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ex4/checkNNGradients.m

+function checkNNGradients(lambda)
+%CHECKNNGRADIENTS Creates a small neural network to check the
+%backpropagation gradients
+%   CHECKNNGRADIENTS(lambda) Creates a small neural network to check the
+%   backpropagation gradients, it will output the analytical gradients
+%   produced by your backprop code and the numerical gradients (computed
+%   using computeNumericalGradient). These two gradient computations should
+%   result in very similar values.
+%
+
+if ~exist('lambda', 'var') || isempty(lambda)
+    lambda = 0;
+end
+
+input_layer_size = 3;
+hidden_layer_size = 5;
+num_labels = 3;
+m = 5;
+
+% We generate some 'random' test data
+Theta1 = debugInitializeWeights(hidden_layer_size, input_layer_size);
+Theta2 = debugInitializeWeights(num_labels, hidden_layer_size);
+% Reusing debugInitializeWeights to generate X
+X  = debugInitializeWeights(m, input_layer_size - 1);
+y  = 1 + mod(1:m, num_labels)';
+
+% Unroll parameters
+nn_params = [Theta1(:) ; Theta2(:)];
+
+% Short hand for cost function
+costFunc = @(p) nnCostFunction(p, input_layer_size, hidden_layer_size, ...
+                               num_labels, X, y, lambda);
+
+[cost, grad] = costFunc(nn_params);
+numgrad = computeNumericalGradient(costFunc, nn_params);
+
+% Visually examine the two gradient computations.  The two columns
+% you get should be very similar. 
+disp([numgrad grad]);
+fprintf(['The above two columns you get should be very similar.\n' ...
+         '(Left-Your Numerical Gradient, Right-Analytical Gradient)\n\n']);
+
+% Evaluate the norm of the difference between two solutions.  
+% If you have a correct implementation, and assuming you used EPSILON = 0.0001 
+% in computeNumericalGradient.m, then diff below should be less than 1e-9
+diff = norm(numgrad-grad)/norm(numgrad+grad);
+
+fprintf(['If your backpropagation implementation is correct, then \n' ...
+         'the relative difference will be small (less than 1e-9). \n' ...
+         '\nRelative Difference: %g\n'], diff);
+
+end

ex4/computeNumericalGradient.m

+function numgrad = computeNumericalGradient(J, theta)
+%COMPUTENUMERICALGRADIENT Computes the gradient using "finite differences"
+%and gives us a numerical estimate of the gradient.
+%   numgrad = COMPUTENUMERICALGRADIENT(J, theta) computes the numerical
+%   gradient of the function J around theta. Calling y = J(theta) should
+%   return the function value at theta.
+
+% Notes: The following code implements numerical gradient checking, and 
+%        returns the numerical gradient.It sets numgrad(i) to (a numerical 
+%        approximation of) the partial derivative of J with respect to the 
+%        i-th input argument, evaluated at theta. (i.e., numgrad(i) should 
+%        be the (approximately) the partial derivative of J with respect 
+%        to theta(i).)
+%                
+
+numgrad = zeros(size(theta));
+perturb = zeros(size(theta));
+e = 1e-4;
+for p = 1:numel(theta)
+    % Set perturbation vector
+    perturb(p) = e;
+    loss1 = J(theta - perturb);
+    loss2 = J(theta + perturb);
+    % Compute Numerical Gradient
+    numgrad(p) = (loss2 - loss1) / (2*e);
+    perturb(p) = 0;
+end
+
+end

ex4/debugInitializeWeights.m

+function W = debugInitializeWeights(fan_out, fan_in)
+%DEBUGINITIALIZEWEIGHTS Initialize the weights of a layer with fan_in
+%incoming connections and fan_out outgoing connections using a fixed
+%strategy, this will help you later in debugging
+%   W = DEBUGINITIALIZEWEIGHTS(fan_in, fan_out) initializes the weights 
+%   of a layer with fan_in incoming connections and fan_out outgoing 
+%   connections using a fix set of values
+%
+%   Note that W should be set to a matrix of size(1 + fan_in, fan_out) as
+%   the first row of W handles the "bias" terms
+%
+
+% Set W to zeros
+W = zeros(fan_out, 1 + fan_in);
+
+% Initialize W using "sin", this ensures that W is always of the same
+% values and will be useful for debugging
+W = reshape(sin(1:numel(W)), size(W)) / 10;
+
+% =========================================================================
+
+end

