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anishLearnsToCodeanishLearnsToCode
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solves week 6 ex 5
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‎README.md

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| [Week 3](#week-3) | [[Quizzes]](#quizzes-2) [[Programming Assignment]](#programming-exercises-1) |
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| [Week 4](#week-4) | [[Quizzes]](#quizzes-3) [[Programming Assignment]](#programming-exercises-2) |
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| [Week 5](#week-5) | [[Quizzes]](#quizzes-4) [[Programming Assignment]](#programming-exercises-3) |
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| [Week 6](#week-6) | [[Quizzes]](#quizzes-5) [[Programming Assignment]](#programming-exercises-4) |
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| [Week 7](#week-7) | [[Quizzes]](#quizzes-6) [[Programming Assignment]](#programming-exercises-5) |
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| [Week 8](#week-8) | [[Quizzes]](#quizzes-7) [[Programming Assignment]](#programming-exercises-6) |
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| [Week 9](#week-9) | [[Quizzes]](#quizzes-8) [[Programming Assignment]](#programming-exercises-7) |
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| [Week 10](#week-10) | [[Quizzes]](#quizzes-9) [[Programming Assignment]](#programming-exercises-8) |
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| [Week 11](#week-11) | [[Quizzes]](#quizzes-10) [[Programming Assignment]](#programming-exercises-9) |
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## Week 1
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- [Neural Networks: Learning](week5/neural-networks-quiz.md)
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### Programming Exercises
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- [Questions and Expalanations](week5/ex4.pdf)
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- [Questions and Explanations](week5/ex4.pdf)
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- [Exercise 4](week5/ex4)
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- [Feedforward and Cost Function](week5/ex4/nnCostFunction.m)
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- [Regularized Cost Function](week5/ex4/nnCostFunction.m)
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## Week 6
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### Quizzes
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- [Advice for Applied Machine Learning](week6/advice-for-applying-machine-learning.md)
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### Programming Exercises
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- [Questions and Explanations](week6/ex5.pdf)
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- [Exercise 5](week6/ex5)
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- [Regularized Linear Regression Cost Function](week6/ex5/linearRegCostFunction.m)
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- [Generate Learning Curve](week6/ex5/learningCurve.m)
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- [Maps Data into Polynomial Feature Space](week6/ex5/polyFeatures.m)
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- [Generates a Cross Validation Curve](week6/ex5/validationCurve.m)
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## Week 7
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### Quizzes
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### Programming Exercises
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## Week 8
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### Quizzes
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### Programming Exercises
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## Week 9
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### Quizzes
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### Programming Exercises
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## Week 10
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### Quizzes
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### Programming Exercises
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## Week 11
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### Quizzes
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### Programming Exercises

‎test.m

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J = (1 / (2 * trainingSampleSize)) * sum((data * hypothesis - result) .^ 2);
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endfunction
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function J = regularizedRegressionCost(theta, X, y, regularizationConstant)
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J = regressionCost(theta, X, y);
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trainingSampleSize = length(y);
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J += (regularizationConstant / (2 * trainingSampleSize)) * sum(theta .^ 2);
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endfunction
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function grad = regressionGradient(hypothesis, X, y)
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trainingSampleSize = size(X, 1);
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grad = (1 / trainingSampleSize) * (((X * hypothesis) - y)' * X)';
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endfunction
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function grad = regularizedRegressionGradient(theta, X, y, lambda)
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grad = regressionGradient(theta, X, y);
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trainingSampleSize = size(X, 1);
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features = size(X, 2) - 1;
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regularizationMask = (lambda / trainingSampleSize) * ones(features + 1, 1);
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regularizationMask(1) = 0;
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grad += regularizationMask .* theta;
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endfunction
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function [minCost, hypothesis, costMemory] = gradientDescent(hypothesis, X, y, iterations, learningRate)
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costMemory = [];
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for i = 1:iterations
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disp(hypothesis);
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plot(costMemory);
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disp('gradient');
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disp(regularizedRegressionGradient(hypothesis, data, y, 10));
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clc;
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X = [1 1 ; 1 2 ; 1 3];
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y = [1 ; 2 ; 3];
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lambda = 0.05;
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theta = trainLineaReg(X, y, lambda);
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disp(theta);

