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initial import week 5

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1 parent 5b0309f commit 591e29e684a1aaa57377e9cde6a1a18be6c2e5ae @schneems committed Nov 14, 2011
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+%% 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;
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+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
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