update on today's lectures

2021-10-21 08:10:45 +02:00
parent 8630bcf4b3
commit f263050011
101 changed files with 3251 additions and 1854 deletions
@@ -0,0 +1,44 @@
+
+from random import random, seed
+import numpy as np
+import matplotlib.pyplot as plt
+from mpl_toolkits.mplot3d import Axes3D
+from matplotlib import cm
+from matplotlib.ticker import LinearLocator, FormatStrFormatter
+import sys
+
+# the number of datapoints
+n = 100
+x = 2*np.random.rand(n,1)
+y = 4+3*x*x+np.random.randn(n,1)
+
+X = np.c_[np.ones((n,1)), x, x*x]
+XT_X = X.T @ X
+
+#Ridge parameter lambda
+lmbda  = 0.001
+Id = lmbda* np.eye(XT_X.shape[0])
+
+beta_linreg = np.linalg.inv(XT_X+Id) @ X.T @ y
+print(beta_linreg)
+# Start plain gradient descent
+beta = np.random.randn(2,1)
+
+eta = 0.1
+Niterations = 100
+
+for iter in range(Niterations):
+    gradients = 2.0/n*X.T @ (X @ (beta)-y)+2*lmbda*beta
+    beta -= eta*gradients
+
+print(beta)
+ypredict = X @ beta
+ypredict2 = X @ beta_linreg
+plt.plot(x, ypredict, "r-")
+plt.plot(x, ypredict2, "b-")
+plt.plot(x, y ,'ro')
+plt.axis([0,2.0,0, 15.0])
+plt.xlabel(r'$x$')
+plt.ylabel(r'$y$')
+plt.title(r'Gradient descent example for Ridge')
+plt.show()