solves week 4 programmign exercise

test.m

@@ -1,38 +1,18 @@
 clc;
+clear;
 
-function result = square(number)
-  result = number * number;
-end
+function value = sigmoid(matrix)
+  value = 1./ (1 + exp(-matrix));
+endfunction
 
-function [sq, cube] = squareAndCube(number)
-  sq = square(number);
-  cube = sq * number;
-end  
+X = [1 1 ; 1 2 ; 1 3];
+all_theta = [0 0 ; 1 1 ; 2 2 ; 3 3];
 
-function cost = costFunction(x, hypothesis, result)
-  trainingExamles = size(x)(1);
-  predictions = x * hypothesis;
-  squareErrors = (predictions - result) .^ 2;
-  cost = 0.5 / trainingExamles * sum(squareErrors);
-end
+hypotheses = X * all_theta';
+disp(hypotheses);
+probabilities = sigmoid(hypotheses);
+disp(probabilities);
 
-
-vector = [1 ; 2; 3; 4; 5];
-
-for i = 1:length(vector),
-  vector(i) = 2^i;
-end
-
-disp(vector);
-disp(square(3))
-[sq, c] = squareAndCube(10);
-disp(sq)
-
-x = [1 1 ; 1 2 ; 1 3];
-hypothesis = [100 ; 0];
-y = [1 ; 2; 3];
-disp(costFunction(x, hypothesis, y));
-
-
-disp(computeCost(x, y, hypothesis));
-gradientDescent()
+[maxProbabilities index] = max(probabilities, [], 2);
+disp(maxProbabilities);
+disp(index);

week3/regularized-logistic-regression.m

@@ -15,7 +15,7 @@
   trainingSamples = length(y);
   J = -(1 / trainingSamples) * sum(
     y .* log(estimatedResults) 
-    + (1 - y) .* log(estimatedResults)
+    + (1 - y) .* log(1 - estimatedResults)
   );
 endfunction
 
@@ -25,7 +25,7 @@
 
   J = (- 1 / trainingSamples) * sum(
     y .* log(estimatedResults) 
-    + (1 - y) .* log(estimatedResults)
+    + (1 - y) .* log(1 - estimatedResults)
   ) + (regularizationFactor() / (2 * trainingSamples)) * (
     sum(theta .^ 2) - theta(1) ^ 2
   );

week4/machine-learning-ex3/ex3/lrCostFunction.m

@@ -1,52 +1,35 @@
 function [J, grad] = lrCostFunction(theta, X, y, lambda)
-%LRCOSTFUNCTION Compute cost and gradient for logistic regression with 
-%regularization
-%   J = LRCOSTFUNCTION(theta, X, y, lambda) computes the cost of using
-%   theta as the parameter for regularized logistic regression and the
-%   gradient of the cost w.r.t. to the parameters. 
-
-% Initialize some useful values
-m = length(y); % number of training examples
-
-% You need to return the following variables correctly 
-J = 0;
-grad = zeros(size(theta));
-
-% ====================== YOUR CODE HERE ======================
-% Instructions: Compute the cost of a particular choice of theta.
-%               You should set J to the cost.
-%               Compute the partial derivatives and set grad to the partial
-%               derivatives of the cost w.r.t. each parameter in theta
-%
-% Hint: The computation of the cost function and gradients can be
-%       efficiently vectorized. For example, consider the computation
-%
-%           sigmoid(X * theta)
-%
-%       Each row of the resulting matrix will contain the value of the
-%       prediction for that example. You can make use of this to vectorize
-%       the cost function and gradient computations. 
-%
-% Hint: When computing the gradient of the regularized cost function, 
-%       there're many possible vectorized solutions, but one solution
-%       looks like:
-%           grad = (unregularized gradient for logistic regression)
-%           temp = theta; 
-%           temp(1) = 0;   % because we don't add anything for j = 0  
-%           grad = grad + YOUR_CODE_HERE (using the temp variable)
-%
-
-
-
-
-
-
-
-
-
-
-% =============================================================
-
-grad = grad(:);
-
+  %LRCOSTFUNCTION Compute cost and gradient for logistic regression with 
+  %regularization
+  %   J = LRCOSTFUNCTION(theta, X, y, lambda) computes the cost of using
+  %   theta as the parameter for regularized logistic regression and the
+  %   gradient of the cost w.r.t. to the parameters. 
+
+  function J = logisticRegressionRegularizedCost(theta, X, y)
+    estimatedResults = sigmoid(X * theta);
+    trainingExamples = length(y);
+
+    J = (- 1 / trainingExamples) * (
+      y'  * log(estimatedResults) 
+      + (1 - y)' * log(1 - estimatedResults)
+    ) + (lambda / (2 * trainingExamples)) * (
+      sum(theta .^ 2) - theta(1) ^ 2
+    );
+  endfunction
+
+  function gradient = gradientVector(theta, X, y)
+    trainingExamples = length(y);
+    gradient = (1 / trainingExamples) * (X' * (sigmoid(X * theta) - y));
+  endfunction
+
+  function gradient = regularizedGradientVector(theta, X, y)
+    trainingExamples = length(y);
+    gradient = gradientVector(theta, X, y);
+    modifiedHypothesis = (lambda / trainingExamples) * theta;
+    modifiedHypothesis(1) = 0;
+    gradient += modifiedHypothesis;
+  endfunction
+
+  J = logisticRegressionRegularizedCost(theta, X, y);
+  grad = regularizedGradientVector(theta, X, y);
 end