ex4/displayData.m

+function [h, display_array] = displayData(X, example_width)
+%DISPLAYDATA Display 2D data in a nice grid
+%   [h, display_array] = DISPLAYDATA(X, example_width) displays 2D data
+%   stored in X in a nice grid. It returns the figure handle h and the 
+%   displayed array if requested.
+
+% Set example_width automatically if not passed in
+if ~exist('example_width', 'var') || isempty(example_width) 
+	example_width = round(sqrt(size(X, 2)));
+end
+
+% Gray Image
+colormap(gray);
+
+% Compute rows, cols
+[m n] = size(X);
+example_height = (n / example_width);
+
+% Compute number of items to display
+display_rows = floor(sqrt(m));
+display_cols = ceil(m / display_rows);
+
+% Between images padding
+pad = 1;
+
+% Setup blank display
+display_array = - ones(pad + display_rows * (example_height + pad), ...
+                       pad + display_cols * (example_width + pad));
+
+% Copy each example into a patch on the display array
+curr_ex = 1;
+for j = 1:display_rows
+	for i = 1:display_cols
+		if curr_ex > m, 
+			break; 
+		end
+		% Copy the patch
+		
+		% Get the max value of the patch
+		max_val = max(abs(X(curr_ex, :)));
+		display_array(pad + (j - 1) * (example_height + pad) + (1:example_height), ...
+		              pad + (i - 1) * (example_width + pad) + (1:example_width)) = ...
+						reshape(X(curr_ex, :), example_height, example_width) / max_val;
+		curr_ex = curr_ex + 1;
+	end
+	if curr_ex > m, 
+		break; 
+	end
+end
+
+% Display Image
+h = imagesc(display_array, [-1 1]);
+
+% Do not show axis
+axis image off
+
+drawnow;
+
+end
+%% Machine Learning Online Class - Exercise 4 Neural Network Learning
+
+%  Instructions
+%  ------------
+% 
+%  This file contains code that helps you get started on the
+%  linear exercise. You will need to complete the following functions 
+%  in this exericse:
+%
+%     sigmoidGradient.m
+%     randInitializeWeights.m
+%     nnCostFunction.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
+
+%% Setup the parameters you will use for this exercise
+input_layer_size  = 400;  % 20x20 Input Images of Digits
+hidden_layer_size = 25;   % 25 hidden units
+num_labels = 10;          % 10 labels, from 1 to 10   
+                          % (note that we have mapped "0" to label 10)
+
+%% =========== Part 1: Loading and Visualizing Data =============
+%  We start the exercise by first loading and visualizing the dataset. 
+%  You will be working with a dataset that contains handwritten digits.
+%
+
+% Load Training Data
+fprintf('Loading and Visualizing Data ...\n')
+
+load('ex4data1.mat');
+m = size(X, 1);
+
+% Randomly select 100 data points to display
+sel = randperm(size(X, 1));
+sel = sel(1:100);
+
+displayData(X(sel, :));
+
+fprintf('Program paused. Press enter to continue.\n');
+pause;
+
+
+%% ================ Part 2: Loading Parameters ================
+% In this part of the exercise, we load some pre-initialized 
+% neural network parameters.
+
+fprintf('\nLoading Saved Neural Network Parameters ...\n')
+
+% Load the weights into variables Theta1 and Theta2
+load('ex4weights.mat');
+
+% Unroll parameters 
+nn_params = [Theta1(:) ; Theta2(:)];
+
+%% ================ Part 3: Compute Cost (Feedforward) ================
