Gradient descent implemented using numpy

Author: olest

01-Simple-Linear-Regression/linreg.gradient.py

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+#!/usr/bin/python
+
+import numpy as np
+
+def gradDescent(x, y, theta, alpha, m, nIter):
+    loss = 0
+    for i in range(0, nIter):
+        h = np.dot(x, theta)
+        loss = (h-y)
+        gradient = np.dot(x.transpose(), loss) / m
+        theta = theta - alpha * gradient
+
+    cost = np.sum(loss ** 2) / (2 * m)
+    print("After %d iterations, cost is %f" % (nIter, cost))
+    return theta
+
+y = np.loadtxt('data/ex2y.dat')
+x = np.loadtxt('data/ex2x.dat')
+
+on = np.ones(np.shape(x))
+# append ones for offset
+x  = np.column_stack((on,x))
+
+m,n     = np.shape(x)
+numIter = 10000
+
+# starting values
+theta = np.array([5,5])
+# learning rate
+alpha = 0.05
+
+# gradient descent
+theta = gradDescent(x, y, theta, alpha, m, numIter)
+print "theta=",theta
+
+# analytical solution
+t1 = np.linalg.inv(np.dot(x.transpose(),x))
+theta2 = np.dot(np.dot(t1,x.transpose()),y)
+print "theta2=",theta2
+