gradient descent implemented

diff_ml_models.py

@@ -0,0 +1,98 @@
+#%%
+''' this is a implementation of the Linear regression model
+from scratch without using any library '''
+import numpy as np
+X = 2* np.random.rand(100,1)
+X
+
+#%%
+#the dependent equation i.e Y's value depends on Y
+Y = 4 + 3 * X + np.random.randn(100, 1)
+Y
+#%%
+#creates 100 X 1 shape matrix with value 1
+np.ones((100,1))
+#%%
+X_b = np.c_[np.ones((100, 1)), X]
+# add x0 = 1 to each instance
+X_b
+
+#%%
+''' the normal equation'''
+theta_best = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(Y) 
+theta_best
+
+#%%
+X_new = np.array([[0], [2]])
+X_new_b = np.c_[np.ones((2, 1)), X_new] # add x0 = 1 to each instance
+y_predict = X_new_b.dot(theta_best)
+y_predict
+
+#%%
+import matplotlib.pyplot as plt
+plt.plot(X_new, y_predict, "r-")
+plt.plot(X, Y, "g.")
+plt.axis([0, 2, 0, 15])
+plt.show()
+
+#%%
+#The equivalent implementation of the above Algorithm with library 
+from sklearn.linear_model import LinearRegression
+lin_reg = LinearRegression()
+lin_reg.fit(X, Y)
+lin_reg.intercept_, lin_reg.coef_
+lin_reg.predict(X_new)
+
+#%%
+''' this is the implementation of the gradient descent algorithm 
+from scratch'''
+eta = 0.1 # learning rate
+n_iterations = 1000
+m = 100
+theta = np.random.randn(2,1)
+theta
+
+#%%
+for iteration in range(n_iterations):
+    gradient = 2/m * X_b.T.dot(X_b.dot(theta) - Y)
+    theta = theta - eta * gradient
+theta
+
+#%%
+''' 
+this is the implementation of the stochastic gradient
+descent algorithm
+'''
+
+epochs = 50 
+t0 , t1 = (5,50)
+
+def learning_rate(t):
+    return t0 / (t + t1)
+
+for epoch in range(epochs):
+    for i in range(m):
+        random_index = np.random.randint(m)
+        x_i = X_b[random_index:(random_index + 1)]
+        y_i = Y[random_index:random_index+1]
+        gradients = 2 * x_i.T.dot(x_i.dot(theta) - y_i)
+        eta = learning_rate(epoch * m + i)
+        theta = theta - eta * gradients
+
+theta
+
+#%%
+from sklearn.preprocessing import PolynomialFeatures
+m = 100
+X_p = 6 * np.random.rand(m, 1) - 3
+Y_p = 0.5 * X_p**2 + X_p + 2 + np.random.randn(m, 1)
+poly_features = PolynomialFeatures(degree=2 , include_bias=False)
+X_poly = poly_features.fit_transform(X_p)
+X_p[0]
+X_poly[0]
+
+#%%
+lin_reg = LinearRegression()
+lin_reg.fit(X_poly,Y_p)
+print(lin_reg.intercept_ , lin_reg.coef_)
+