+%  To the neural network, you should first start by implementing the
+%  feedforward part of the neural network that returns the cost only. You
+%  should complete the code in nnCostFunction.m to return cost. After
+%  implementing the feedforward to compute the cost, you can verify that
+%  your implementation is correct by verifying that you get the same cost
+%  as us for the fixed debugging parameters.
+%
+%  We suggest implementing the feedforward cost *without* regularization
+%  first so that it will be easier for you to debug. Later, in part 4, you
+%  will get to implement the regularized cost.
+%
+fprintf('\nFeedforward Using Neural Network ...\n')
+
+% Weight regularization parameter (we set this to 0 here).
+lambda = 0;
+
+J = nnCostFunction(nn_params, input_layer_size, hidden_layer_size, ...
+                   num_labels, X, y, lambda);
+
+fprintf(['Cost at parameters (loaded from ex4weights): %f '...
+         '\n(this value should be about 0.287629)\n'], J);
+
+fprintf('\nProgram paused. Press enter to continue.\n');
+pause;
+
+%% =============== Part 4: Implement Regularization ===============
+%  Once your cost function implementation is correct, you should now
+%  continue to implement the regularization with the cost.
+%
+
+fprintf('\nChecking Cost Function (w/ Regularization) ... \n')
+
+% Weight regularization parameter (we set this to 1 here).
+lambda = 1;
+
+J = nnCostFunction(nn_params, input_layer_size, hidden_layer_size, ...
+                   num_labels, X, y, lambda);
+
+fprintf(['Cost at parameters (loaded from ex4weights): %f '...
+         '\n(this value should be about 0.383770)\n'], J);
+
+fprintf('Program paused. Press enter to continue.\n');
+pause;
+
+
+%% ================ Part 5: Sigmoid Gradient  ================
+%  Before you start implementing the neural network, you will first
+%  implement the gradient for the sigmoid function. You should complete the
+%  code in the sigmoidGradient.m file.
+%
+
+fprintf('\nEvaluating sigmoid gradient...\n')
+
+g = sigmoidGradient([1 -0.5 0 0.5 1]);
+fprintf('Sigmoid gradient evaluated at [1 -0.5 0 0.5 1]:\n  ');
+fprintf('%f ', g);
+fprintf('\n\n');
+
+fprintf('Program paused. Press enter to continue.\n');
+pause;
+
+
+%% ================ Part 6: Initializing Pameters ================
+%  In this part of the exercise, you will be starting to implment a two
+%  layer neural network that classifies digits. You will start by
+%  implementing a function to initialize the weights of the neural network
+%  (randInitializeWeights.m)
+
+fprintf('\nInitializing Neural Network Parameters ...\n')
+
+initial_Theta1 = randInitializeWeights(input_layer_size, hidden_layer_size);
+initial_Theta2 = randInitializeWeights(hidden_layer_size, num_labels);
+
+% Unroll parameters
+initial_nn_params = [initial_Theta1(:) ; initial_Theta2(:)];
+
+
+%% =============== Part 7: Implement Backpropagation ===============
+%  Once your cost matches up with ours, you should proceed to implement the
+%  backpropagation algorithm for the neural network. You should add to the
+%  code you've written in nnCostFunction.m to return the partial
+%  derivatives of the parameters.
+%
+fprintf('\nChecking Backpropagation... \n');
+
+%  Check gradients by running checkNNGradients
