diff --git a/ex5.pdf b/ex5.pdf new file mode 100644 index 0000000..8200c93 Binary files /dev/null and b/ex5.pdf differ diff --git a/ex5/ex5.m b/ex5/ex5.m new file mode 100644 index 0000000..c62e800 --- /dev/null +++ b/ex5/ex5.m @@ -0,0 +1,220 @@ +%% Machine Learning Online Class +% Exercise 5 | Regularized Linear Regression and Bias-Variance +% +% Instructions +% ------------ +% +% This file contains code that helps you get started on the +% exercise. You will need to complete the following functions: +% +% linearRegCostFunction.m +% learningCurve.m +% validationCurve.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 + +%% =========== Part 1: Loading and Visualizing Data ============= +% We start the exercise by first loading and visualizing the dataset. +% The following code will load the dataset into your environment and plot +% the data. +% + +% Load Training Data +fprintf('Loading and Visualizing Data ...\n') + +% Load from ex5data1: +% You will have X, y, Xval, yval, Xtest, ytest in your environment +load ('ex5data1.mat'); + +% m = Number of examples +m = size(X, 1); + +% Plot training data +plot(X, y, 'rx', 'MarkerSize', 10, 'LineWidth', 1.5); +xlabel('Change in water level (x)'); +ylabel('Water flowing out of the dam (y)'); + +fprintf('Program paused. Press enter to continue.\n'); +pause; + +%% =========== Part 2: Regularized Linear Regression Cost ============= +% You should now implement the cost function for regularized linear +% regression. +% + +theta = [1 ; 1]; +J = linearRegCostFunction([ones(m, 1) X], y, theta, 1); + +fprintf(['Cost at theta = [1 ; 1]: %f '... + '\n(this value should be about 303.993192)\n'], J); + +fprintf('Program paused. Press enter to continue.\n'); +pause; + +%% =========== Part 3: Regularized Linear Regression Gradient ============= +% You should now implement the gradient for regularized linear +% regression. +% + +theta = [1 ; 1]; +[J, grad] = linearRegCostFunction([ones(m, 1) X], y, theta, 1); + +fprintf(['Gradient at theta = [1 ; 1]: [%f; %f] '... + '\n(this value should be about [-15.303016; 598.250744])\n'], ... + grad(1), grad(2)); + +fprintf('Program paused. Press enter to continue.\n'); +pause; + + +%% =========== Part 4: Train Linear Regression ============= +% Once you have implemented the cost and gradient correctly, the +% trainLinearReg function will use your cost function to train +% regularized linear regression. +% +% Write Up Note: The data is non-linear, so this will not give a great +% fit. +% + +% Train linear regression with lambda = 0 +lambda = 0; +[theta] = trainLinearReg([ones(m, 1) X], y, lambda); + +% Plot fit over the data +plot(X, y, 'rx', 'MarkerSize', 10, 'LineWidth', 1.5); +xlabel('Change in water level (x)'); +ylabel('Water flowing out of the dam (y)'); +hold on; +plot(X, [ones(m, 1) X]*theta, '--', 'LineWidth', 2) +hold off; + +fprintf('Program paused. Press enter to continue.\n'); +pause; + + +%% =========== Part 5: Learning Curve for Linear Regression ============= +% Next, you should implement the learningCurve function. +% +% Write Up Note: Since the model is underfitting the data, we expect to +% see a graph with "high bias" -- slide 8 in ML-advice.pdf +% + +lambda = 0; +[error_train, error_val] = ... + learningCurve([ones(m, 1) X], y, ... + [ones(size(Xval, 1), 1) Xval], yval, ... + lambda); + +plot(1:m, error_train, 1:m, error_val); +title('Learning curve for linear regression') +legend('Train', 'Cross Validation') +xlabel('Number of training examples') +ylabel('Error') +axis([0 13 0 150]) + +fprintf('# Training Examples\tTrain Error\tCross Validation Error\n'); +for i = 1:m + fprintf(' \t%d\t\t%f\t%f\n', i, error_train(i), error_val(i)); +end + +fprintf('Program paused. Press enter to continue.\n'); +pause; + +%% =========== Part 6: Feature Mapping for Polynomial Regression ============= +% One solution to this is to use polynomial regression. You should now +% complete polyFeatures to map each example into its powers +% + +p = 8; + +% Map X onto Polynomial Features and Normalize +X_poly = polyFeatures(X, p); +[X_poly, mu, sigma] = featureNormalize(X_poly); % Normalize +X_poly = [ones(m, 1), X_poly]; % Add Ones + +% Map X_poly_test and normalize (using mu and sigma) +X_poly_test = polyFeatures(Xtest, p); +X_poly_test = bsxfun(@minus, X_poly_test, mu); +X_poly_test = bsxfun(@rdivide, X_poly_test, sigma); +X_poly_test = [ones(size(X_poly_test, 1), 1), X_poly_test]; % Add Ones + +% Map X_poly_val and normalize (using mu and sigma) +X_poly_val = polyFeatures(Xval, p); +X_poly_val = bsxfun(@minus, X_poly_val, mu); +X_poly_val = bsxfun(@rdivide, X_poly_val, sigma); +X_poly_val = [ones(size(X_poly_val, 1), 1), X_poly_val]; % Add Ones + +fprintf('Normalized Training Example 1:\n'); +fprintf(' %f \n', X_poly(1, :)); + +fprintf('\nProgram paused. Press enter to continue.