Linear Regression with Batch Gradient Descent

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"""
    demo01_lr.py linear regression
"""

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.pyplot as mp
from mpl_toolkits.mplot3d import axes3d

train_x = np.array([0.5, 0.6, 0.8, 1.1, 1.4])
train_y = np.array([5.0, 5.5, 6.0, 6.8, 7.0])
test_x = np.array([0.45, 0.55, 1.0, 1.3, 1.5])
test_y = np.array([4.8, 5.3, 6.4, 6.9, 7.3])

times = 1000	# 定义梯度下降次数
lrate = 0.01	# 记录每次梯度下降参数变化率
epoches = []	# 记录每次梯度下降的索引
w0, w1, losses = [1], [1], []
for i in range(1, times + 1):
    epoches.append(i)
    # 损失函数值
    loss = (((w0[-1] + w1[-1] * train_x) - train_y) ** 2).sum() / 2
    losses.append(loss)

    # 计算梯度
    d0 = ((w0[-1] + w1[-1] * train_x) - train_y).sum()
    d1 = (((w0[-1] + w1[-1] * train_x) - train_y) * train_x).sum()
    # print('{:4}> w0={:.8f}, w1={:.8f}, loss={:.8f}'.format(epoches[-1], w0[-1], w1[-1], losses[-1]))
    w0.append(w0[-1] - lrate * d0)
    w1.append(w1[-1] - lrate * d1)

# 通过最优的w0和w1,求出所有样本x的预测值y
pred_y = w0[-1] + w1[-1] * train_x
plt.figure('Linear Regression', facecolor='lightgray')
plt.title('Linear Regression', fontsize=20)
plt.xlabel('x', fontsize=14)
plt.ylabel('y', fontsize=14)
plt.tick_params(labelsize=10)
plt.grid(linestyle=':')
plt.scatter(train_x, train_y, marker='s', c='dodgerblue', alpha=0.5, s=80, label='Sample')
plt.plot(train_x, pred_y, marker='D', c='orangered', alpha=0.5, label='Regression Line', linewidth=2)
plt.legend()
plt.savefig('sample-and-prediction')

# 绘制w0 w1 loss的变化曲线图
mp.figure('Training Progress', facecolor='lightgray')
mp.title('Training Progress', fontsize=16)
# w0
mp.subplot(311)
mp.ylabel('w0', fontsize=14)
mp.grid(linestyle=':')
mp.plot(epoches, w0[:-1], color='dodgerblue',
        label='w0')
mp.legend()

# w1
mp.subplot(312)
mp.ylabel('w1', fontsize=14)
mp.grid(linestyle=':')
mp.plot(epoches, w1[:-1], color='dodgerblue',
        label='w1')
mp.legend()
# loss
mp.subplot(313)
mp.ylabel('loss', fontsize=14)
mp.grid(linestyle=':')
mp.plot(epoches, losses, color='orangered',
        label='loss')
mp.legend()
mp.tight_layout()
plt.savefig('weight-and-loss.png')

# 基于三维曲面绘制梯度下降的过程中的每个散点
n = 500
w0_grid, w1_grid = np.meshgrid(np.linspace(0, 9, n),
                               np.linspace(0, 3.5, n))
loss = np.zeros_like(w0_grid)
for x, y in zip(train_x, train_y):
    loss += (w0_grid + w1_grid * x - y)**2 / 2
mp.figure('Loss Function', facecolor='lightgray')
ax3d = mp.gca(projection='3d')
ax3d.set_xlabel('w0', fontsize=14)
ax3d.set_ylabel('w1', fontsize=14)
ax3d.set_zlabel('loss', fontsize=14)
ax3d.plot_surface(w0_grid, w1_grid, loss, cmap='jet')
ax3d.plot(w0[:-1], w1[:-1], losses, 'o-',
          color='red')
# mp.tight_layout()
plt.savefig('gradient3D.png')

# 以等高线的方式绘制梯度下降的过程。
mp.figure('Batch Gradient Descent', facecolor='lightgray')
mp.title('Batch Gradient Descent', fontsize=20)
mp.xlabel('w0', fontsize=14)
mp.ylabel('w1', fontsize=14)
mp.tick_params(labelsize=10)
mp.grid(linestyle=':')
mp.contourf(w0_grid, w1_grid, loss, 10, cmap='jet')
cntr = mp.contour(w0_grid, w1_grid, loss, 10,
                  colors='black', linewidths=0.5)
mp.clabel(cntr, inline_spacing=0.1, fmt='%.2f',
          fontsize=8)
mp.plot(w0, w1, 'o-', c='orangered', label='BGD')
mp.legend()
plt.savefig('gradient-contour.png')

plt.show()