线性回归算法

1. 算法思想

       寻找使计算误差最小的拟合曲线，可基于梯度下降算法对最小二乘形式的损失函数进行优化，最终获得模型回归系数(w、b)。

优点：计算简单；

缺点：不能拟合非线性数据；

2. 代码实现

1. 采用的数据集是UCI鲍鱼年龄预测数据集

2. 损失函数是均方差损失，优化算法是随机梯度下降算法。

import numpy as np
import matplotlib.pyplot as plt

def load_dataset(file_path):
    x = []
    y = []
    with open(file_path, 'r') as file:
        lines = file.readlines()
    for line in lines:
        one_line = line.strip().split('\t')
        one_line = [float(i) for i in one_line]
        x.append(one_line[:-1])
        y.append(one_line[-1])
    return np.array(x), np.array(y)

# 归一化数据集
def dataset_norm(x):
    x_min = np.min(x)
    x_max = np.max(x)
    return (x-x_min)/(x_max-x_min)

# 切分数据集
def split_train_test(x,y,ration=0.8):
    split_idx = np.int(x.shape[0]*ration)
    x_train = x[:split_idx]
    y_train = y[:split_idx]
    x_val = x[split_idx:]
    y_val = y[split_idx:]
    return x_train, y_train, x_val, y_val

# 计算w b的梯度更新值
def delta_w_b(x,y,pred_y):
    delta_w = (y-pred_y)*x
    delta_b = y-pred_y
    return delta_w, delta_b

# 计算损失
def cal_loss(y, pred_y):
    return (y-pred_y)**2/2

# 迭代训练
def train_model(epoches, alpha, x_train, y_train, w, b):
    loss = []
    for epoch in range(epoches):
        sum_loss = 0
        for idx in range(num_train):
            pred_y = np.dot(w, x_train[idx]) + b
            delta_w, delta_b = delta_w_b(x_train[idx],y_train[idx],pred_y)
            w = w + alpha*delta_w
            b = b + alpha*delta_b
            sum_loss += cal_loss(y_train[idx], pred_y)
        loss.extend([sum_loss/num_train])
        print("当前迭代过程的训练损失： ", sum_loss/num_train)
    return w, b, loss

# 测试模型
def val_model(x_val, y_val, w, b):
    y_val_pred = np.dot(w, x_val.T) + b
    print("测试集预测结果的维度：",y_val_pred.shape)
    num = y_val_pred.shape[1]
    y_val_pred = y_val_pred[0]
    val_loss = []
    for idx in range(num):
        temp_loss = y_val_pred[idx]-y_val[idx]
        val_loss.extend([temp_loss])
    return val_loss

# 绘制迭代过程的损失曲线
def view_loss(loss):
    x_axis = [i for i in range(len(loss))]
    plt.plot(x_axis, loss)
    plt.show()

if __name__=='__main__':
    file_path = "abalone.txt"
    x, y = load_dataset(file_path)
    print("数据集维度：", x.shape, y.shape)

    x = dataset_norm(x)
    y = dataset_norm(y)

    x_train, y_train, x_val, y_val = split_train_test(x, y)
    num_train = x_train.shape[0]
    print("训练集维度：",x_train.shape, "测试集维度：",x_val.shape)

    # 初始化权重和bias
    np.random.seed(1)
    w = np.random.random((1,8))
    b = np.random.random((1))
    print("权重和bias的维度：",w.shape, b.shape)

    w, b, train_loss = train_model(300, 0.01, x_train, y_train, w, b)
    view_loss(train_loss)

    val_loss = val_model(x_val, y_val, w, b)
    view_loss(val_loss)