Coursera: Machine Learning (Week 2) [Assignment Solution] - Andrew NG

▸ Linear regression and get to see it work on data.

I have recently completed the Machine Learning course from Coursera by Andrew NG.

While doing the course we have to go through various quiz and assignments.

Here, I am sharing my solutions for the weekly assignments throughout the course.

These solutions are for reference only.

> It is recommended that you should solve the assignments by yourself honestly then only it makes sense to complete the course.

> But, In case you stuck in between, feel free to refer to the solutions provided by me.

NOTE:

Don't just copy paste the code for the sake of completion. 

Even if you copy the code, make sure you understand the code first.

Since there is NO assignment in week-1, Let's start with the week-2 assignment....

In this exercise, you will implement linear regression and get to see it work on data. Before starting on this programming exercise, we strongly recommend watching the video lectures and completing the review questions for the associated topics.

Recommended Machine Learning Courses:

1. Coursera: Machine Learning  
2. Coursera: Deep Learning Specialization
3. Coursera: Machine Learning with Python
4. Coursera: Advanced Machine Learning Specialization
5. Udemy: Machine Learning
6. LinkedIn: Machine Learning
7. Eduonix: Machine Learning
8. edX: Machine Learning
9. Fast.ai: Introduction to Machine Learning for Coders

It consist of the following files:

• ex1.m - Octave/MATLAB script that steps you through the exercise
• ex1 multi.m - Octave/MATLAB script for the later parts of the exercise
• ex1data1.txt - Dataset for linear regression with one variable
• ex1data2.txt - Dataset for linear regression with multiple variables
• submit.m - Submission script that sends your solutions to our servers
• [*] warmUpExercise.m - Simple example function in Octave/MATLAB
• [*] plotData.m - Function to display the dataset
• [*] computeCost.m - Function to compute the cost of linear regression
• [*] gradientDescent.m - Function to run gradient descent
• [#] computeCostMulti.m - Cost function for multiple variables
• [#] gradientDescentMulti.m - Gradient descent for multiple variables
• [#] featureNormalize.m - Function to normalize features
• [#] normalEqn.m - Function to compute the normal equations
• Video - YouTube videos featuring Free IOT/ML tutorials

* indicates files you will need to complete
# indicates optional exercises

warmUpExercise.m :

function A = warmUpExercise()
  %WARMUPEXERCISE Example function in octave
  %   A = WARMUPEXERCISE() is an example function that returns the 5x5 identity matrix
  
   A = []; 
  % ============= YOUR CODE HERE ==============
  % Instructions: Return the 5x5 identity matrix 
  %               In octave, we return values by defining which variables
  %               represent the return values (at the top of the file)
  %               and then set them accordingly. 
  
   A = eye(5);  %It's a built-in function to create identity matrix
  
  % ===========================================
end

plotData.m :

function plotData(x, y)
  %PLOTDATA Plots the data points x and y into a new figure 
  %   PLOTDATA(x,y) plots the data points and gives the figure axes labels of
  %   population and profit.
  
  figure; % open a new figure window
  
  % ====================== YOUR CODE HERE ======================
  % Instructions: Plot the training data into a figure using the 
  %               "figure" and "plot" commands. Set the axes labels using
  %               the "xlabel" and "ylabel" commands. Assume the 
  %               population and revenue data have been passed in
  %               as the x and y arguments of this function.
  %
  % Hint: You can use the 'rx' option with plot to have the markers
  %       appear as red crosses. Furthermore, you can make the
  %       markers larger by using plot(..., 'rx', 'MarkerSize', 10);
  
  plot(x, y, 'rx', 'MarkerSize', 10); % Plot the data
  ylabel('Profit in $10,000s'); % Set the y-axis label
  xlabel('Population of City in 10,000s'); % Set the x-axis label
  
  % ============================================================
end

computeCost.m :

function J = computeCost(X, y, theta)
  %COMPUTECOST Compute cost for linear regression
  %   J = COMPUTECOST(X, y, theta) computes the cost of using theta as the
  %   parameter for linear regression to fit the data points in X and y
  
  % Initialize some useful values
  m = length(y); % number of training examples
  
  % You need to return the following variables correctly 
  J = 0;
  
  % ====================== YOUR CODE HERE ======================
  % Instructions: Compute the cost of a particular choice of theta
  %               You should set J to the cost.
  
  %%%%%%%%%%%%% CORRECT %%%%%%%%%
  % h = X*theta;
  % temp = 0; 
  % for i=1:m
  %   temp = temp + (h(i) - y(i))^2;
  % end
  % J = (1/(2*m)) * temp;
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  
  %%%%%%%%%%%%% CORRECT: Vectorized Implementation %%%%%%%%%
  J = (1/(2*m))*sum(((X*theta)-y).^2);
  %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%

  % =========================================================================
end

gradientDescent.m :

function [theta, J_history] = gradientDescent(X, y, theta, alpha, num_iters)
  %GRADIENTDESCENT Performs gradient descent to learn theta
  %   theta = GRADIENTDESCENT(X, y, theta, alpha, num_iters) updates theta by 
  %   taking num_iters gradient steps with learning rate alpha
  
  % Initialize some useful values
  m = length(y); % number of training examples
  J_history = zeros(num_iters, 1);
  
  for iter = 1:num_iters
  
   % ====================== YOUR CODE HERE ======================
   % Instructions: Perform a single gradient step on the parameter vector
   %               theta. 
   %
   % Hint: While debugging, it can be useful to print out the values
   %       of the cost function (computeCost) and gradient here.
   %
   
