简单线性回归-最小二乘法及梯度下降法

# 0. 引入依赖 import numpy as np import matplotlib.pyplot as plt # 1. 导入数据（data.csv） points = np.genfromtxt('data.csv', delimiter=',') points[0,0] # 提取points中的两列数据，分别作为x，y x = points[:, 0] y = points[:, 1] # 用plt画出散点图 # plt.scatter(x, y) # plt.show() # 2. 定义损失函数：最小平方损失函数 # 损失函数是系数的函数，另外还要传入数据的x，y def compute_cost(w, b, points): total_cost = 0 M = len(points) # 逐点计算平方损失误差，然后求平均数 for i in range(M): x = points[i, 0] y = points[i, 1] total_cost += (y - w * x - b) ** 2 return total_cost / M # 3. 定义模型的超参数 alpha = 0.0001 # 根据实际去调节 initial_w = 0 # 初始w，可以随机生成 initial_b = 0 # 初始b，可以随机生成 num_iter = 10 # 迭代次数 # 4. 定义核心梯度下降算法函数 def grad_desc(points, initial_w, initial_b, alpha, num_iter): w = initial_w b = initial_b # 定义一个list保存所有的损失函数值，用来显示下降的过程 cost_list = [] # 迭代，获取每次的损失函数值以及更行w、b for i in range(num_iter): cost_list.append(compute_cost(w, b, points)) w, b = step_grad_desc(w, b, alpha, points) return [w, b, cost_list] def step_grad_desc(current_w, current_b, alpha, points): sum_grad_w = 0 sum_grad_b = 0 M = len(points) # 对每个点，代入公式求和 for i in range(M): x = points[i, 0] y = points[i, 1] sum_grad_w += (current_w * x + current_b - y) * x sum_grad_b += current_w * x + current_b - y # 用公式求当前梯度 grad_w = 2 / M * sum_grad_w grad_b = 2 / M * sum_grad_b # 梯度下降，更新当前的w和b updated_w = current_w - alpha * grad_w updated_b = current_b - alpha * grad_b return updated_w, updated_b # 5. 测试：运行梯度下降算法计算最优的w和b w, b, cost_list = grad_desc( points, initial_w, initial_b, alpha, num_iter ) print("w is: ", w) print("b is: ", b) cost = compute_cost(w, b, points) print("cost is: ", cost) # plt.plot(cost_list) # plt.show() # 画图 # 6. 画出拟合曲线 plt.scatter(x, y) # 针对每一个x，计算出预测的y值 pred_y = w * x + b plt.plot(x, pred_y, c='r') plt.show()