‎week6/ex5.pdf

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‎week6/ex5/ex5.m

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%% Machine Learning Online Class
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% Exercise 5 | Regularized Linear Regression and Bias-Variance
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%
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% Instructions
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% ------------
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%
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% This file contains code that helps you get started on the
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% exercise. You will need to complete the following functions:
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%
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% linearRegCostFunction.m
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% learningCurve.m
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% validationCurve.m
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%
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% For this exercise, you will not need to change any code in this file,
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% or any other files other than those mentioned above.
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%
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%% Initialization
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clear ; close all; clc
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%% =========== Part 1: Loading and Visualizing Data =============
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% We start the exercise by first loading and visualizing the dataset.
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% The following code will load the dataset into your environment and plot
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% the data.
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%
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% Load Training Data
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fprintf('Loading and Visualizing Data ...\n')
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% Load from ex5data1:
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% You will have X, y, Xval, yval, Xtest, ytest in your environment
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load ('ex5data1.mat');
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% m = Number of examples
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m = size(X, 1);
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% Plot training data
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plot(X, y, 'rx', 'MarkerSize', 10, 'LineWidth', 1.5);
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xlabel('Change in water level (x)');
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ylabel('Water flowing out of the dam (y)');
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fprintf('Program paused. Press enter to continue.\n');
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pause;
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%% =========== Part 2: Regularized Linear Regression Cost =============
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% You should now implement the cost function for regularized linear
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% regression.
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%
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theta = [1 ; 1];
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J = linearRegCostFunction([ones(m, 1) X], y, theta, 1);
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fprintf(['Cost at theta = [1 ; 1]: %f '...
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'\n(this value should be about 303.993192)\n'], J);
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fprintf('Program paused. Press enter to continue.\n');
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pause;
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%% =========== Part 3: Regularized Linear Regression Gradient =============
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% You should now implement the gradient for regularized linear
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% regression.
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%
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theta = [1 ; 1];
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[J, grad] = linearRegCostFunction([ones(m, 1) X], y, theta, 1);
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fprintf(['Gradient at theta = [1 ; 1]: [%f; %f] '...
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'\n(this value should be about [-15.303016; 598.250744])\n'], ...
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grad(1), grad(2));
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fprintf('Program paused. Press enter to continue.\n');
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pause;
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%% =========== Part 4: Train Linear Regression =============
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% Once you have implemented the cost and gradient correctly, the
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% trainLinearReg function will use your cost function to train
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% regularized linear regression.
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%
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% Write Up Note: The data is non-linear, so this will not give a great
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% fit.
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%
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% Train linear regression with lambda = 0
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lambda = 0;
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[theta] = trainLinearReg([ones(m, 1) X], y, lambda);
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% Plot fit over the data
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plot(X, y, 'rx', 'MarkerSize', 10, 'LineWidth', 1.5);
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xlabel('Change in water level (x)');
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ylabel('Water flowing out of the dam (y)');
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hold on;
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plot(X, [ones(m, 1) X]*theta, '--', 'LineWidth', 2)
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hold off;
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fprintf('Program paused. Press enter to continue.\n');
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pause;
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%% =========== Part 5: Learning Curve for Linear Regression =============
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% Next, you should implement the learningCurve function.
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%
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% Write Up Note: Since the model is underfitting the data, we expect to
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% see a graph with "high bias" -- Figure 3 in ex5.pdf
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%
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lambda = 0;
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[error_train, error_val] = ...
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learningCurve([ones(m, 1) X], y, ...
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[ones(size(Xval, 1), 1) Xval], yval, ...
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lambda);
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plot(1:m, error_train, 1:m, error_val);
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title('Learning curve for linear regression')
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legend('Train', 'Cross Validation')
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xlabel('Number of training examples')
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ylabel('Error')
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axis([0 13 0 150])
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fprintf('# Training Examples\tTrain Error\tCross Validation Error\n');
