仅使用python标准库（不使用numpy）写一个小批量梯度下降的线性回归算法

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看到一个有意思的题目：仅使用python的标准库，完成一个小批量梯度下降的线性回归算法

平常使用numpy这样的计算库习惯了，只允许使用标准库还有点不习惯，下面就使用这个过程来写一个。

import random
from typing import List# 生成测试数据
def generate_data(num_samples: int, weights: List[float], bias: float, noise=0.1) -> (List[List[float]], List[float]):X = [[random.uniform(-10, 10) for _ in range(len(weights))] for _ in range(num_samples)]y = [sum(w * x for w, x in zip(weights, x_i)) + bias + random.uniform(-noise, noise) for x_i in X]return X, y# 计算损失
def mse(y_true: List[float], y_pred: List[float]):return 0.5 * sum((yt - yp) for yt, yp in zip(y_true, y_pred)) ** 2# 将矩阵转置
def transpose(mat: List[List[float]]):row, col = len(mat), len(mat[0])# 固定列，访问行result = [[mat[r][c] for r in range(row)] for c in range(col)]return result# 计算矩阵乘法
def matmul(mat: List[List[float]], vec: List[float]):return [sum(r * c for r, c in zip(row, vec)) for row in mat]# 计算梯度
def compute_grad(y_true_batch: List[float], y_pred_batch: List[float], x_batch: List[List[float]]):batch_size = len(y_true_batch)residual = [yt - yp for yt, yp in zip(y_true_batch, y_pred_batch)]# 根据 y = x @ w + b# grad_w = -x.T @ residualgrad_w = matmul(transpose(x_batch), residual)grad_w = [-gw / batch_size for gw in grad_w]grad_b = -sum(residual) / batch_size# grad_w: List[float]# grad_b: floatreturn grad_w, grad_b# 开启训练
def train():lr = 0.01epochs = 50batch_size = 16dim_feat = 3num_samples = 500weights = [random.random() * 0.1 for _ in range(dim_feat)]bias = random.random() * 0.1print('original params')print('w:', weights)print('b:', bias)X, y = generate_data(num_samples, weights, bias, noise=0.1)for epoch in range(epochs):for i in range(0, num_samples, batch_size):x_batch = X[i:i+batch_size]y_batch = y[i:i+batch_size]y_pred = [item + bias for item in matmul(x_batch, weights)]loss = mse(y_batch, y_pred)grad_w, grad_b = compute_grad(y_batch, y_pred, x_batch)weights = [w - lr * gw for w, gw in zip(weights, grad_w)]bias -= lr * grad_bprint(f'Epoch: {epoch + 1}, Loss = {loss:.3f}')print('trained params')print('w:', weights)print('b:', bias)train()

输出结果如下

original params
w: [0.04845598598148951, 0.007741816562531545, 0.02436678108587098]
b: 0.01644073086522535
Epoch: 1, Loss = 0.000
Epoch: 2, Loss = 0.000
Epoch: 3, Loss = 0.000
Epoch: 4, Loss = 0.000
Epoch: 5, Loss = 0.000
Epoch: 6, Loss = 0.000
Epoch: 7, Loss = 0.000
Epoch: 8, Loss = 0.000
Epoch: 9, Loss = 0.000
Epoch: 10, Loss = 0.000
Epoch: 11, Loss = 0.000
Epoch: 12, Loss = 0.000
Epoch: 13, Loss = 0.000
Epoch: 14, Loss = 0.000
Epoch: 15, Loss = 0.000
Epoch: 16, Loss = 0.000
Epoch: 17, Loss = 0.000
Epoch: 18, Loss = 0.000
Epoch: 19, Loss = 0.000
Epoch: 20, Loss = 0.000
Epoch: 21, Loss = 0.000
Epoch: 22, Loss = 0.000
Epoch: 23, Loss = 0.000
Epoch: 24, Loss = 0.000
Epoch: 25, Loss = 0.000
Epoch: 26, Loss = 0.000
Epoch: 27, Loss = 0.000
Epoch: 28, Loss = 0.000
Epoch: 29, Loss = 0.000
Epoch: 30, Loss = 0.000
Epoch: 31, Loss = 0.000
Epoch: 32, Loss = 0.000
Epoch: 33, Loss = 0.000
Epoch: 34, Loss = 0.000
Epoch: 35, Loss = 0.000
Epoch: 36, Loss = 0.000
Epoch: 37, Loss = 0.000
Epoch: 38, Loss = 0.000
Epoch: 39, Loss = 0.000
Epoch: 40, Loss = 0.000
Epoch: 41, Loss = 0.000
Epoch: 42, Loss = 0.000
Epoch: 43, Loss = 0.000
Epoch: 44, Loss = 0.000
Epoch: 45, Loss = 0.000
Epoch: 46, Loss = 0.000
Epoch: 47, Loss = 0.000
Epoch: 48, Loss = 0.000
Epoch: 49, Loss = 0.000
Epoch: 50, Loss = 0.000
trained params
w: [0.05073234817652038, 0.007306286342947243, 0.023218625946243507]
b: 0.016648404245261664