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Grad descent multi var and normal eq done. (End of Ex 1.)
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‎ex1/ex1_multi.py‎

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#!/usr/bin/env python
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import numpy as np
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import pandas as pd
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from pandas import Series, DataFrame
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import matplotlib.pyplot as plt
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## Helper functions
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colName = ['ones', 'size', 'rooms']
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def featureNormalize(X):
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# Goodness, this is easy with pandas.
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X_norm = (X - X.mean())/X.std()
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mu = X.mean()
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sigma = X.std()
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return X_norm, mu, sigma
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def predictValues(X, theta):
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predictedValues = X.apply(lambda x:
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(x[colName[0]]*theta[0] +
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x[colName[1]]*theta[1] +
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x[colName[2]]*theta[2]),
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axis=1)
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return predictedValues
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def computeCostMulti(X, y, theta):
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m = len(y)
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predictedValues = predictValues(X, theta)
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sumOfSquareErrors = (predictedValues - y['price']).apply(np.square).sum()
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cost = sumOfSquareErrors / (2*m)
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return cost
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def gradientDescentMulti(X, y, theta, alpha, num_iters, verbose=False):
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m = len(y) # number of training examples
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costHistory = []
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if verbose:
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print 'theta input ', theta
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print 'initial cost %e' % computeCostMulti(X, y, theta)
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colName = ['ones', 'size', 'rooms']
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for i in xrange(num_iters):
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predictedValues = predictValues(X, theta)
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for i in [0,1,2]:
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theta[i] = theta[i] - alpha / m * ((predictedValues - y['price']) * X[colName[i]]).sum()
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cost = computeCostMulti(X, y, theta)
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costHistory.append(cost)
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if verbose:
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print ' %04i theta' % i, theta
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print ' %04i cost %e' % (i, cost)
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return theta, Series(costHistory)
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def normalEqn(X, y):
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X = X[[colName[0], colName[1], colName[2]]]
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xtx = np.dot(X.transpose(), X)
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pinv = np.linalg.pinv(xtx)
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theta = np.dot(pinv,np.dot(X.transpose(),y))
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theta = theta.flatten()
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return theta
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if __name__ == '__main__':
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## Initialization
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## ================ Part 1: Feature Normalization ================
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## Clear and Close Figures
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plt.close('all')
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print 'Loading data ...'
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## Load Data
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data = pd.read_csv('ex1data2.txt', header=None, names=['size', 'rooms', 'price'])
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X = data[['size', 'rooms']]
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y = data[['price']]
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m = len(y)
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# Print out some data points
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print 'First 10 examples from the dataset:'
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print data.head(10)
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# Scale features and set them to zero mean
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print 'Normalizing Features ...'
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X, mu, sigma = featureNormalize(X)
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# Add intercept term to X
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X['ones'] = np.ones(m)
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## ================ Part 2: Gradient Descent ================
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print 'Running gradient descent ...'
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# Choose some alpha value
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alpha = 0.01
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num_iters = 1000
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# Init Theta and Run Gradient Descent
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theta_grad = np.zeros(3)
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theta_grad, costHistory = gradientDescentMulti(X, y, theta_grad, alpha, num_iters, verbose=False)
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# Plot the convergence graph
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print 'Theta found by gradient descent, %04i iter:' % num_iters
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print theta_grad
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f1 = plt.figure()
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p1 = costHistory.plot()
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p1.axes.set_title('Evolution of cost')
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p1.axes.yaxis.label.set_text('Cost function')
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p1.axes.xaxis.label.set_text('Iteration')
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f1.show()
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# Estimate the price of a 1650 sq-ft, 3 br house
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X1 = DataFrame({'ones':[1],
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'size':[(1650-mu['size'])/sigma['size']],
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'rooms':[(3-mu['rooms'])/sigma['rooms']]})
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X1 = X1[colName]
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price_grad = predictValues(X1, theta_grad)[0]
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print 'Predicted price of a 1650 sq-ft, 3 br house '\
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'(using gradient descent): \n$%.2f\n' % price_grad
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## ================ Part 3: Normal Equations ================
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print 'Solving with normal equations...'
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# Calculate the parameters from the normal equation
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theta_norm = normalEqn(X, y)
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# Display normal equation's result
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print 'Theta computed from the normal equations:'
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print theta_norm
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# Estimate the price of a 1650 sq-ft, 3 br house
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price_norm = np.dot(X1, theta_norm)
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print 'Predicted price of a 1650 sq-ft, 3 br house '\
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'(using normal equations): \n$%.2f\n' % price_norm
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print 'Fractional difference: %.2f%%' % ( (price_norm - price_grad)/((price_grad+price_norm)/2)*100 )

‎ex1/gradientDescent.py‎

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@@ -48,7 +48,7 @@ def gradientDescent(X, y, theta, alpha, num_iters, verbose=False):
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predictedValues = X['population'].apply(lambda x: theta[0] + theta[1]*x)
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# Okay, here the column of ones would have made it a wee bit nicer here.
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# Okay, the column of ones would have made it a wee bit nicer here.
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theta[0] = theta[0] - alpha / m * (predictedValues - y['profit']).sum()
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theta[1] = theta[1] - alpha / m * ((predictedValues - y['profit']) * X['population']).sum()
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plt.plot(seq, fitLine(seq), 'r', label='Linear regression')
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plt.legend(loc='upper left')
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f2.show()
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# Predict values for population sizes of 35,000 and 70,000
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predict1 = np.dot([1, 3.5], theta)
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print 'For population = 35,000, we predict a profit of %.2f' % (predict1*10000)
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predict2 = np.dot([1, 7], theta)

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