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for i = 1:m
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fprintf(' \t%d\t\t%f\t%f\n', i, error_train(i), error_val(i));
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end
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fprintf('Program paused. Press enter to continue.\n');
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pause;
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%% =========== Part 6: Feature Mapping for Polynomial Regression =============
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% One solution to this is to use polynomial regression. You should now
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% complete polyFeatures to map each example into its powers
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%
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p = 8;
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% Map X onto Polynomial Features and Normalize
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X_poly = polyFeatures(X, p);
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[X_poly, mu, sigma] = featureNormalize(X_poly); % Normalize
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X_poly = [ones(m, 1), X_poly]; % Add Ones
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% Map X_poly_test and normalize (using mu and sigma)
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X_poly_test = polyFeatures(Xtest, p);
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X_poly_test = bsxfun(@minus, X_poly_test, mu);
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X_poly_test = bsxfun(@rdivide, X_poly_test, sigma);
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X_poly_test = [ones(size(X_poly_test, 1), 1), X_poly_test]; % Add Ones
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% Map X_poly_val and normalize (using mu and sigma)
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X_poly_val = polyFeatures(Xval, p);
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X_poly_val = bsxfun(@minus, X_poly_val, mu);
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X_poly_val = bsxfun(@rdivide, X_poly_val, sigma);
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X_poly_val = [ones(size(X_poly_val, 1), 1), X_poly_val]; % Add Ones
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fprintf('Normalized Training Example 1:\n');
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fprintf(' %f \n', X_poly(1, :));
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fprintf('\nProgram paused. Press enter to continue.\n');
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pause;
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%% =========== Part 7: Learning Curve for Polynomial Regression =============
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% Now, you will get to experiment with polynomial regression with multiple
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% values of lambda. The code below runs polynomial regression with
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% lambda = 0. You should try running the code with different values of
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% lambda to see how the fit and learning curve change.
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%
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lambda = 0;
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[theta] = trainLinearReg(X_poly, y, lambda);
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% Plot training data and fit
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figure(1);
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plot(X, y, 'rx', 'MarkerSize', 10, 'LineWidth', 1.5);
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plotFit(min(X), max(X), mu, sigma, theta, p);
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xlabel('Change in water level (x)');
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ylabel('Water flowing out of the dam (y)');
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title (sprintf('Polynomial Regression Fit (lambda = %f)', lambda));
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figure(2);
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[error_train, error_val] = ...
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learningCurve(X_poly, y, X_poly_val, yval, lambda);
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plot(1:m, error_train, 1:m, error_val);
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title(sprintf('Polynomial Regression Learning Curve (lambda = %f)', lambda));
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xlabel('Number of training examples')
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ylabel('Error')
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axis([0 13 0 100])
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legend('Train', 'Cross Validation')
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fprintf('Polynomial Regression (lambda = %f)\n\n', lambda);
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fprintf('# Training Examples\tTrain Error\tCross Validation Error\n');
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for i = 1:m
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fprintf(' \t%d\t\t%f\t%f\n', i, error_train(i), error_val(i));
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end
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fprintf('Program paused. Press enter to continue.\n');
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pause;
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%% =========== Part 8: Validation for Selecting Lambda =============
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% You will now implement validationCurve to test various values of
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% lambda on a validation set. You will then use this to select the
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% "best" lambda value.
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%
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[lambda_vec, error_train, error_val] = ...
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validationCurve(X_poly, y, X_poly_val, yval);
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close all;
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plot(lambda_vec, error_train, lambda_vec, error_val);
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legend('Train', 'Cross Validation');
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xlabel('lambda');
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ylabel('Error');
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fprintf('lambda\t\tTrain Error\tValidation Error\n');
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for i = 1:length(lambda_vec)
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fprintf(' %f\t%f\t%f\n', ...
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lambda_vec(i), error_train(i), error_val(i));
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end
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fprintf('Program paused. Press enter to continue.\n');
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pause;

‎week6/ex5/ex5data1.mat

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‎week6/ex5/featureNormalize.m

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function [X_norm, mu, sigma] = featureNormalize(X)
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%FEATURENORMALIZE Normalizes the features in X
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% FEATURENORMALIZE(X) returns a normalized version of X where
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% the mean value of each feature is 0 and the standard deviation
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% is 1. This is often a good preprocessing step to do when
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% working with learning algorithms.
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mu = mean(X);
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X_norm = bsxfun(@minus, X, mu);
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sigma = std(X_norm);
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X_norm = bsxfun(@rdivide, X_norm, sigma);
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end

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