NumPy實現線性迴歸（二）

regression_numpy2.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_f(x, y, p, w, b):
    # 基於損失函數手動偏微分
    def dloss_dp(p, y):
        return (2 * (p - y)) / p.size

    def dp_dw(x, w, b):
        return x
        
    def dp_db(x, w, b):
        return 1.0
    
    # 反向傳播計算梯度    
    dloss_dtp = dloss_dp(p, y)
    dloss_dw = dloss_dtp * dp_dw(x, w, b)
    dloss_db = dloss_dtp * dp_db(x, w, b)
    return np.array([dloss_dw.sum(), dloss_db.sum()])
    
def training_loop(epochs, lr, params, x, y, verbose = False):
    for epoch in range(1, epochs + 1):
        w, b = params
        p = model(x, w, b)
        grad = grad_f(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,  # 學習率
    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()