Morten Hjorth-Jensen
45 lines
978 B
Python
45 lines
978 B
Python
from random import random, seed
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import numpy as np
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import matplotlib.pyplot as plt
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from mpl_toolkits.mplot3d import Axes3D
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from matplotlib import cm
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from matplotlib.ticker import LinearLocator, FormatStrFormatter
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import sys
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# the number of datapoints
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m = 100
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x = 2*np.random.rand(m,1)
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y = 4+3*x+np.random.randn(m,1)
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xb = np.c_[np.ones((m,1)), x]
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XT_X = xb.T @ xb
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#Ridge parameter lambda
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lmbda = 0.001
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Id = lmbda* np.eye(XT_X.shape[0])
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beta_linreg = np.linalg.inv(XT_X+Id) @ xb.T @ y
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print(beta_linreg)
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# Start plain gradient descent
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beta = np.random.randn(2,1)
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eta = 0.1
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Niterations = 100
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for iter in range(Niterations):
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gradients = 2.0/m*xb.T @ (xb @ (beta)-y)+2*lmbda*beta
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beta -= eta*gradients
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print(beta)
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ypredict = xb @ beta
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ypredict2 = xb @ beta_linreg
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plt.plot(x, ypredict, "r-")
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plt.plot(x, ypredict2, "b-")
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plt.plot(x, y ,'ro')
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plt.axis([0,2.0,0, 15.0])
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plt.xlabel(r'$x$')
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plt.ylabel(r'$y$')
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plt.title(r'Gradient descent example for Ridge')
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plt.show()
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