize]
batch_labels = prices[cursor: cursor + actual_batchsize].reshape(actual_batchsize, 1)

predict = model(batch_inputs, W, b)

loss = loss_func(predict, batch_labels)

G = 2*(predict - batch_labels) / actual_batchsize

dW = batch_inputs.T @ G
db = G

W -= lr*dW
b -= lr*db
b = np.mean(b)
cursor += batch_size
print("Loss: {}".format(loss))

5.4 预测功能

inputs = np.array((normalize2(90, areas_raw), normalize2(2025, years_raw))).reshape(1, 2)
predict = model(inputs, W, b)
predict = d_normalize2(predict, prices_raw)

pass

6. 完整代码

# -*- coding: utf-8 -*-
# NumPy Pandas Matplotlib
import numpy as np
import matplotlib.pyplot as plt'''
双特征，矩阵化
'''def normalize1(sample, data):max_value = np.max(data)min_value = np.min(data)return (sample - min_value) / (max_value - min_value)def d_normalize1(sample, data):max_value = np.max(data)min_value = np.min(data)return sample * (max_value - min_value) + min_valuedef normalize2(sample, data):mean = np.mean(data)stds = np.std(data)return (sample - mean) / stdsdef d_normalize2(sample, data):mean = np.mean(data)stds = np.std(data)return sample * stds + meandef model(X, W, b):return X@W + bdef loss_func(predict, label):return (predict - label)**2if __name__ == "__main__":np.random.seed(17)prices_raw = np.arange(37294, 87294, 5000) + np.random.randn(10)* 3000years_raw  = np.arange(2014, 2024)areas_raw  = np.arange(80, 140, 6) + np.random.randn(10)# X = np.vstack((areas_raw, years_raw)).Tprices = normalize2(prices_raw, prices_raw)years  = normalize2(years_raw, years_raw)areas  = normalize2(areas_raw, areas_raw)X = np.vstack((areas, years)).Tepoch = 100in_features  = 2out_features = 1W = np.zeros((in_features, out_features))b = 0.lr = 0.01batch_size = 3for e in range(epoch):cursor = 0while cursor <= len(X):actual_batchsize = min(len(X)- cursor, batch_size)batch_inputs = X[cursor: cursor + actual_batchsize]batch_labels = prices[cursor: cursor + actual_batchsize].reshape(actual_batchsize, 1)predict = model(batch_inputs, W, b)loss = loss_func(predict, batch_labels)G = 2* ( predict - batch_labels) / actual_batchsizedW = batch_inputs.T @ Gdb = GW -= lr* dWb -= lr* dbb = np.mean(b)cursor += batch_sizeprint("Loss: {}".format(loss))inputs = np.array((normalize2(90, areas_raw), normalize2(2025, years_raw))).reshape(1, 2)predict = model(inputs, W, b)predict = d_normalize2(predict, prices_raw)pass

7. 运行结果