week4/machine-learning-ex3/ex3/oneVsAll.m

@@ -1,66 +1,27 @@
 function [all_theta] = oneVsAll(X, y, num_labels, lambda)
-%ONEVSALL trains multiple logistic regression classifiers and returns all
-%the classifiers in a matrix all_theta, where the i-th row of all_theta 
-%corresponds to the classifier for label i
-%   [all_theta] = ONEVSALL(X, y, num_labels, lambda) trains num_labels
-%   logistic regression classifiers and returns each of these classifiers
-%   in a matrix all_theta, where the i-th row of all_theta corresponds 
-%   to the classifier for label i
-
-% Some useful variables
-m = size(X, 1);
-n = size(X, 2);
-
-% You need to return the following variables correctly 
-all_theta = zeros(num_labels, n + 1);
-
-% Add ones to the X data matrix
-X = [ones(m, 1) X];
-
-% ====================== YOUR CODE HERE ======================
-% Instructions: You should complete the following code to train num_labels
-%               logistic regression classifiers with regularization
-%               parameter lambda. 
-%
-% Hint: theta(:) will return a column vector.
-%
-% Hint: You can use y == c to obtain a vector of 1's and 0's that tell you
-%       whether the ground truth is true/false for this class.
-%
-% Note: For this assignment, we recommend using fmincg to optimize the cost
-%       function. It is okay to use a for-loop (for c = 1:num_labels) to
-%       loop over the different classes.
-%
-%       fmincg works similarly to fminunc, but is more efficient when we
-%       are dealing with large number of parameters.
-%
-% Example Code for fmincg:
-%
-%     % Set Initial theta
-%     initial_theta = zeros(n + 1, 1);
-%     
-%     % Set options for fminunc
-%     options = optimset('GradObj', 'on', 'MaxIter', 50);
-% 
-%     % Run fmincg to obtain the optimal theta
-%     % This function will return theta and the cost 
-%     [theta] = ...
-%         fmincg (@(t)(lrCostFunction(t, X, (y == c), lambda)), ...
-%                 initial_theta, options);
-%
-
-
-
-
-
-
-
-
-
-
-
-
-% =========================================================================
-
-
+  %ONEVSALL trains multiple logistic regression classifiers and returns all
+  %the classifiers in a matrix all_theta, where the i-th row of all_theta 
+  %corresponds to the classifier for label i
+  %   [all_theta] = ONEVSALL(X, y, num_labels, lambda) trains num_labels
+  %   logistic regression classifiers and returns each of these classifiers
+  %   in a matrix all_theta, where the i-th row of all_theta corresponds 
+  %   to the classifier for label i
+
+
+  dataSetSize = size(X, 1);
+  features = size(X, 2);
+  all_theta = zeros(num_labels, features + 1);
+
+  % Add ones to the X data matrix
+  X = [ones(dataSetSize, 1) X];
+
+  initial_theta = zeros(features + 1, 1);
+
+  % Set options for fminuncg
+  options = optimset('GradObj', 'on', 'MaxIter', 50);
+
+  for c = 1:num_labels
+    [theta, cost] = fmincg (@(t)(lrCostFunction(t, X, (y == c), lambda)), initial_theta, options);
+    all_theta(c,:) = theta(:);
+  endfor
 end

