siolves quiz on regularization with 100% accuracy

test.m

@@ -35,3 +35,4 @@
 
 
 disp(computeCost(x, y, hypothesis));
+gradientDescent()

week2/linear-regression.m

@@ -0,0 +1,23 @@
+clc;
+clear;
+
+function theta = normalizedLinearRegression(theta, X, y)
+  theta = inv(X' * X) * X' * y;
+endfunction
+
+function theta = normalizedLinearRegressionWithRegularization(theta, X, y)
+  regularizationParameter = 100;
+  features = size(X)(2) - 1;
+  regularizationMatrix = regularizationParameter * eye(features + 1);
+  regularizationMatrix(1, 1) = 0;
+  theta = inv(X' * X + regularizationMatrix) * X' * y;
+endfunction
+
+hypothesis = [0 ; 0];
+data = [1 1 ; 1 2 ; 1 3];
+result = [1 ; 2 ; 3];
+optimizedHypothesis = normalizedLinearRegression(hypothesis, data, result);
+disp(round(optimizedHypothesis));
+
+optimizedHypothesis = normalizedLinearRegressionWithRegularization(hypothesis, data, result);
+disp(optimizedHypothesis);

week3/logistic-regression-quiz.md

@@ -0,0 +1,8 @@
+## Logistic Regression Quiz 
+
+![Question 1](assets/logistic-regresion-quiz-1.PNG)
+![Question 2](assets/logistic-regresion-quiz-2-b.PNG)
+![Question 3]()
+![Question 4](assets/logistic-regresion-quiz-4.PNG)
+![Question 4](assets/logistic-regresion-quiz-4-2.PNG)
+![Question 5]()

week3/logistic_regression.m

@@ -0,0 +1,17 @@
+clc;
+clear;
+
+function [value, gradient] = costFunction(theta) 
+  value = (theta(1) - 5)^2 + (theta(2) - 10)^2;
+  gradient = zeros(2, 1);
+  gradient(1) =   2 * (theta(1) - 5);
+  gradient(2) =   2 * (theta(2) - 10);
+endfunction
+
+
+options = optimset('GradObj', 'on', 'MaxIter', 100);
+initialTheta = zeros(2, 1);
+[theta, functionVal, exitFlag] = fminunc(@costFunction, initialTheta, options);
+disp(theta);
+disp(functionVal);
+disp(exitFlag);

week3/regularization-quiz.md

@@ -0,0 +1,7 @@
+# Regularization Quiz
+
+![Question 1](assets/regularization-1.PNG) 
+![Question 2](assets/regularization-2.PNG) 
+![Question 3](assets/regularization-3.PNG) 
+![Question 4](assets/regularization-4.PNG) 
+![Question 5](assets/regularization-5.PNG) 

