NumPy實現線性迴歸（一）

regression_numpy.py

import numpy as np
import cv2
import matplotlib.pyplot as plt

def model(x, w, b):
    return w * x + b
    
def mse_loss(p, y):
    return ((p - y) ** 2).mean()

def grad_loss(x, y, p, w, b):
    # 函式 f 的梯度
    def numerical_grad(f, params):
        h = 1e-4
        grad = np.zeros_like(params)
        
        for i in range(params.size):
            tmp = params[i]
            params[i] = tmp + h
            fxh1 = f(params)
            params[i] = tmp - h
            fxh2 = f(params)
            grad[i] = (fxh1 - fxh2) / (2 * h)
            params[i] = tmp
        
        return grad
    
    return numerical_grad(
        # 計算損失
        # 進一步建立損失函數
        lambda params: mse_loss(model(x, params[0], params[1]), y), 
        np.array([w, b])
    )

def training_loop(epochs, lr, params, x, y, verbose = True):
    for epoch in range(1, epochs + 1):
        w, b = params
        p = model(x, w, b)
        grad = grad_loss(x, y, p, w, b)
        params = params - lr * grad
        if verbose:
            print('週期', epoch, '--')
            print('\t損失：', float(mse_loss(p, y)))
            print('\t模型參數：', params)
            
    return params

# https://openhome.cc/Gossip/DCHardWay/images/PolynomialRegression-1.JPG
img = cv2.imread('PolynomialRegression-1.JPG', cv2.IMREAD_GRAYSCALE)
idx = np.where(img < 127)       # 黑點的索引

x = idx[1]
y = -idx[0] + img.shape[0] # 反轉 y 軸

plt.gca().set_aspect(1)
plt.scatter(x, y)

w, b = training_loop(
    epochs = 100, 
    lr = 0.001, 
    params = np.array([1.0, 0.0]), 
    x = x, 
    y = y
)

x = np.linspace(0, 50, 50)
y = w * x + b

plt.plot(x, y)
plt.show()