week4/machine-learning-ex3/ex3/predict.m

@@ -8,7 +8,15 @@
 num_labels = size(Theta2, 1);
 
 % You need to return the following variables correctly 
-p = zeros(size(X, 1), 1);
+% p = zeros(m, 1);
+
+% add x0 in x
+a1 = [ones(m, 1) X];
+a2 = sigmoid(a1 * Theta1');
+a2 = [ones(m, 1) a2];
+a3 = sigmoid(a2 * Theta2');
+[maxProbability index] = max(a3, [], 2);
+p = index;
 
 % ====================== YOUR CODE HERE ======================
 % Instructions: Complete the following code to make predictions using

week4/machine-learning-ex3/ex3/predictOneVsAll.m

@@ -1,42 +1,20 @@
 function p = predictOneVsAll(all_theta, X)
-%PREDICT Predict the label for a trained one-vs-all classifier. The labels 
-%are in the range 1..K, where K = size(all_theta, 1). 
-%  p = PREDICTONEVSALL(all_theta, X) will return a vector of predictions
-%  for each example in the matrix X. Note that X contains the examples in
-%  rows. all_theta is a matrix where the i-th row is a trained logistic
-%  regression theta vector for the i-th class. You should set p to a vector
-%  of values from 1..K (e.g., p = [1; 3; 1; 2] predicts classes 1, 3, 1, 2
-%  for 4 examples) 
-
-m = size(X, 1);
-num_labels = size(all_theta, 1);
-
-% You need to return the following variables correctly 
-p = zeros(size(X, 1), 1);
-
-% Add ones to the X data matrix
-X = [ones(m, 1) X];
-
-% ====================== YOUR CODE HERE ======================
-% Instructions: Complete the following code to make predictions using
-%               your learned logistic regression parameters (one-vs-all).
-%               You should set p to a vector of predictions (from 1 to
-%               num_labels).
-%
-% Hint: This code can be done all vectorized using the max function.
-%       In particular, the max function can also return the index of the 
-%       max element, for more information see 'help max'. If your examples 
-%       are in rows, then, you can use max(A, [], 2) to obtain the max 
-%       for each row.
-%       
-
-
-
-
-
-
-
-% =========================================================================
-
-
+  %PREDICT Predict the label for a trained one-vs-all classifier. The labels 
+  %are in the range 1..K, where K = size(all_theta, 1). 
+  %  p = PREDICTONEVSALL(all_theta, X) will return a vector of predictions
+  %  for each example in the matrix X. Note that X contains the examples in
+  %  rows. all_theta is a matrix where the i-th row is a trained logistic
+  %  regression theta vector for the i-th class. You should set p to a vector
+  %  of values from 1..K (e.g., p = [1; 3; 1; 2] predicts classes 1, 3, 1, 2
+  %  for 4 examples) 
+
+  trainingDataSize = size(X)(1);
+
+  % Add ones to the X data matrix
+  X = [ones(trainingDataSize, 1) X];
+
+  hypotheses = X * all_theta';
+  probabilities = sigmoid(hypotheses);
+  [maxProbability index] = max(probabilities, [], 2);
+  p = index;
 end

week4/machine-learning-ex3/ex3/token.mat

@@ -0,0 +1,15 @@
+# Created by Octave 5.2.0, Mon Jun 15 03:58:24 2020 GMT <unknown@anishLearnsToCode>
+# name: email
+# type: sq_string
+# elements: 1
+# length: 21
+[email protected]
+
+
+# name: token
+# type: sq_string
+# elements: 1
+# length: 16
+RV8uyaZ6iH1Bc0On
+
+