First part of assignment 2

mlclass-ex1/computeCostMulti.m

@@ -6,16 +6,15 @@
 % Initialize some useful values
 m = length(y); % number of training examples
 
-% You need to return the following variables correctly 
+% 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.
 
-
-
-
+err = (X * theta) - y;
+J = 1 / (2 * m) * (err' * err);
 
 % =========================================================================
 

mlclass-ex1/ex1_multi.m

@@ -3,11 +3,11 @@
 %
 %  Instructions
 %  ------------
-% 
+%
 %  This file contains code that helps you get started on the
-%  linear regression exercise. 
+%  linear regression exercise.
 %
-%  You will need to complete the following functions in this 
+%  You will need to complete the following functions in this
 %  exericse:
 %
 %     warmUpExercise.m
@@ -43,8 +43,8 @@
 fprintf('First 10 examples from the dataset: \n');
 fprintf(' x = [%.0f %.0f], y = %.0f \n', [X(1:10,:) y(1:10,:)]');
 
-fprintf('Program paused. Press enter to continue.\n');
-pause;
+%fprintf('Program paused. Press enter to continue.\n');
+%pause;
 
 % Scale features and set them to zero mean
 fprintf('Normalizing Features ...\n');
@@ -54,19 +54,18 @@
 % Add intercept term to X
 X = [ones(m, 1) X];
 
-
 %% ================ Part 2: Gradient Descent ================
 
 % ====================== YOUR CODE HERE ======================
 % Instructions: We have provided you with the following starter
 %               code that runs gradient descent with a particular
-%               learning rate (alpha). 
+%               learning rate (alpha).
 %
-%               Your task is to first make sure that your functions - 
-%               computeCost and gradientDescent already work with 
+%               Your task is to first make sure that your functions -
+%               computeCost and gradientDescent already work with
 %               this starter code and support multiple variables.
 %
-%               After that, try running gradient descent with 
+%               After that, try running gradient descent with
 %               different values of alpha and see which one gives
 %               you the best result.
 %
@@ -85,7 +84,7 @@
 alpha = 0.01;
 num_iters = 100;
 
-% Init Theta and Run Gradient Descent 
+% Init Theta and Run Gradient Descent
 theta = zeros(3, 1);
 [theta, J_history] = gradientDescentMulti(X, y, theta, alpha, num_iters);
 
@@ -104,7 +103,11 @@
 % ====================== YOUR CODE HERE ======================
 % Recall that the first column of X is all-ones. Thus, it does
 % not need to be normalized.
-price = 0; % You should change this
+
+Xi = ([1650 3] .- mu) ./ sigma;
+Xi = [ones(1) Xi];
+
+price = Xi * theta; % You should change this
 
 
 % ============================================================
@@ -120,12 +123,12 @@
 fprintf('Solving with normal equations...\n');
 
 % ====================== YOUR CODE HERE ======================
-% Instructions: The following code computes the closed form 
+% Instructions: The following code computes the closed form
 %               solution for linear regression using the normal
-%               equations. You should complete the code in 
+%               equations. You should complete the code in
 %               normalEqn.m
 %
-%               After doing so, you should complete this code 
+%               After doing so, you should complete this code
 %               to predict the price of a 1650 sq-ft, 3 br house.
 %
 

mlclass-ex1/featureNormalize.m

@@ -1,5 +1,5 @@
 function [X_norm, mu, sigma] = featureNormalize(X)
-%FEATURENORMALIZE Normalizes the features in 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
@@ -13,26 +13,26 @@
 % ====================== 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 
+%               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. 
+%               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. 
+%               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.
-%       
-
-
-
-
-
-
+%
 
+for i = 1:size(X,2);
+  mu(i) = mean(X(:,i));
+  sigma(i) = std(X(:,i));
+end;
 
+X_norm = bsxfun(@minus, X, mu);
+X_norm = bsxfun(@rdivide, X_norm, sigma);
 
 % ============================================================
 

mlclass-ex1/gradientDescentMulti.m

@@ -11,25 +11,19 @@
 
     % ====================== YOUR CODE HERE ======================
     % Instructions: Perform a single gradient step on the parameter vector
-    %               theta. 
+    %               theta.
     %
     % Hint: While debugging, it can be useful to print out the values
     %       of the cost function (computeCostMulti) and gradient here.
     %
 
-
-
-
-
-
-
-
-
-
+    h = (X * theta);
+    delta = ((h .- y)' * X)';
+    theta = theta .- ((alpha / m) * delta);
 
     % ============================================================
 
-    % Save the cost J in every iteration    
+    % Save the cost J in every iteration
     J_history(iter) = computeCostMulti(X, y, theta);
 
 end

mlclass-ex2/costFunction.m

@@ -0,0 +1,31 @@
+function [J, grad] = costFunction(theta, X, y)
+%COSTFUNCTION Compute cost and gradient for logistic regression
+%   J = COSTFUNCTION(theta, X, y) computes the cost of using theta as the
+%   parameter for logistic regression and the gradient of the cost
+%   w.r.t. to the parameters.
+
+% Initialize some useful values
+m = length(y); % number of training examples
+
+% You need to return the following variables correctly
+J = 0;
+grad = zeros(size(theta));
+
+% ====================== YOUR CODE HERE ======================
+% Instructions: Compute the cost of a particular choice of theta.
+%               You should set J to the cost.
+%               Compute the partial derivatives and set grad to the partial
+%               derivatives of the cost w.r.t. each parameter in theta
+%
+% Note: grad should have the same dimensions as theta
+%
+
+hypothesis = sigmoid(X * theta);
+err = (-1 .* y .* log(hypothesis)) - ((1 .- y) .* log(1 .- hypothesis));
+J = 1 / m * sum(err);
+
+grad = (1 / m) * ((hypothesis - y)' * X)';
+
+% =============================================================
+
+end