\n'); +pause; + + + +%% =========== Part 7: Learning Curve for Polynomial Regression ============= +% Now, you will get to experiment with polynomial regression with multiple +% values of lambda. The code below runs polynomial regression with +% lambda = 0. You should try running the code with different values of +% lambda to see how the fit and learning curve change. +% + +lambda = 0; +[theta] = trainLinearReg(X_poly, y, lambda); + +% Plot training data and fit +figure(1); +plot(X, y, 'rx', 'MarkerSize', 10, 'LineWidth', 1.5); +plotFit(min(X), max(X), mu, sigma, theta, p); +xlabel('Change in water level (x)'); +ylabel('Water flowing out of the dam (y)'); +title (sprintf('Polynomial Regression Fit (lambda = %f)', lambda)); + +figure(2); +[error_train, error_val] = ... + learningCurve(X_poly, y, X_poly_val, yval, lambda); +plot(1:m, error_train, 1:m, error_val); + +title(sprintf('Polynomial Regression Learning Curve (lambda = %f)', lambda)); +xlabel('Number of training examples') +ylabel('Error') +axis([0 13 0 100]) +legend('Train', 'Cross Validation') + +fprintf('Polynomial Regression (lambda = %f)\n\n', lambda); +fprintf('# Training Examples\tTrain Error\tCross Validation Error\n'); +for i = 1:m + fprintf(' \t%d\t\t%f\t%f\n', i, error_train(i), error_val(i)); +end + +fprintf('Program paused. Press enter to continue.\n'); +pause; + +%% =========== Part 8: Validation for Selecting Lambda ============= +% You will now implement validationCurve to test various values of +% lambda on a validation set. You will then use this to select the +% "best" lambda value. +% + +[lambda_vec, error_train, error_val] = ... + validationCurve(X_poly, y, X_poly_val, yval); + +close all; +plot(lambda_vec, error_train, lambda_vec, error_val); +legend('Train', 'Cross Validation'); +xlabel('lambda'); +ylabel('Error'); + +fprintf('lambda\t\tTrain Error\tValidation Error\n'); +for i = 1:length(lambda_vec) + fprintf(' %f\t%f\t%f\n', ... + lambda_vec(i), error_train(i), error_val(i)); +end + +fprintf('Program paused. Press enter to continue.\n'); +pause; diff --git a/ex5/ex5data1.mat b/ex5/ex5data1.mat new file mode 100644 index 0000000..5a17abd Binary files /dev/null and b/ex5/ex5data1.mat differ diff --git a/ex5/featureNormalize.m b/ex5/featureNormalize.m new file mode 100644 index 0000000..da03bee --- /dev/null +++ b/ex5/featureNormalize.m @@ -0,0 +1,17 @@ +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. + +mu = mean(X); +X_norm = bsxfun(@minus, X, mu); + +sigma = std(X_norm); +X_norm = bsxfun(@rdivide, X_norm, sigma); + + +% ============================================================ + +end diff --git a/ex5/fmincg.m b/ex5/fmincg.m new file mode 100644 index 0000000..34bf539 --- /dev/null +++ b/ex5/fmincg.m @@ -0,0 +1,175 @@ +function [X, fX, i] = fmincg(f, X, options, P1, P2, P3, P4, P5) +% Minimize a continuous differentialble multivariate function. Starting point +% is given by "X" (D by 1), and the function named in the string "f", must +% return a function value and a vector of partial derivatives. The Polack- +% Ribiere flavour of conjugate gradients is used to compute search directions, +% and a line search using quadratic and cubic polynomial approximations and the +% Wolfe-Powell stopping criteria is used together with the slope ratio method +% for guessing initial step sizes. Additionally a bunch of checks are made to +% make sure that exploration is taking place and that extrapolation will not +% be unboundedly large. The "length" gives the length of the run: if it is +% positive, it gives the maximum number of line searches, if negative its +% absolute gives the maximum allowed number of function evaluations. You can +% (optionally) give "length" a second component, which will indicate the +% reduction in function value to be expected in the first line-search (defaults +% to 1.0). The function returns when either its length is up, or if no further +% progress can be made (ie, we are at a minimum, or so close that due to +% numerical problems, we cannot get any closer). If the function terminates +% within a few iterations, it could be an indication that the function value +% and derivatives are not consistent (ie, there may be a bug in the +% implementation of your "f" function). The function returns the found +% solution "X", a vector of function values "fX" indicating the progress made +% and "i" the number of iterations (line searches or function evaluations, +% depending on the sign of "length") used. +% +% Usage: [X, fX, i] = fmincg(f, X, options, P1, P2, P3, P4, P5) +% +% See also: checkgrad +% +% Copyright (C) 2001 and 2002 by Carl Edward Rasmussen. Date 2002-02-13 +% +% +% (C) Copyright 1999, 2000 & 2001, Carl Edward Rasmussen +% +% Permission is granted for anyone to copy, use, or modify these +% programs and accompanying documents for purposes of research or +% education, provided this copyright notice is retained, and note is +% made of any changes that have been