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import os
import numpy as np
import pandas as pd
import matplotlib.pyplot as plt
%matplotlib inline
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path = os.getcwd() + '/' + 'ex1data1.txt'
data = pd.read_csv(path, header=None, names=['X', 'Y'])
#data.head()
data
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data.describe()
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data.plot(kind='scatter', x='X', y='Y', figsize=(12,8))
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def computeCost(X, y, theta):
inner = np.power(((X * theta.T) - y), 2)
return np.sum(inner) / (2 * len(X))
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# append a ones column to the front of the data set
data.insert(0, 'Ones', 1)
# set X (training data) and y (target variable)
cols = data.shape[1]
X = data.iloc[:,0:cols-1]
y = data.iloc[:,cols-1:cols]
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# convert from data frames to numpy matrices
X = np.matrix(X.values)
y = np.matrix(y.values)
theta = np.matrix(np.array([0,0]))
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X.shape, theta.shape, y.shape
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computeCost(X, y, theta)
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def gradientDescent(X, y, theta, alpha, iters):
temp = np.matrix(np.zeros(theta.shape))
parameters = int(theta.ravel().shape[1])
cost = np.zeros(iters)
Wtheta = np.zeros(shape=(iters,2))
for i in range(iters):
error = (X * theta.T) - y
for j in range(parameters):
term = np.multiply(error, X[:,j])
temp[0,j] = theta[0,j] - ((alpha / len(X)) * np.sum(term))
theta = temp
cost[i] = computeCost(X, y, theta)
Wtheta [i,0] = theta[0,0]
Wtheta [i,1] = theta[0,1]
#print (theta)
return Wtheta, cost
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# initialize variables for learning rate and iterations
alpha = 0.01
iters = 1000
# perform gradient descent to "fit" the model parameters
W, cost = gradientDescent(X, y, theta, alpha, iters)
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x = np.linspace(data.X.min(), data.X.max(), 10)
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fig, ax = plt.subplots(figsize=(12,8))
for i in range(iters):
f = W[i, 0] + (W[i, 1] * x)
ax.plot(x, f, 'b')
f = W[iters-1, 0] + (W[iters-1, 1] * x)
ax.plot(x, f,'r')
ax.scatter(data.X, data.Y, label='Traning Data')
ax.legend(loc=2)
ax.set_xlabel('X')
ax.set_ylabel('Y')
ax.set_title('Predicted Y vs. X Size')
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fig, ax = plt.subplots(figsize=(12,8))
ax.plot(np.arange(iters), cost, 'r')
ax.set_xlabel('Iterations')
ax.set_ylabel('Cost')
ax.set_title('Error vs. Training Epoch')
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