mlclass-ex2/costFunctionReg.m

@@ -0,0 +1,27 @@
+function [J, grad] = costFunctionReg(theta, X, y, lambda)
+%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization
+%   J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using
+%   theta as the parameter for regularized logistic regression and the
+%   gradient of the cost w.r.t. to the parameters. 
+
+% Initialize some useful values
+m = length(y); % number of training examples
+
+% You need to return the following variables correctly 
+J = 0;
+grad = zeros(size(theta));
+
+% ====================== YOUR CODE HERE ======================
+% Instructions: Compute the cost of a particular choice of theta.
+%               You should set J to the cost.
+%               Compute the partial derivatives and set grad to the partial
+%               derivatives of the cost w.r.t. each parameter in theta
+
+
+
+
+
+
+% =============================================================
+
+end

mlclass-ex2/ex2.m

@@ -0,0 +1,135 @@
+%% Machine Learning Online Class - Exercise 2: Logistic Regression
+%
+%  Instructions
+%  ------------
+%
+%  This file contains code that helps you get started on the logistic
+%  regression exercise. You will need to complete the following functions
+%  in this exericse:
+%
+%     sigmoid.m
+%     costFunction.m
+%     predict.m
+%     costFunctionReg.m
+%
+%  For this exercise, you will not need to change any code in this file,
+%  or any other files other than those mentioned above.
+%
+
+%% Initialization
+clear ; close all; clc
+
+%% Load Data
+%  The first two columns contains the exam scores and the third column
+%  contains the label.
+
+data = load('ex2data1.txt');
+X = data(:, [1, 2]); y = data(:, 3);
+
+%% ==================== Part 1: Plotting ====================
+%  We start the exercise by first plotting the data to understand the
+%  the problem we are working with.
+
+%fprintf(['Plotting data with + indicating (y = 1) examples and o ' ...
+         %'indicating (y = 0) examples.\n']);
+
+%plotData(X, y);
+
+%% Put some labels
+%hold on;
+%% Labels and Legend
+%xlabel('Exam 1 score')
+%ylabel('Exam 2 score')
+
+%% Specified in plot order
+%legend('Admitted', 'Not admitted')
+%hold off;
+
+%fprintf('\nProgram paused. Press enter to continue.\n');
+%pause;
+
+
+%% ============ Part 2: Compute Cost and Gradient ============
+%  In this part of the exercise, you will implement the cost and gradient
+%  for logistic regression. You neeed to complete the code in
+%  costFunction.m
+
+%  Setup the data matrix appropriately, and add ones for the intercept term
+[m, n] = size(X);
+
+% Add intercept term to x and X_test
+X = [ones(m, 1) X];
+
+% Initialize fitting parameters
+initial_theta = zeros(n + 1, 1);
+
+% Compute and display initial cost and gradient
+[cost, grad] = costFunction(initial_theta, X, y);
+
+fprintf('Cost at initial theta (zeros): %f\n', cost);
+fprintf('Gradient at initial theta (zeros): \n');
+fprintf(' %f \n', grad);
+
+%fprintf('\nProgram paused. Press enter to continue.\n');
+%pause;
+
+
+%% ============= Part 3: Optimizing using fminunc  =============
+%  In this exercise, you will use a built-in function (fminunc) to find the
+%  optimal parameters theta.
+
+%  Set options for fminunc
+options = optimset('GradObj', 'on', 'MaxIter', 400);
+
+%  Run fminunc to obtain the optimal theta
+%  This function will return theta and the cost
+[theta, cost] = ...
+	fminunc(@(t)(costFunction(t, X, y)), initial_theta, options);
+
+% Print theta to screen
+fprintf('Cost at theta found by fminunc: %f\n', cost);
+fprintf('theta: \n');
+fprintf(' %f \n', theta);
+
+ %Plot Boundary
+%plotDecisionBoundary(theta, X, y);
+
+ %Put some labels
+%hold on;
+ %Labels and Legend
+%xlabel('Exam 1 score')
+%ylabel('Exam 2 score')
+
+ %Specified in plot order
+%legend('Admitted', 'Not admitted')
+%hold off;
+
+%fprintf('\nProgram paused. Press enter to continue.\n');
+%pause;
+
+%% ============== Part 4: Predict and Accuracies ==============
+%  After learning the parameters, you'll like to use it to predict the outcomes
+%  on unseen data. In this part, you will use the logistic regression model
+%  to predict the probability that a student with score 20 on exam 1 and
+%  score 80 on exam 2 will be admitted.
+%
+%  Furthermore, you will compute the training and test set accuracies of
+%  our model.
+%
+%  Your task is to complete the code in predict.m
+
+%  Predict probability for a student with score 45 on exam 1
+%  and score 85 on exam 2
+
+prob = sigmoid([1 45 85] * theta);
+fprintf(['For a student with scores 45 and 85, we predict an admission ' ...
+         'probability of %f\n\n'], prob);
+
+% Compute accuracy on our training set
+p = predict(theta, X);
+
+fprintf('Train Accuracy: %f\n', mean(double(p == y)) * 100);
+
+%fprintf('\nProgram paused. Press enter to continue.\n');
+%pause;
+