+checkNNGradients;
+
+fprintf('\nProgram paused. Press enter to continue.\n');
+pause;
+
+
+%% =============== Part 8: Implement Regularization ===============
+%  Once your backpropagation implementation is correct, you should now
+%  continue to implement the regularization with the cost and gradient.
+%
+
+fprintf('\nChecking Backpropagation (w/ Regularization) ... \n')
+
+%  Check gradients by running checkNNGradients
+lambda = 3;
+checkNNGradients(lambda);
+
+% Also output the costFunction debugging values
+debug_J  = nnCostFunction(nn_params, input_layer_size, ...
+                          hidden_layer_size, num_labels, X, y, lambda);
+
+fprintf(['\n\nCost at (fixed) debugging parameters (w/ lambda = 10): %f ' ...
+         '\n(this value should be about 0.576051)\n\n'], debug_J);
+
+fprintf('Program paused. Press enter to continue.\n');
+pause;
+
+
+%% =================== Part 8: Training NN ===================
+%  You have now implemented all the code necessary to train a neural 
+%  network. To train your neural network, we will now use "fmincg", which
+%  is a function which works similarly to "fminunc". Recall that these
+%  advanced optimizers are able to train our cost functions efficiently as
+%  long as we provide them with the gradient computations.
+%
+fprintf('\nTraining Neural Network... \n')
+
+%  After you have completed the assignment, change the MaxIter to a larger
+%  value to see how more training helps.
+options = optimset('MaxIter', 50);
+
+%  You should also try different values of lambda
+lambda = 1;
+
+% Create "short hand" for the cost function to be minimized
+costFunction = @(p) nnCostFunction(p, ...
+                                   input_layer_size, ...
+                                   hidden_layer_size, ...
+                                   num_labels, X, y, lambda);
+
+% Now, costFunction is a function that takes in only one argument (the
+% neural network parameters)
+[nn_params, cost] = fmincg(costFunction, initial_nn_params, options);
+
+% Obtain Theta1 and Theta2 back from nn_params
+Theta1 = reshape(nn_params(1:hidden_layer_size * (input_layer_size + 1)), ...
+                 hidden_layer_size, (input_layer_size + 1));
+
+Theta2 = reshape(nn_params((1 + (hidden_layer_size * (input_layer_size + 1))):end), ...
+                 num_labels, (hidden_layer_size + 1));
+
+fprintf('Program paused. Press enter to continue.\n');
+pause;
+
+
+%% ================= Part 9: Visualize Weights =================
+%  You can now "visualize" what the neural network is learning by 
+%  displaying the hidden units to see what features they are capturing in 
+%  the data.
+
+fprintf('\nVisualizing Neural Network... \n')
+
+displayData(Theta1(:, 2:end));
+
+fprintf('\nProgram paused. Press enter to continue.\n');
+pause;
+
+%% ================= Part 10: Implement Predict =================
+%  After training the neural network, we would like to use it to predict
+%  the labels. You will now implement the "predict" function to use the
+%  neural network to predict the labels of the training set. This lets
+%  you compute the training set accuracy.
+
+pred = predict(Theta1, Theta2, X);
+
+fprintf('\nTraining Set Accuracy: %f\n', mean(double(pred == y)) * 100);
+
+