week3/regularized-logistic-regression.m

@@ -0,0 +1,79 @@
+clc;
+clear;
+close;
+
+function lambda = regularizationFactor()
+  lambda = 10;
+endfunction
+
+function value = sigmoid(matrix)
+  value = 1 ./ (1 + exp(-matrix));
+endfunction
+
+function J = logisticRegressionCost(theta, X, y)
+  estimatedResults = sigmoid(X * theta);
+  trainingSamples = length(y);
+  J = -(1 / trainingSamples) * sum(
+    y .* log(estimatedResults) 
+    + (1 - y) .* log(estimatedResults)
+  );
+endfunction
+
+function J = logisticRegressionRegularizedCost(theta, X, y)
+  estimatedResults = sigmoid(X * theta);
+  trainingSamples = length(y);
+
+  J = (- 1 / trainingSamples) * sum(
+    y .* log(estimatedResults) 
+    + (1 - y) .* log(estimatedResults)
+  ) + (regularizationFactor() / (2 * trainingSamples)) * (
+    sum(theta .^ 2) - theta(1) ^ 2
+  );
+endfunction
+
+function gradient = gradientVector(theta, X, y)
+  trainingExamples = length(y);
+  gradient = (1 / trainingExamples) * (X' * (sigmoidFunction(X * theta) - y));
+endfunction
+
+function gradient = regularizedGradientVector(theta, X, y)
+  trainingExamples = length(y);
+  gradient = gradientVector(theta, X, y);
+  modifiedHypothesis = (regularizationFactor() / trainingExamples) * theta;
+  modifiedHypothesis(1) = 0;
+  gradient += modifiedHypothesis;
+endfunction
+
+function [theta, costMemory, minCost] = gradientDescent(theta, X, y, iterations, learningRate)
+  costMemory = [logisticRegressionCost(theta, X, y)];
+  for i = 1:iterations
+    theta = theta - learningRate * gradientVector(theta, X, y);
+    costMemory = [costMemory logisticRegressionCost(theta, X, y)];
+  endfor
+  minCost = logisticRegressionCost(theta, X, y);
+endfunction
+
+function [theta, costs, minCost] = regularizedGradientDescent(theta, X, y, iterations, learningRate)
+  costs = [logisticRegressionRegularizedCost(theta, X, y)];
+  for i = 1:iterations
+    theta = theta - learningRate * regularizedGradientVector(theta, X, y);
+    costs = [costs logisticRegressionRegularizedCost(theta, X, y)];
+  endfor
+  minCost = logisticRegressionRegularizedCost(theta, X, y);
+endfunction
+
+hypothesis = [0 ; 0];
+data = [1 1 ; 1 2 ; 1 3];
+result = [1 ; 1 ; 1];
+
+[theta, costMemory, minCost] = gradientDescent(hypothesis, data, result, 3000, 0.05);
+% disp(theta);
+disp(minCost);
+subplot(2, 2, 1); plot(costMemory);
+subplot(2, 2, 2); imagesc(theta);
+
+[theta, costMemory, minCost] = regularizedGradientDescent(hypothesis, data, result, 3000, 0.05);
+% disp(theta);
+disp(minCost);
+subplot(2, 2, 3); plot(costMemory);
+subplot(2, 2, 4); imagesc(theta);

week3/test.m

@@ -0,0 +1,60 @@
+clear;
+clc;
+
+function value = sigmoidFunction(matrix)
+  value = (1 ./ (1 + exp(-matrix)));
+endfunction
+
+function J = cost(theta, X, y)
+  trainingExamples = length(y);
+  J = (1 / (2 * trainingExamples)) * sum((sigmoidFunction(X * theta) - y) .^ 2);
+endfunction
+
+function J = regularizedCost(theta, X, y)
+  trainingExamples = length(y);
+  regularizationParameter = 100;
+
+  J = (1 / (2 * trainingExamples)) * (
+      sum((sigmoidFunction(X * theta) - y) .^ 2)
+      + regularizationParameter * (sum(theta .^ 2) - theta(1) ^ 2)
+  );
+endfunction
+
+function gradient = gradientVector(theta, X, y)
+  trainingExamples = length(y);
+  gradient = (1 / trainingExamples) * (X' * (sigmoidFunction(X * theta) - y));
+endfunction
+
+function gradient = regularizedGradientVector(theta, X, y)
+  trainingExamples = length(y);
+  regularizationParameter = 100;
+  gradient = (1 / trainingExamples) * (
+    X' * (sigmoidFunction(X * theta) - y) 
+    + regularizationParameter * theta
+  );
+endfunction
+
+function [value, gradient] = optimizationFunction(theta)
+  data = [1 1 ; 1 2 ; 1 3];
+  result = [1 ; 2 ; 3];
+  value = cost(theta, data, result);
+  gradient = gradientVector(theta, data, result);
+endfunction
+
+function [theta, costMemory, minCost] = gradientDescent(theta, X, y, iterations, learningRate)
+  costMemory = [cost(theta, X, y)];
+  for i = 1:iterations
+    theta = theta - learningRate * gradientVector(theta, X, y);
+    costMemory = [costMemory cost(theta, X, y)];
+  end
+  minCost = cost(theta, X, y);
+endfunction
+
+data = [1 1 ; 1 2 ; 1 3];
+result = [1 ; 2 ; 3];
+hypothesis = [10 ; 0];
+
+[theta, costMemory, minCost] = gradientDescent(hypothesis, data, result, 100, 0.03);
+disp(theta);
+disp(minCost);
+plot(costMemory);