bag bag - 1 year ago 54
Python Question

Univariate Linear Regression outputting NaN

I'm currently writing an implementation of univariate linear regression on python:

# implementation of univariate linear regression
import numpy as np


def cost_function(hypothesis, y, m):
return (1 / (2 * m)) * ((hypothesis - y) ** 2).sum()


def hypothesis(X, theta):
return X.dot(theta)


def gradient_descent(X, y, theta, m, alpha):
for i in range(1500):
temp1 = theta[0][0] - alpha * (1 / m) * (hypothesis(X, theta) - y).sum()
temp2 = theta[1][0] - alpha * (1 / m) * ((hypothesis(X, theta) - y) * X[:, 1]).sum()
theta[0][0] = temp1
theta[1][0] = temp2

return theta

if __name__ == '__main__':
data = np.loadtxt('data.txt', delimiter=',')

y = data[:, 1]
m = y.size
X = np.ones(shape=(m, 2))
X[:, 1] = data[:, 0]
theta = np.zeros(shape=(2, 1))
alpha = 0.01

print(gradient_descent(X, y, theta, m, alpha))


This code will output NaN for theta, after going to infinity - I can't figure out what's going wrong, but it's surely something to do with my changing of theta in the gradient descent function.

The data I'm using is a simple linear regression pairs dataset I got online - and that loads in correctly.

Can anyone point me in the right direction?

Answer Source

The problem you're seeing is that when you do X[:,1] or data[:,1], you get objects of shape (m,). When you multiply an object of shape (m,) with a matrix of shape (m,1), you get a matrix of size (m,m)

a = np.array([1,2,3])
b = np.array([[4],[5],[6]])
(a*b).shape #prints (3,3)

If you do y=y.reshape((m,1)) in your if __name__ block and inside your gradient_descent function you do

X_1 = X[:,1].reshape((m,1))

Should fix the problem. Right now what's happening is that when you do

((hypothesis(X, theta) - y) * X[:, 1])

you're getting a 100 by 100 matrix, which is not what you want.

Full code I used for testing is:

# implementation of univariate linear regression
import numpy as np


def cost_function(hypothesis, y, m):
  return (1 / (2 * m)) * ((hypothesis - y) ** 2).sum()


def hypothesis(X, theta):
  return X.dot(theta)


def gradient_descent(X, y, theta, m, alpha):
  X_1 = X[:,1]
  X_1 = X_1.reshape((m,1))
  for i in range(1500):
    temp1 = theta[0][0] - alpha * (1 / m) * (hypothesis(X, theta) - y).sum()
    temp2 = theta[1][0] - alpha * (1 / m) * ((hypothesis(X, theta) - y) * X_1).sum()
    theta[0][0] = temp1
    theta[1][0] = temp2

  return theta

if __name__ == '__main__':
  data= np.random.normal(size=(100,2))

  y = 30*data[:,0] + data[:, 1]
  m = y.size
  X = np.ones(shape=(m, 2))
  y = y.reshape((m,1))
  X[:, 1] = data[:, 0]
  theta = np.zeros(shape=(2, 1))
  alpha = 0.01

  print(gradient_descent(X, y, theta, m, alpha))
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