Li Hongyi machine learning - pockmon demo implementation

The source code of Li Hongyi's machine learning-pockmon demo is implemented as follows, and the personal understanding of the relevant code is given in the comments.

import numpy as np
import matplotlib.pyplot as plt

x_data = [338., 333., 328., 207., 226., 25., 179., 60., 208., 606.]
y_data = [640., 633., 619., 393., 428., 27., 193., 66., 226., 1591.]
# y_data = b + w * x_data

x = np.arange(-200, -100, 1)  # bias
y = np.arange(-5, 5, 0.1)  # weight
z = np.zeros((len(x), len(y))) # The zeros function indicates that the output array is 301 rows and 101 columns
X, Y = np.meshgrid(x, y) # Expand the matrix, X is expanded to a horizontal vector matrix of 11*301, and Y is expanded to a column vector matrix of 101*301
for i in range(len(x)):
    for j in range(len(y)):
        b = x[i]
        w = y[j]
        z[j][i] = 0
        for n in range(len(x_data)):
            z[j][i] = z[j][i] + (y_data[n] - b - w*x_data[n])**2 # z[j][i] is b=x[i] and When w=y[j], the size of the corresponding Loss Function
        z[j][i] = z[j][i]/len(x_data) # training set bias value for a single data

# ydata = b + w * xdata
b = -120  # initial b
w = -4  # initial w
lr = 1  # learning rate
iteration = 100000 # The number of iterations to run

# store initial values for plotting
b_history = [b]
w_history = [w]

lr_b = 0 # Assign different learning rate values ​​to b and w respectively
lr_w = 0

# iterations
for i in range(iteration): # After 100000 iterations, see the final result
    b_grad = 0.0 # reassign b_grad to 0
    w_grad = 0.0 # reassign w_grad to 0
    for n in range(len(x_data)):
        # It should be noted here that the derivation is the L function, so the corresponding variables are w, b, which is to see the movement of w and b on their respective axes
        # Therefore, x_data, y_data are only data, be sure to distinguish! ! !
        b_grad = b_grad - 2.0*(y_data[n] - b - w*x_data[n])*1.0
        w_grad = w_grad - 2.0*(y_data[n] - b - w*x_data[n])*x_data[n]

    # Because these two values ​​are the sum of the sum of the squares of b_grad and w_grad, it is convenient to apply the following Adagrad method
    lr_b = lr_b + b_grad ** 2
    lr_w = lr_w + w_grad ** 2

    # update parameters
    b = b - lr/np. sqrt(lr_b) * b_grad # The Adagrad method is used here (as the number of iterations increases, lr will become smaller and smaller)
    w = w - lr/np. sqrt(lr_w) * w_grad # This can find minima more efficiently

    # store parameters for plotting
    b_history.append(b)
    w_history.append(w)

# plot the figure
plt.contourf(x, y, z, 50, alpha=0.5, cmap=plt.get_cmap('jet'))
plt.plot([-188.4], [2.67], 'x', ms=12, markeredgewidth=3, color='orange')
plt.plot(b_history, w_history, 'o-', ms=3, lw=1.5, color='black')
plt.xlim(-200, -100)
plt.ylim(-5, 5)
plt.xlabel(r'$b$', fontsize=16)
plt.ylabel(r'$w$', fontsize=16)
plt.show()