ex4/ex4data1.mat

Binary file added.

ex4/ex4weights.mat

Binary file added.
+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');

ex4/nnCostFunction.m

+function [J grad] = nnCostFunction(nn_params, ...
+                                   input_layer_size, ...
+                                   hidden_layer_size, ...
+                                   num_labels, ...
+                                   X, y, lambda)
+%NNCOSTFUNCTION Implements the neural network cost function for a two layer
+%neural network which performs classification
+%   [J grad] = NNCOSTFUNCTON(nn_params, hidden_layer_size, num_labels, ...
+%   X, y, lambda) computes the cost and gradient of the neural network. The
+%   parameters for the neural network are "unrolled" into the vector
+%   nn_params and need to be converted back into the weight matrices. 
+% 
+%   The returned parameter grad should be a "unrolled" vector of the
+%   partial derivatives of the neural network.
+%
+
+% Reshape nn_params back into the parameters Theta1 and Theta2, the weight matrices
+% for our 2 layer neural network
+Theta1 = reshape(nn_params(1:hidden_layer_size * (input_layer_size + 1)), ...
+                 hidden_layer_size, (input_layer_size + 1));
+
+Theta2 = reshape(nn_params((1 + (hidden_layer_size * (input_layer_size + 1))):end), ...
+                 num_labels, (hidden_layer_size + 1));
+
+% Setup some useful variables
+m = size(X, 1);
+         
+% You need to return the following variables correctly 
+J = 0;
+Theta1_grad = zeros(size(Theta1));
+Theta2_grad = zeros(size(Theta2));
+
+% ====================== YOUR CODE HERE ======================
+% Instructions: You should complete the code by working through the
+%               following parts.
+%
+% Part 1: Feedforward the neural network and return the cost in the
+%         variable J. After implementing Part 1, you can verify that your
+%         cost function computation is correct by verifying the cost
+%         computed in ex4.m
+%
+% Part 2: Implement the backpropagation algorithm to compute the gradients
+%         Theta1_grad and Theta2_grad. You should return the partial derivatives of
+%         the cost function with respect to Theta1 and Theta2 in Theta1_grad and
+%         Theta2_grad, respectively. After implementing Part 2, you can check
+%         that your implementation is correct by running checkNNGradients
+%
+%         Note: The vector y passed into the function is a vector of labels
+%               containing values from 1..K. You need to map this vector into a 
+%               binary vector of 1's and 0's to be used with the neural network
+%               cost function.
+%
+%         Hint: We recommend implementing backpropagation using a for-loop
+%               over the training examples if you are implementing it for the 
+%               first time.
+%
+% Part 3: Implement regularization with the cost function and gradients.
+%
+%         Hint: You can implement this around the code for
+%               backpropagation. That is, you can compute the gradients for
+%               the regularization separately and then add them to Theta1_grad
+%               and Theta2_grad from Part 2.
+%
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+% -------------------------------------------------------------
+
+% =========================================================================
+
+% Unroll gradients
+grad = [Theta1_grad(:) ; Theta2_grad(:)];
+
+
+end
+function p = predict(Theta1, Theta2, X)
+%PREDICT Predict the label of an input given a trained neural network
+%   p = PREDICT(Theta1, Theta2, X) outputs the predicted label of X given the
+%   trained weights of a neural network (Theta1, Theta2)
+
+% Useful values
+m = size(X, 1);
+num_labels = size(Theta2, 1);
+
+% You need to return the following variables correctly 
+p = zeros(size(X, 1), 1);
+
+h1 = sigmoid([ones(m, 1) X] * Theta1');
+h2 = sigmoid([ones(m, 1) h1] * Theta2');
+[dummy, p] = max(h2, [], 2);
+
+% =========================================================================
+
+
+end

ex4/randInitializeWeights.m

+function W = randInitializeWeights(L_in, L_out)
+%RANDINITIALIZEWEIGHTS Randomly initialize the weights of a layer with L_in
+%incoming connections and L_out outgoing connections
+%   W = RANDINITIALIZEWEIGHTS(L_in, L_out) randomly initializes the weights 
+%   of a layer with L_in incoming connections and L_out outgoing 
+%   connections. 
+%
+%   Note that W should be set to a matrix of size(L_out, 1 + L_in) as
+%   the column row of W handles the "bias" terms
+%
+
+% You need to return the following variables correctly 
+W = zeros(L_out, 1 + L_in);
+
+% ====================== YOUR CODE HERE ======================
+% Instructions: Initialize W randomly so that we break the symmetry while
+%               training the neural network.
+%
+% Note: The first row of W corresponds to the parameters for the bias units
+%
+
+
+
+
+
+
+
+
+
+% =========================================================================
+
+end
+function g = sigmoid(z)
+%SIGMOID Compute sigmoid functoon
+%   J = SIGMOID(z) computes the sigmoid of z.
+
+g = 1.0 ./ (1.0 + exp(-z));
+end

