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_value def normalize2(sample, data): mean = np.mean(data) stds = np.std(data) return (sample - mean) / stds def d_normalize2(sample, data): mean = np.mean(data) stds = np.std(data) return sample * stds + mean def model(X, W, b): return X@W + b def loss_func(predict, label): return (predict - label)**2 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 prices = normalize2(prices_raw, prices_raw) years = normalize2(years_raw, years_raw) areas = normalize2(areas_raw, areas_raw) X = np.vstack((areas, years)).T epoch = 100 in_features = 2 out_features = 1 W = np.zeros((in_features, out_features)) b = 0. lr = 0.01 batch_size = 3 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)) 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