gradient descent python

import numpy as np
import matplotlib.pyplot as plt
from sklearn.datasets import load_wine
from sklearn.preprocessing import StandardScaler


data = load_wine()
X = data.data[:, :1]  # Use the first feature for simplicity
y = data.target.astype(float)

scaler = StandardScaler()
X = scaler.fit_transform(X)


X_b = np.c_[np.ones((X.shape[0], 1)), X]  # shape (n_samples, 2)

theta = np.random.randn(2)
learning_rate = 0.1
iterations = 100
m = len(y)


loss_history = []


for i in range(iterations):
    predictions = X_b.dot(theta)
    errors = predictions - y
    gradient = (2/m) * X_b.T.dot(errors)
    theta = theta - learning_rate * gradient

    loss = (1/m) * np.sum(errors**2)  # MSE
    loss_history.append(loss)

plt.plot(range(iterations), loss_history, color='blue')
plt.xlabel("Iterations")
plt.ylabel("Mean Squared Error")
plt.title("Gradient Descent on Wine Data")
plt.show()

print("Final parameters:", theta)