ex4/sigmoidGradient.m

+function g = sigmoidGradient(z)
+%SIGMOIDGRADIENT returns the gradient of the sigmoid function
+%evaluated at z
+%   g = SIGMOIDGRADIENT(z) computes the gradient of the sigmoid function
+%   evaluated at z. This should work regardless if z is a matrix or a
+%   vector. In particular, if z is a vector or matrix, you should return
+%   the gradient for each element.
+
+g = zeros(size(z));
+
+% ====================== YOUR CODE HERE ======================
+% Instructions: Compute the gradient of the sigmoid function evaluated at
+%               each value of z (z can be a matrix, vector or scalar).
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+% =============================================================
+
+
+
+
+end
+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 = '4';
+end
+
+function [partNames] = validParts()
+  partNames = { 'Feedforward and Cost Function', ...
+                'Regularized Cost Function', ...
+                'Sigmoid Gradient', ...
+                'Neural Network Gradient (Backpropagation)' ...
+                'Regularized Gradient' ...
+                };
+end
+
+function srcs = sources()
+  % Separated by part
+  srcs = { { 'nnCostFunction.m' }, ...
+           { 'nnCostFunction.m' }, ...
+           { 'sigmoidGradient.m' }, ...
+           { 'nnCostFunction.m' }, ...
+           { 'nnCostFunction.m' } };
+end
+
+function out = output(partId, auxstring)
+  % Random Test Cases
+  X = reshape(3 * sin(1:1:30), 3, 10);
+  Xm = reshape(sin(1:32), 16, 2) / 5;
+  ym = 1 + mod(1:16,4)';
+  t1 = sin(reshape(1:2:24, 4, 3));
+  t2 = cos(reshape(1:2:40, 4, 5));
+  t  = [t1(:) ; t2(:)];
+  if partId == 1
+    [J] = nnCostFunction(t, 2, 4, 4, Xm, ym, 0);
+    out = sprintf('%0.5f ', J);
+  elseif partId == 2
+    [J] = nnCostFunction(t, 2, 4, 4, Xm, ym, 1.5);
+    out = sprintf('%0.5f ', J);
+  elseif partId == 3
+    out = sprintf('%0.5f ', sigmoidGradient(X));
+  elseif partId == 4
+    [J, grad] = nnCostFunction(t, 2, 4, 4, Xm, ym, 0);
+    out = sprintf('%0.5f ', J);
+    out = [out sprintf('%0.5f ', grad)];
+  elseif partId == 5
+    [J, grad] = nnCostFunction(t, 2, 4, 4, Xm, ym, 1.5);
+    out = sprintf('%0.5f ', J);
+    out = [out sprintf('%0.5f ', grad)];
+  end 
+end
+
+
+% ====================== SERVER CONFIGURATION ===========================
+
+% ***************** REMOVE -staging WHEN YOU DEPLOY *********************
+function url = site_url()
+  url = 'http://www.coursera.org/ml';
+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
+% 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
+
Binary file added.
+#!/usr/bin/env python
+
+from scipy.io import loadmat
+import matplotlib.pylab as plt
+from sklearn import linear_model
+import numpy as np
+
+def error(clf, xs, ys):
+    return np.power(clf.predict(xs) - ys, 2).sum() / (2 * xs.shape[0])
+
+alphas = 
+
+
+def go():
+    data = loadmat('ex5/ex5data1.mat')
+    xs = range(1, data['X'].shape[0]+1)
+    tys = []
+    vys = []
+    for m in xs:
+        clf = linear_model.RidgeRegression()
+        clf.fit(data['X'][:m], data['y'][:m])
+        tys.append(error(clf, data['Xtest'][:m], data['ytest'][:m]))
+        vys.append(error(clf, data['Xval'][:m], data['yval'][:m]))
+
+
+    fig = plt.figure()
+    ax = fig.add_subplot(111)
+    ax.plot(xs, tys, label='Train')
+    ax.plot(xs, vys, label='Cross Validation')
+    plt.legend()
+    fig.show()
+
+    return fig
+
+if __name__ == '__main__':
+    fig = go()
+    fig.ginput()
+%% 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;

ex5/ex5data1.mat

Binary file added.

ex5/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.
+
+mu = mean(X);
+X_norm = bsxfun(@minus, X, mu);
+
+sigma = std(X_norm);
+X_norm = bsxfun(@rdivide, X_norm, sigma);
+
+
+% ============================================================
+
+end
+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');

ex5/learningCurve.m

+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

ex5/linearRegCostFunction.m

+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
+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

ex5/polyFeatures.m

+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
+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://www.coursera.org/ml';
+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};