Updating linear regression slides

doc/src/Regression/Regression.do.txt

@@ -267,6 +267,69 @@ meaning that the solution for $\hat{\beta}$ is the one which minimizes the resid
 
 !eblock
 
+!split
+===== Simple regression model =====
+Add info about the equations
+!bc pycod
+# Importing various packages
+from random import random, seed
+import numpy as np
+import matplotlib.pyplot as plt
+
+x = 2*np.random.rand(100,1)
+y = 4+3*x+np.random.randn(100,1)
+
+xb = np.c_[np.ones((100,1)), x]
+theta = np.linalg.inv(xb.T.dot(xb)).dot(xb.T).dot(y)
+xnew = np.array([[0],[2]])
+xbnew = np.c_[np.ones((2,1)), xnew]
+ypredict = xbnew.dot(theta)
+
+plt.plot(xnew, ypredict, "r-")
+plt.plot(x, y ,'ro')
+plt.axis([0,2.0,0, 15.0])
+plt.xlabel(r'$x$')
+plt.ylabel(r'$y$')
+plt.title(r'Linear Regression')
+plt.show()
+
+!ec
+
+
+
+
+
+
+!split
+===== Simple regression model, now using _scikit-learn_ =====
+Add info about the equations
+!bc pycod
+# Importing various packages
+from random import random, seed
+import numpy as np
+import matplotlib.pyplot as plt
+from sklearn.linear_model import LinearRegression
+
+x = 2*np.random.rand(100,1)
+y = 4+3*x+np.random.randn(100,1)
+linreg = LinearRegression()
+linreg.fit(x,y)
+xnew = np.array([[0],[2]])
+ypredict = linreg.predict(xnew)
+
+plt.plot(xnew, ypredict, "r-")
+plt.plot(x, y ,'ro')
+plt.axis([0,2.0,0, 15.0])
+plt.xlabel(r'$x$')
+plt.ylabel(r'$y$')
+plt.title(r'Random numbers ')
+plt.show()
+!ec
+
+
+
+
+
 !split
 ===== The $\chi^2$ function  =====
 !bblock
@@ -433,6 +496,83 @@ The LSM suffers often from both being underdetermined and overdetermined in the
 
 
 
+
+
+
+
+
+
+
+
+!split
+===== Simple regression model with gradient descent  =====
+Add info about the equations, play around with different learning rates
+!bc pycod
+# Importing various packages
+from math import exp, sqrt
+from random import random, seed
+import numpy as np
+import matplotlib.pyplot as plt
+
+x = 2*np.random.rand(100,1)
+y = 4+3*x+np.random.randn(100,1)
+
+xb = np.c_[np.ones((100,1)), x]
+theta_linreg = np.linalg.inv(xb.T.dot(xb)).dot(xb.T).dot(y)
+print(theta_linreg)
+theta = np.random.randn(2,1)
+
+eta = 0.1
+Niterations = 1000
+m = 100
+
+for iter in range(Niterations):
+    gradients = 2.0/m*xb.T.dot(xb.dot(theta)-y)
+    theta -= eta*gradients
+
+print(theta)
+xnew = np.array([[0],[2]])
+xbnew = np.c_[np.ones((2,1)), xnew]
+ypredict = xbnew.dot(theta)
+ypredict2 = xbnew.dot(theta_linreg)
+plt.plot(xnew, ypredict, "r-")
+plt.plot(xnew, 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'Random numbers ')
+plt.show()
+!ec
+
+
+!split
+===== Simple regression model with stochastic gradient descent  =====
+Add info about the equations, play around with different learning rates
+!bc pycod
+# Importing various packages
+from math import exp, sqrt
+from random import random, seed
+import numpy as np
+import matplotlib.pyplot as plt
+from sklearn.linear_model import SGDRegressor
+
+x = 2*np.random.rand(100,1)
+y = 4+3*x+np.random.randn(100,1)
+
+xb = np.c_[np.ones((100,1)), x]
+theta_linreg = np.linalg.inv(xb.T.dot(xb)).dot(xb.T).dot(y)
+print(theta_linreg)
+sgdreg = SGDRegressor(n_iter = 50, penalty=None, eta0=0.1)
+sgdreg.fit(x,y.ravel())
+print(sgdreg.intercept_, sgdreg.coef_)
+
+!ec
+
+
+
+
+
 !split
 ===== The singular value decompostion  =====
 !bblock