made. +% +% These programs and documents are distributed without any warranty, +% express or implied. As the programs were written for research +% purposes only, they have not been tested to the degree that would be +% advisable in any important application. All use of these programs is +% entirely at the user's own risk. +% +% [ml-class] Changes Made: +% 1) Function name and argument specifications +% 2) Output display +% + +% Read options +if exist('options', 'var') && ~isempty(options) && isfield(options, 'MaxIter') + length = options.MaxIter; +else + length = 100; +end + + +RHO = 0.01; % a bunch of constants for line searches +SIG = 0.5; % RHO and SIG are the constants in the Wolfe-Powell conditions +INT = 0.1; % don't reevaluate within 0.1 of the limit of the current bracket +EXT = 3.0; % extrapolate maximum 3 times the current bracket +MAX = 20; % max 20 function evaluations per line search +RATIO = 100; % maximum allowed slope ratio + +argstr = ['feval(f, X']; % compose string used to call function +for i = 1:(nargin - 3) + argstr = [argstr, ',P', int2str(i)]; +end +argstr = [argstr, ')']; + +if max(size(length)) == 2, red=length(2); length=length(1); else red=1; end +S=['Iteration ']; + +i = 0; % zero the run length counter +ls_failed = 0; % no previous line search has failed +fX = []; +[f1 df1] = eval(argstr); % get function value and gradient +i = i + (length<0); % count epochs?! +s = -df1; % search direction is steepest +d1 = -s'*s; % this is the slope +z1 = red/(1-d1); % initial step is red/(|s|+1) + +while i < abs(length) % while not finished + i = i + (length>0); % count iterations?! + + X0 = X; f0 = f1; df0 = df1; % make a copy of current values + X = X + z1*s; % begin line search + [f2 df2] = eval(argstr); + i = i + (length<0); % count epochs?! + d2 = df2'*s; + f3 = f1; d3 = d1; z3 = -z1; % initialize point 3 equal to point 1 + if length>0, M = MAX; else M = min(MAX, -length-i); end + success = 0; limit = -1; % initialize quanteties + while 1 + while ((f2 > f1+z1*RHO*d1) | (d2 > -SIG*d1)) & (M > 0) + limit = z1; % tighten the bracket + if f2 > f1 + z2 = z3 - (0.5*d3*z3*z3)/(d3*z3+f2-f3); % quadratic fit + else + A = 6*(f2-f3)/z3+3*(d2+d3); % cubic fit + B = 3*(f3-f2)-z3*(d3+2*d2); + z2 = (sqrt(B*B-A*d2*z3*z3)-B)/A; % numerical error possible - ok! + end + if isnan(z2) | isinf(z2) + z2 = z3/2; % if we had a numerical problem then bisect + end + z2 = max(min(z2, INT*z3),(1-INT)*z3); % don't accept too close to limits + z1 = z1 + z2; % update the step + X = X + z2*s; + [f2 df2] = eval(argstr); + M = M - 1; i = i + (length<0); % count epochs?! + d2 = df2'*s; + z3 = z3-z2; % z3 is now relative to the location of z2 + end + if f2 > f1+z1*RHO*d1 | d2 > -SIG*d1 + break; % this is a failure + elseif d2 > SIG*d1 + success = 1; break; % success + elseif M == 0 + break; % failure + end + A = 6*(f2-f3)/z3+3*(d2+d3); % make cubic extrapolation + B = 3*(f3-f2)-z3*(d3+2*d2); + z2 = -d2*z3*z3/(B+sqrt(B*B-A*d2*z3*z3)); % num. error possible - ok! + if ~isreal(z2) | isnan(z2) | isinf(z2) | z2 < 0 % num prob or wrong sign? + if limit < -0.5 % if we have no upper limit + z2 = z1 * (EXT-1); % the extrapolate the maximum amount + else + z2 = (limit-z1)/2; % otherwise bisect + end + elseif (limit > -0.5) & (z2+z1 > limit) % extraplation beyond max? + z2 = (limit-z1)/2; % bisect + elseif (limit < -0.5) & (z2+z1 > z1*EXT) % extrapolation beyond limit + z2 = z1*(EXT-1.0); % set to extrapolation limit + elseif z2 < -z3*INT + z2 = -z3*INT; + elseif (limit > -0.5) & (z2 < (limit-z1)*(1.0-INT)) % too close to limit? + z2 = (limit-z1)*(1.0-INT); + end + f3 = f2; d3 = d2; z3 = -z2; % set point 3 equal to point 2 + z1 = z1 + z2; X = X + z2*s; % update current estimates + [f2 df2] = eval(argstr); + M = M - 1; i = i + (length<0); % count epochs?! + d2 = df2'*s; + end % end of line search + + if success % if line search succeeded + f1 = f2; fX = [fX' f1]'; + fprintf('%s %4i | Cost: %4.6e\r', S, i, f1); + s = (df2'*df2-df1'*df2)/(df1'*df1)*s - df2; % Polack-Ribiere direction + tmp = df1; df1 = df2; df2 = tmp; % swap derivatives + d2 = df1'*s; + if d2 > 0 % new slope must be negative + s = -df1; % otherwise use steepest direction + d2 = -s'*s; + end + z1 = z1 * min(RATIO, d1/(d2-realmin)); % slope ratio but max RATIO + d1 = d2; + ls_failed = 0; % this line search did not fail + else + X = X0; f1 = f0; df1 = df0; % restore point from before failed line search + if ls_failed | i > abs(length) % line search failed twice in a row + break; % or we ran out of time, so we give up + end + tmp = df1; df1 = df2; df2 = tmp; % swap derivatives + s = -df1; % try steepest + d1 = -s'*s; + z1 = 1/(1-d1); + ls_failed = 1; % this line search failed + end + if exist('OCTAVE_VERSION') + fflush(stdout); + end +end +fprintf('\n'); diff --git a/ex5/learningCurve.m b/ex5/learningCurve.m new file mode 100644 index 0000000..6ea4333 --- /dev/null +++ b/ex5/learningCurve.m @@ -0,0 +1,66 @@ +function [error_train, error_val] = ... + learningCurve(X, y, Xval, yval, lambda) +%LEARNINGCURVE Generates the train and cross validation set errors needed +%to plot a learning curve +% [error_train, error_val] = ... +% LEARNINGCURVE(X, y, Xval, yval, lambda) returns the train and +% cross validation set errors for a learning curve. In particular, +% it returns two vectors of the same length - error_train and +% error_val. Then, error_train(i) contains the training error for +% i examples (and similarly for error_val(i)). +% +% In this function, you will compute the train and test errors for +% dataset sizes from 1 up to m. In practice, when working with larger +% datasets, you might want to do this in larger intervals. +% + +% Number of training examples +m = size(X, 1); + +% You need to return these values correctly +error_train = zeros(m, 1); +error_val = zeros(m, 1); + +% ====================== YOUR CODE HERE ====================== +% Instructions: Fill in this function to return training errors in +% error_train and the cross validation errors in error_val. +% i.e., error_train(i) and +% error_val(i) should give you the errors +% obtained after training on i examples. +% +% Note: You should evaluate the training error on the first i training +% examples (i.e., X(1:i, :) and y(1:i)). +% +% For the cross-validation error, you should instead evaluate on +% the _entire_ cross validation set (Xval and yval). +% +% Note: If you are using your cost function (linearRegCostFunction) +% to compute the training and cross validation error, you should +% call the function with the lambda argument set to 0. +% Do note that you will still need to use lambda when running +% the training to obtain the theta parameters. +% +% Hint: You can loop over the examples with the following: +% +% for i = 1:m +% % Compute train/cross validation errors using training examples +% % X(1:i, :) and y(1:i), storing the result in +% % error_train(i) and error_val(i) +% .... +% +% end +% + +% ---------------------- Sample Solution ---------------------- + + + + + + + +% ------------------------------------------------------------- + +% ========================================================================= + +end diff --git a/ex5/linearRegCostFunction.m b/ex5/linearRegCostFunction.m new file mode 100644 index 0000000..6addf6b --- /dev/null +++ b/ex5/linearRegCostFunction.m @@ -0,0 +1,37 @@ +function [J, grad] = linearRegCostFunction(X, y, theta, lambda) +%LINEARREGCOSTFUNCTION Compute cost and gradient for regularized linear +%regression with multiple variables +% [J, grad] = LINEARREGCOSTFUNCTION(X, y, theta, lambda) computes the +% cost of using theta as the parameter for linear regression to fit the +% data points in X and y. Returns the cost in J and the gradient in grad + +% 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 and gradient of regularized linear +% regression for a particular choice of theta. +% +% You should set J to the cost and grad to the gradient. +% + + + + + + + + + + + + +% ========================================================================= + +grad = grad(:); + +end diff --git a/ex5/plotFit.m b/ex5/plotFit.m new file mode 100644 index 0000000..8dba7cf --- /dev/null +++ b/ex5/plotFit.m @@ -0,0 +1,28 @@ +function plotFit(min_x, max_x, mu, sigma, theta, p) +%PLOTFIT Plots a learned polynomial regression fit over an existing figure. +%Also works with linear regression. +% PLOTFIT(min_x, max_x, mu, sigma, theta, p) plots the learned polynomial +% fit with power p and feature normalization (mu, sigma). + +% Hold on to the current figure +hold on; + +% We plot a range slightly bigger than the min and max values to get +% an idea of how the fit will vary outside the range of the data points +x = (min_x - 15: 0.05 : max_x + 25)'; + +% Map the X values +X_poly = polyFeatures(x, p); +X_poly = bsxfun(@minus, X_poly, mu); +X_poly = bsxfun(@rdivide, X_poly, sigma); + +% Add ones +X_poly = [ones(size(x, 1), 1) X_poly]; + +% Plot +plot(x, X_poly * theta, '--', 'LineWidth', 2) + +% Hold off to the current figure +hold off + +end diff --git a/ex5/polyFeatures.m b/ex5/polyFeatures.m new file mode 100644 index 0000000..f496f48 --- /dev/null +++ b/ex5/polyFeatures.m @@ -0,0 +1,25 @@ +function [X_poly] = polyFeatures(X, p) +%POLYFEATURES Maps X (1D vector) into the p-th power +% [X_poly] = POLYFEATURES(X, p) takes a data matrix X (size m x 1) and +% maps each example into its polynomial features where +% X_poly(i, :) = [X(i) X(i).^2 X(i).^3 ... X(i).