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stanford-cs229
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assignment 1 data and code 

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-cs229 notes necessary for assignment 1
-assignment 1 data
-code for logistic regression
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cs229-prob.pdf 0 → 100644
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ps1/data/logistic_x.txt 0 → 100644
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ps1/data/quasar_test.csv 0 → 100644
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ps1/data/quasar_train.csv 0 → 100644
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ps1/ps1-code.py 0 → 100644
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import numpy as np
import matplotlib.pyplot as plt
x = np.loadtxt(open("data/logistic_x.txt","r")) #input array
y = np.loadtxt(open("data/logistic_y.txt","r")) #target array
m = x.shape[0] #number of training examples
x = np.c_[np.ones(m),x] #append intercept term to x
y = np.expand_dims(y, axis=1) #reshape y for array broadcasting
theta = np.zeros((x.shape[1],1)) #theta: parameter array
def sigmoid_function(x):
x = np.clip( x, -500, 500 ) #prevent overflow
x = 1.0/( 1 + np.exp( -x ))
return x
def gradient_J(theta,x,y):
#gradJ: gradient of the logistic cost function with respect to the parameter array theta
a = np.multiply(y,x)
b = 1-sigmoid_function(np.multiply(y,np.dot(x,theta)))
grad_J = (-1/m)*np.sum(np.multiply(a,b),axis=0)
if theta.shape[0] != grad_J.shape[0]:
print("The dimensions of the gradient of the cost function J with respect to the vector theta are incorrect.")
return grad_J
def hessian_J(theta,x,y):
a = sigmoid_function(y*np.dot(x,theta))
right_term = a*(1-a)
left_term = np.einsum("ij,ik->ijk",x,x)
H = np.einsum('ijk,il->jk',left_term,right_term)
return H/m
def rel_error(x, y):
""" returns relative error """
return np.max(np.abs(x - y) / (np.maximum(1e-8, np.abs(x) + np.abs(y))))
def newton(theta,x,y,tolerance=0.01,itercount=False):
niter=0
while True:
G = gradient_J(theta,x,y)
H = hessian_J(theta,x,y)
c = np.expand_dims(np.dot(np.linalg.inv(H),G),axis=1)
theta_1 = theta - c
if (rel_error(theta_1,theta)<tolerance):
break
theta = theta_1
niter+=1
if itercount:
print('Number of loop iterations:',niter)
return theta
theta = newton(theta,x,y)
print("parameter vector theta:",theta)
#Plot Training data and decision boundary fit by logistic regression
#plt.title("Training data and decision boundary fit by logistic regression")
plus = np.where(y>0)[0]
minus = np.where(y<0)[0]
plt.scatter(x[plus,1],x[plus,2],color = "r", marker="+",label="y= 1")
plt.scatter(x[minus,1],x[minus,2],color="b", marker="_",label="y= -1")
h = np.dot(x,theta)
plt.xlabel("x1")
plt.ylabel("x2")
def boundary(theta,x):
a = -theta[1]/theta[2]
b = -theta[0]/theta[2]
return a*x + b
# define bounds of the domain
min1, max1 = x[:, 1].min()-1, x[:, 1].max()+1
min2, max2 = x[:, 2].min()-1, x[:, 2].max()+1
#plot decision boundary
xbound = np.arange(min1,max1,0.1)
ybound = boundary(theta,xbound)
plt.plot(xbound,ybound,label="decision boundary")
plt.legend()
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