   %%%%%%%%% CORRECT %%%%%%%
   %error = (X * theta) - y;
   %temp0 = theta(1) - ((alpha/m) * sum(error .* X(:,1)));
   %temp1 = theta(2) - ((alpha/m) * sum(error .* X(:,2)));
   %theta = [temp0; temp1];
   %%%%%%%%%%%%%%%%%%%%%%%%%
  
   %%%%%%%%% CORRECT %%%%%%%  
   %error = (X * theta) - y;
   %temp0 = theta(1) - ((alpha/m) * X(:,1)'*error);
   %temp1 = theta(2) - ((alpha/m) * X(:,2)'*error);
   %theta = [temp0; temp1];
   %%%%%%%%%%%%%%%%%%%%%%%%%
  
   %%%%%%%%% CORRECT %%%%%%%
   error = (X * theta) - y;
   theta = theta - ((alpha/m) * X'*error);
   %%%%%%%%%%%%%%%%%%%%%%%%%
   
   % ============================================================
  
   % Save the cost J in every iteration    
   J_history(iter) = computeCost(X, y, theta);
  
  end
end

computeCostMulti.m :

function J = computeCostMulti(X, y, theta)
  %COMPUTECOSTMULTI Compute cost for linear regression with multiple variables
  %   J = COMPUTECOSTMULTI(X, y, theta) computes the cost of using theta as the
  %   parameter for linear regression to fit the data points in X and y
  
  % Initialize some useful values
  m = length(y); % number of training examples
  
  % You need to return the following variables correctly 
  J = 0;
  
  % ====================== YOUR CODE HERE ======================
  % Instructions: Compute the cost of a particular choice of theta
  %               You should set J to the cost.
  
  J = (1/(2*m))*(sum(((X*theta)-y).^2));

  % =========================================================================

end

gradientDescentMulti.m :

function [theta, J_history] = gradientDescentMulti(X, y, theta, alpha, num_iters)
  %GRADIENTDESCENTMULTI Performs gradient descent to learn theta
  %   theta = GRADIENTDESCENTMULTI(x, y, theta, alpha, num_iters) updates theta by
  %   taking num_iters gradient steps with learning rate alpha
  
  % Initialize some useful values
  m = length(y); % number of training examples
  J_history = zeros(num_iters, 1);
  
  for iter = 1:num_iters
  
   % ====================== YOUR CODE HERE ======================
   % Instructions: Perform a single gradient step on the parameter vector
   %               theta. 
   %
   % Hint: While debugging, it can be useful to print out the values
   %       of the cost function (computeCostMulti) and gradient here.
   %
  
   %%%%%%%% CORRECT %%%%%%%%%%   
   error = (X * theta) - y;
   theta = theta - ((alpha/m) * X'*error);
   %%%%%%%%%%%%%%%%%%%%%%%%%%%
  
   % ============================================================
  
   % Save the cost J in every iteration    
   J_history(iter) = computeCostMulti(X, y, theta);
  
  end
end

Check-out our free tutorials on IOT (Internet of Things):

featureNormalize.m :

function [X_norm, mu, sigma] = featureNormalize(X)
  %FEATURENORMALIZE Normalizes the features in X 
  %   FEATURENORMALIZE(X) returns a normalized version of X where
  %   the mean value of each feature is 0 and the standard deviation
  %   is 1. This is often a good preprocessing step to do when
  %   working with learning algorithms.
  
  % You need to set these values correctly
  X_norm = X;
  mu = zeros(1, size(X, 2));
  sigma = zeros(1, size(X, 2));
  
  % ====================== YOUR CODE HERE ======================
  % Instructions: First, for each feature dimension, compute the mean
  %               of the feature and subtract it from the dataset,
  %               storing the mean value in mu. Next, compute the 
  %               standard deviation of each feature and divide
  %               each feature by it's standard deviation, storing
  %               the standard deviation in sigma. 
  %
  %               Note that X is a matrix where each column is a 
  %               feature and each row is an example. You need 
  %               to perform the normalization separately for 
  %               each feature. 
  %
  % Hint: You might find the 'mean' and 'std' functions useful.
  %       
  
  mu = mean(X);
  sigma = std(X);
  X_norm = (X - mu)./sigma;
  
  % ============================================================
end

normalEqn.m :

function [theta] = normalEqn(X, y)
  %NORMALEQN Computes the closed-form solution to linear regression 
  %   NORMALEQN(X,y) computes the closed-form solution to linear 
  %   regression using the normal equations.
  
  theta = zeros(size(X, 2), 1);
  
  % ====================== YOUR CODE HERE ======================
  % Instructions: Complete the code to compute the closed form solution
  %               to linear regression and put the result in theta.
  %
  
  % ---------------------- Sample Solution ----------------------
  
  theta = pinv(X'*X)*X'*y;
   
  % -------------------------------------------------------------
  % ============================================================
end

I tried to provide optimized solutions like vectorized implementation for each assignment. If you think that more optimization can be done, then put suggest the corrections / improvements.

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Click here to see solutions for all Machine Learning Coursera Assignments.

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Click here to see more codes for Arduino Mega (ATMega 2560) and similar Family.

Feel free to ask doubts in the comment section. I will try my best to solve it.

If you find this helpful by any mean like, comment and share the post.

This is the simplest way to encourage me to keep doing such work.

Thanks and Regards,

-Akshay P. Daga