^p]; +% + + +% You need to return the following variables correctly. +X_poly = zeros(numel(X), p); + +% ====================== YOUR CODE HERE ====================== +% Instructions: Given a vector X, return a matrix X_poly where the p-th +% column of X contains the values of X to the p-th power. +% +% + + + + + + +% ========================================================================= + +end diff --git a/ex5/submit.m b/ex5/submit.m new file mode 100644 index 0000000..1684fc2 --- /dev/null +++ b/ex5/submit.m @@ -0,0 +1,577 @@ +function submit(partId, webSubmit) +%SUBMIT Submit your code and output to the ml-class servers +% SUBMIT() will connect to the ml-class server and submit your solution + + fprintf('==\n== [ml-class] Submitting Solutions | Programming Exercise %s\n==\n', ... + homework_id()); + if ~exist('partId', 'var') || isempty(partId) + partId = promptPart(); + end + + if ~exist('webSubmit', 'var') || isempty(webSubmit) + webSubmit = 0; % submit directly by default + end + + % Check valid partId + partNames = validParts(); + if ~isValidPartId(partId) + fprintf('!! Invalid homework part selected.\n'); + fprintf('!! Expected an integer from 1 to %d.\n', numel(partNames) + 1); + fprintf('!! Submission Cancelled\n'); + return + end + + if ~exist('ml_login_data.mat','file') + [login password] = loginPrompt(); + save('ml_login_data.mat','login','password'); + else + load('ml_login_data.mat'); + [login password] = quickLogin(login, password); + save('ml_login_data.mat','login','password'); + end + + if isempty(login) + fprintf('!! Submission Cancelled\n'); + return + end + + fprintf('\n== Connecting to ml-class ... '); + if exist('OCTAVE_VERSION') + fflush(stdout); + end + + % Setup submit list + if partId == numel(partNames) + 1 + submitParts = 1:numel(partNames); + else + submitParts = [partId]; + end + + for s = 1:numel(submitParts) + thisPartId = submitParts(s); + if (~webSubmit) % submit directly to server + [login, ch, signature, auxstring] = getChallenge(login, thisPartId); + if isempty(login) || isempty(ch) || isempty(signature) + % Some error occured, error string in first return element. + fprintf('\n!! Error: %s\n\n', login); + return + end + + % Attempt Submission with Challenge + ch_resp = challengeResponse(login, password, ch); + + [result, str] = submitSolution(login, ch_resp, thisPartId, ... + output(thisPartId, auxstring), source(thisPartId), signature); + + partName = partNames{thisPartId}; + + fprintf('\n== [ml-class] Submitted Assignment %s - Part %d - %s\n', ... + homework_id(), thisPartId, partName); + fprintf('== %s\n', strtrim(str)); + + if exist('OCTAVE_VERSION') + fflush(stdout); + end + else + [result] = submitSolutionWeb(login, thisPartId, output(thisPartId), ... + source(thisPartId)); + result = base64encode(result); + + fprintf('\nSave as submission file [submit_ex%s_part%d.txt (enter to accept default)]:', ... + homework_id(), thisPartId); + saveAsFile = input('', 's'); + if (isempty(saveAsFile)) + saveAsFile = sprintf('submit_ex%s_part%d.txt', homework_id(), thisPartId); + end + + fid = fopen(saveAsFile, 'w'); + if (fid) + fwrite(fid, result); + fclose(fid); + fprintf('\nSaved your solutions to %s.\n\n', saveAsFile); + fprintf(['You can now submit your solutions through the web \n' ... + 'form in the programming exercises. Select the corresponding \n' ... + 'programming exercise to access the form.\n']); + + else + fprintf('Unable to save to %s\n\n', saveAsFile); + fprintf(['You can create a submission file by saving the \n' ... + 'following text in a file: (press enter to continue)\n\n']); + pause; + fprintf(result); + end + end + end +end + +% ================== CONFIGURABLES FOR EACH HOMEWORK ================== + +function id = homework_id() + id = '5'; +end + +function [partNames] = validParts() + partNames = { 'Regularized Linear Regression Cost Function', ... + 'Regularized Linear Regression Gradient', ... + 'Learning Curve', ... + 'Polynomial Feature Mapping' ... + 'Validation Curve' ... + }; +end + +function srcs = sources() + % Separated by part + srcs = { { 'linearRegCostFunction.m' }, ... + { 'linearRegCostFunction.m' }, ... + { 'learningCurve.m' }, ... + { 'polyFeatures.m' }, ... + { 'validationCurve.m' } }; +end + +function out = output(partId, auxstring) + % Random Test Cases + X = [ones(10,1) sin(1:1.5:15)' cos(1:1.5:15)']; + y = sin(1:3:30)'; + Xval = [ones(10,1) sin(0:1.5:14)' cos(0:1.5:14)']; + yval = sin(1:10)'; + if partId == 1 + [J] = linearRegCostFunction(X, y, [0.1 0.2 0.3]', 0.5); + out = sprintf('%0.5f ', J); + elseif partId == 2 + [J, grad] = linearRegCostFunction(X, y, [0.1 0.2 0.3]', 0.5); + out = sprintf('%0.5f ', grad); + elseif partId == 3 + [error_train, error_val] = ... + learningCurve(X, y, Xval, yval, 1); + out = sprintf('%0.5f ', [error_train(:); error_val(:)]); + elseif partId == 4 + [X_poly] = polyFeatures(X(2,:)', 8); + out = sprintf('%0.5f ', X_poly); + elseif partId == 5 + [lambda_vec, error_train, error_val] = ... + validationCurve(X, y, Xval, yval); + out = sprintf('%0.5f ', ... + [lambda_vec(:); error_train(:); error_val(:)]); + end +end + +% ====================== SERVER CONFIGURATION =========================== + +% ***************** REMOVE -staging WHEN YOU DEPLOY ********************* +function url = site_url() + url = 'http://class.coursera.org/ml-007'; +end + +function url = challenge_url() + url = [site_url() '/assignment/challenge']; +end + +function url = submit_url() + url = [site_url() '/assignment/submit']; +end + +% ========================= CHALLENGE HELPERS ========================= + +function src = source(partId) + src = ''; + src_files = sources(); + if partId <= numel(src_files) + flist = src_files{partId}; + for i = 1:numel(flist) + fid = fopen(flist{i}); + if (fid == -1) + error('Error opening %s (is it missing?)', flist{i}); + end + line = fgets(fid); + while ischar(line) + src = [src line]; + line = fgets(fid); + end + fclose(fid); + src = [src '||||||||']; + end + end +end + +function ret = isValidPartId(partId) + partNames = validParts(); + ret = (~isempty(partId)) && (partId >= 1) && (partId <= numel(partNames) + 1); +end + +function partId = promptPart() + fprintf('== Select which part(s) to submit:\n'); + partNames = validParts(); + srcFiles = sources(); + for i = 1:numel(partNames) + fprintf('== %d) %s [', i, partNames{i}); + fprintf(' %s ', srcFiles{i}{:}); + fprintf(']\n'); + end + fprintf('== %d) All of the above \n==\nEnter your choice [1-%d]: ', ... + numel(partNames) + 1, numel(partNames) + 1); + selPart = input('', 's'); + partId = str2num(selPart); + if ~isValidPartId(partId) + partId = -1; + end +end + +function [email,ch,signature,auxstring] = getChallenge(email, part) + str = urlread(challenge_url(), 'post', {'email_address', email, 'assignment_part_sid', [homework_id() '-' num2str(part)], 'response_encoding', 'delim'}); + + str = strtrim(str); + r = struct; + while(numel(str) > 0) + [f, str] = strtok (str, '|'); + [v, str] = strtok (str, '|'); + r = setfield(r, f, v); + end + + email = getfield(r, 'email_address'); + ch = getfield(r, 'challenge_key'); + signature = getfield(r, 'state'); + auxstring = getfield(r, 'challenge_aux_data'); +end + +function [result, str] = submitSolutionWeb(email, part, output, source) + + result = ['{"assignment_part_sid":"' base64encode([homework_id() '-' num2str(part)], '') '",' ... + '"email_address":"' base64encode(email, '') '",' ... + '"submission":"' base64encode(output, '') '",' ... + '"submission_aux":"' base64encode(source, '') '"' ... + '}']; + str = 'Web-submission'; +end + +function [result, str] = submitSolution(email, ch_resp, part, output, ... + source, signature) + + params = {'assignment_part_sid', [homework_id() '-' num2str(part)], ... + 'email_address', email, ... + 'submission', base64encode(output, ''), ... + 'submission_aux', base64encode(source, ''), ... + 'challenge_response', ch_resp, ... + 'state', signature}; + + str = urlread(submit_url(), 'post', params); + + % Parse str to read for success / failure + result = 0; + +end + +% =========================== LOGIN HELPERS =========================== + +function [login password] = loginPrompt() + % Prompt for password + [login password] = basicPrompt(); + + if isempty(login) || isempty(password) + login = []; password = []; + end +end + + +function [login password] = basicPrompt() + login = input('Login (Email address): ', 's'); + password = input('Password: ', 's'); +end + +function [login password] = quickLogin(login,password) + disp(['You are currently logged in as ' login '.']); + cont_token = input('Is this you? (y/n - type n to reenter password)','s'); + if(isempty(cont_token) || cont_token(1)=='Y'||cont_token(1)=='y') + return; + else + [login password] = loginPrompt(); + end +end + +function [str] = challengeResponse(email, passwd, challenge) + str = sha1([challenge passwd]); +end + +% =============================== SHA-1 ================================ + +function hash = sha1(str) + + % Initialize variables + h0 = uint32(1732584193); + h1 = uint32(4023233417); + h2 = uint32(2562383102); + h3 = uint32(271733878); + h4 = uint32(3285377520); + + % Convert to word array + strlen = numel(str); + + % Break string into chars and append the bit 1 to the message + mC = [double(str) 128]; + mC = [mC zeros(1, 4-mod(numel(mC), 4), 'uint8')]; + + numB = strlen * 8; + if exist('idivide') + numC = idivide(uint32(numB + 65), 512, 'ceil'); + else + numC = ceil(double(numB + 65)/512); + end + numW = numC * 16; + mW = zeros(numW, 1, 'uint32'); + + idx = 1; + for i = 1:4:strlen + 1 + mW(idx) = bitor(bitor(bitor( ... + bitshift(uint32(mC(i)), 24), ... + bitshift(uint32(mC(i+1)), 16)), ... + bitshift(uint32(mC(i+2)), 8)), ... + uint32(mC(i+3))); + idx = idx + 1; + end + + % Append length of message + mW(numW - 1) = uint32(bitshift(uint64(numB), -32)); + mW(numW) = uint32(bitshift(bitshift(uint64(numB), 32), -32)); + + % Process the message in successive 512-bit chs + for cId = 1 : double(numC) + cSt = (cId - 1) * 16 + 1; + cEnd = cId * 16; + ch = mW(cSt : cEnd); + + % Extend the sixteen 32-bit words into eighty 32-bit words + for j = 17 : 80 + ch(j) = ch(j - 3); + ch(j) = bitxor(ch(j), ch(j - 8)); + ch(j) = bitxor(ch(j), ch(j - 14)); + ch(j) = bitxor(ch(j), ch(j - 16)); + ch(j) = bitrotate(ch(j), 1); + end + + % Initialize hash value for this ch + a = h0; + b = h1; + c = h2; + d = h3; + e = h4; + + % Main loop + for i = 1 : 80 + if(i >= 1 && i <= 20) + f = bitor(bitand(b, c), bitand(bitcmp(b), d)); + k = uint32(1518500249); + elseif(i >= 21 && i <= 40) + f = bitxor(bitxor(b, c), d); + k = uint32(1859775393); + elseif(i >= 41 && i <= 60) + f = bitor(bitor(bitand(b, c), bitand(b, d)), bitand(c, d)); + k = uint32(2400959708); + elseif(i >= 61 && i <= 80) + f = bitxor(bitxor(b, c), d); + k = uint32(3395469782); + end + + t = bitrotate(a, 5); + t = bitadd(t, f); + t = bitadd(t, e); + t = bitadd(t, k); + t = bitadd(t, ch(i)); + e = d; + d = c; + c = bitrotate(b, 30); + b = a; + a = t; + + end + h0 = bitadd(h0, a); + h1 = bitadd(h1, b); + h2 = bitadd(h2, c); + h3 = bitadd(h3, d); + h4 = bitadd(h4, e); + + end + + hash = reshape(dec2hex(double([h0 h1 h2 h3 h4]), 8)', [1 40]); + + hash = lower(hash); + +end + +function ret = bitadd(iA, iB) + ret = double(iA) + double(iB); + ret = bitset(ret, 33, 0); + ret = uint32(ret); +end + +function ret = bitrotate(iA, places) + t = bitshift(iA, places - 32); + ret = bitshift(iA, places); + ret = bitor(ret, t); +end + +% =========================== Base64 Encoder ============================ +% Thanks to Peter John Acklam +% + +function y = base64encode(x, eol) +%BASE64ENCODE Perform base64 encoding on a string. +% +% BASE64ENCODE(STR, EOL) encode the given string STR. EOL is the line ending +% sequence to use; it is optional and defaults to '\n' (ASCII decimal 10). +% The returned encoded string is broken into lines of no more than 76 +% characters each, and each line will end with EOL unless it is empty. Let +% EOL be empty if you do not want the encoded string broken into lines. +% +% STR and EOL don't have to be strings (i.e., char arrays). The only +% requirement is that they are vectors containing values in the range 0-255. +% +% This function may be used to encode strings into the Base64 encoding +% specified in RFC 2045 - MIME (Multipurpose Internet Mail Extensions). The +% Base64 encoding is designed to represent arbitrary sequences of octets in a +% form that need not be humanly readable. A 65-character subset +% ([A-Za-z0-9+/=]) of US-ASCII is used, enabling 6 bits to be represented per +% printable character. +% +% Examples +% -------- +% +% If you want to encode a large file, you should encode it in chunks that are +% a multiple of 57 bytes. This ensures that the base64 lines line up and +% that you do not end up with padding in the middle. 57 bytes of data fills +% one complete base64 line (76 == 57*4/3): +% +% If ifid and ofid are two file identifiers opened for reading and writing, +% respectively, then you can base64 encode the data with +% +% while ~feof(ifid) +% fwrite(ofid, base64encode(fread(ifid, 60*57))); +% end +% +% or, if you have enough memory, +% +% fwrite(ofid, base64encode(fread(ifid))); +% +% See also BASE64DECODE. + +% Author: Peter John Acklam +% Time-stamp: 2004-02-03 21:36:56 +0100 +% E-mail: pjacklam@online.no +% URL: http://home.online.no/~pjacklam + + if isnumeric(x) + x = num2str(x); + end + + % make sure we have the EOL value + if nargin < 2 + eol = sprintf('\n'); + else + if sum(size(eol) > 1) > 1 + error('EOL must be a vector.'); + end + if any(eol(:) > 255) + error('EOL can not contain values larger than 255.'); + end + end + + if sum(size(x) > 1) > 1 + error('STR must be a vector.'); + end + + x = uint8(x); + eol = uint8(eol); + + ndbytes = length(x); % number of decoded bytes + nchunks = ceil(ndbytes / 3); % number of chunks/groups + nebytes = 4 * nchunks; % number of encoded bytes + + % add padding if necessary, to make the length of x a multiple of 3 + if rem(ndbytes, 3) + x(end+1 : 3*nchunks) = 0; + end + + x = reshape(x, [3, nchunks]); % reshape the data + y = repmat(uint8(0), 4, nchunks); % for the encoded data + + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + % Split up every 3 bytes into 4 pieces + % + % aaaaaabb bbbbcccc ccdddddd + % + % to form + % + % 00aaaaaa 00bbbbbb 00cccccc 00dddddd + % + y(1,:) = bitshift(x(1,:), -2); % 6 highest bits of x(1,:) + + y(2,:) = bitshift(bitand(x(1,:), 3), 4); % 2 lowest bits of x(1,:) + y(2,:) = bitor(y(2,:), bitshift(x(2,:), -4)); % 4 highest bits of x(2,:) + + y(3,:) = bitshift(bitand(x(2,:), 15), 2); % 4 lowest bits of x(2,:) + y(3,:) = bitor(y(3,:), bitshift(x(3,:), -6)); % 2 highest bits of x(3,:) + + y(4,:) = bitand(x(3,:), 63); % 6 lowest bits of x(3,:) + + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + % Now perform the following mapping + % + % 0 - 25 -> A-Z + % 26 - 51 -> a-z + % 52 - 61 -> 0-9 + % 62 -> + + % 63 -> / + % + % We could use a mapping vector like + % + % ['A':'Z', 'a':'z', '0':'9', '+/'] + % + % but that would require an index vector of class double. + % + z = repmat(uint8(0), size(y)); + i = y <= 25; z(i) = 'A' + double(y(i)); + i = 26 <= y & y <= 51; z(i) = 'a' - 26 + double(y(i)); + i = 52 <= y & y <= 61; z(i) = '0' - 52 + double(y(i)); + i = y == 62; z(i) = '+'; + i = y == 63; z(i) = '/'; + y = z; + + %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% + % Add padding if necessary. + % + npbytes = 3 * nchunks - ndbytes; % number of padding bytes + if npbytes + y(end-npbytes+1 : end) = '='; % '=' is used for padding + end + + if isempty(eol) + + % reshape to a row vector + y = reshape(y, [1, nebytes]); + + else + + nlines = ceil(nebytes / 76); % number of lines + neolbytes = length(eol); % number of bytes in eol string + + % pad data so it becomes a multiple of 76 elements + y = [y(:) ; zeros(76 * nlines - numel(y), 1)]; + y(nebytes + 1 : 76 * nlines) = 0; + y = reshape(y, 76, nlines); + + % insert eol strings + eol = eol(:); + y(end + 1 : end + neolbytes, :) = eol(:, ones(1, nlines)); + + % remove padding, but keep the last eol string + m = nebytes + neolbytes * (nlines - 1); + n = (76+neolbytes)*nlines - neolbytes; + y(m+1 : n) = ''; + + % extract and reshape to row vector + y = reshape(y, 1, m+neolbytes); + + end + + % output is a character array + y = char(y); + +end diff --git a/ex5/submitWeb.m b/ex5/submitWeb.m new file mode 100644 index 0000000..e429365 --- /dev/null +++ b/ex5/submitWeb.m @@ -0,0 +1,20 @@ +% submitWeb Creates files from your code and output for web submission. +% +% If the submit function does not work for you, use the web-submission mechanism. +% Call this function to produce a file for the part you wish to submit. Then, +% submit the file to the class servers using the "Web Submission" button on the +% Programming Exercises page on the course website. +% +% You should call this function without arguments (submitWeb), to receive +% an interactive prompt for submission; optionally you can call it with the partID +% if you so wish. Make sure your working directory is set to the directory +% containing the submitWeb.m file and your assignment files. + +function submitWeb(partId) + if ~exist('partId', 'var') || isempty(partId) + partId = []; + end + + submit(partId, 1); +end + diff --git a/ex5/trainLinearReg.m b/ex5/trainLinearReg.m new file mode 100644 index 0000000..eb89860 --- /dev/null +++ b/ex5/trainLinearReg.m @@ -0,0 +1,21 @@ +function [theta] = trainLinearReg(X, y, lambda) +%TRAINLINEARREG Trains linear regression given a dataset (X, y) and a +%regularization parameter lambda +% [theta] = TRAINLINEARREG (X, y, lambda) trains linear regression using +% the dataset (X, y) and regularization parameter lambda. Returns the +% trained parameters theta. +% + +% Initialize Theta +initial_theta = zeros(size(X, 2), 1); + +% Create "short hand" for the cost function to be minimized +costFunction = @(t) linearRegCostFunction(X, y, t, lambda); + +% Now, costFunction is a function that takes in only one argument +options = optimset('MaxIter', 200, 'GradObj', 'on'); + +% Minimize using fmincg +theta = fmincg(costFunction, initial_theta, options); + +end diff --git a/ex5/validationCurve.m b/ex5/validationCurve.m new file mode 100644 index 0000000..24b56bc --- /dev/null +++ b/ex5/validationCurve.m @@ -0,0 +1,53 @@ +function [lambda_vec, error_train, error_val] = ... + validationCurve(X, y, Xval, yval) +%VALIDATIONCURVE Generate the train and validation errors needed to +%plot a validation curve that we can use to select lambda +% [lambda_vec, error_train, error_val] = ... +% VALIDATIONCURVE(X, y, Xval, yval) returns the train +% and validation errors (in error_train, error_val) +% for different values of lambda. You are given the training set (X, +% y) and validation set (Xval, yval). +% + +% Selected values of lambda (you should not change this) +lambda_vec = [0 0.001 0.003 0.01 0.03 0.1 0.3 1 3 10]'; + +% You need to return these variables correctly. +error_train = zeros(length(lambda_vec), 1); +error_val = zeros(length(lambda_vec), 1); + +% ====================== YOUR CODE HERE ====================== +% Instructions: Fill in this function to return training errors in +% error_train and the validation errors in error_val. The +% vector lambda_vec contains the different lambda parameters +% to use for each calculation of the errors, i.e, +% error_train(i), and error_val(i) should give +% you the errors obtained after training with +% lambda = lambda_vec(i) +% +% Note: You can loop over lambda_vec with the following: +% +% for i = 1:length(lambda_vec) +% lambda = lambda_vec(i); +% % Compute train / val errors when training linear +% % regression with regularization parameter lambda +% % You should store the result in error_train(i) +% % and error_val(i) +% .... +% +% end +% +% + + + + + + + + + + +% ========================================================================= + +end