Andrew Ng机器学习week2(Linear Regression)编程习题

Andrew Ng机器学习week2(Linear Regression)编程习题

1、Warm-up Exercise

function A = warmUpExercise()%WARMUPEXERCISE Example function in octave%   A = WARMUPEXERCISE() is an example function that returns the 5x5 identity matrixA = [];% ============= YOUR CODE HERE ==============% Instructions: Return the 5x5 identity matrix %               In octave, we return values by defining which variables%               represent the return values (at the top of the file)%               and then set them accordingly. A = eye(5);% ===========================================end

2、Computing Cost（for One Variable)

function J = computeCost(X, y, theta)%COMPUTECOST Compute cost for linear regression%   J = COMPUTECOST(X, y, theta) computes the cost of using theta as the%   parameter for linear regression to fit the data points in X and y% Initialize some useful valuesm = length(y); % number of training examples% You need to return the following variables correctly J = 0;% ====================== YOUR CODE HERE ======================% Instructions: Compute the cost of a particular choice of theta%               You should set J to the cost.J = sum((X * theta - y) .^ 2) / (2 * m);% =========================================================================end

3、Gradient Descent（for One Variable）

function [theta, J_history] = gradientDescent(X, y, theta, alpha, num_iters)%GRADIENTDESCENT Performs gradient descent to learn theta%   theta = GRADIENTDESCENT(X, y, theta, alpha, num_iters) updates theta by %   taking num_iters gradient steps with learning rate alpha% Initialize some useful valuesm = length(y); % number of training examplesJ_history = zeros(num_iters, 1);for iter = 1:num_iters    % ====================== YOUR CODE HERE ======================    % Instructions: Perform a single gradient step on the parameter vector    %               theta.     %    % Hint: While debugging, it can be useful to print out the values    %       of the cost function (computeCost) and gradient here.    %    theta = theta - alpha * (X' * (X * theta - y)) / m;    % ============================================================    % Save the cost J in every iteration        J_history(iter) = computeCost(X, y, theta);endforend

4、Feature Normalization

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.% You need to set these values correctlyX_norm = X;mu = zeros(1, size(X, 2));sigma = zeros(1, size(X, 2));% ====================== YOUR CODE HERE ======================% Instructions: First, for each feature dimension, compute the mean%               of the feature and subtract it from the dataset,%               storing the mean value in mu. Next, compute the %               standard deviation of each feature and divide%               each feature by it's standard deviation, storing%               the standard deviation in sigma. %%               Note that X is a matrix where each column is a %               feature and each row is an example. You need %               to perform the normalization separately for %               each feature. %% Hint: You might find the 'mean' and 'std' functions useful.%       len = length(X);mu = mean(X);sigma = std(X);X_norm = (X - ones(len, 1) * mu) ./ (ones(len, 1) * sigma);% ============================================================end

5、Computing Cost（for Multiple Variables）

function J = computeCostMulti(X, y, theta)%COMPUTECOSTMULTI Compute cost for linear regression with multiple variables%   J = COMPUTECOSTMULTI(X, y, theta) computes the cost of using theta as the%   parameter for linear regression to fit the data points in X and y% Initialize some useful valuesm = length(y); % number of training examples% You need to return the following variables correctly J = 0;% ====================== YOUR CODE HERE ======================% Instructions: Compute the cost of a particular choice of theta%               You should set J to the cost.J = sum((X * theta - y) .^ 2) / (2 * m);% =========================================================================end

6、Gradient Descent （for Multiple Variables）

function [theta, J_history] = gradientDescentMulti(X, y, theta, alpha, num_iters)%GRADIENTDESCENTMULTI Performs gradient descent to learn theta%   theta = GRADIENTDESCENTMULTI(x, y, theta, alpha, num_iters) updates theta by%   taking num_iters gradient steps with learning rate alpha% Initialize some useful valuesm = length(y); % number of training examplesJ_history = zeros(num_iters, 1);for iter = 1:num_iters    % ====================== YOUR CODE HERE ======================    % Instructions: Perform a single gradient step on the parameter vector    %               theta.     %    % Hint: While debugging, it can be useful to print out the values    %       of the cost function (computeCostMulti) and gradient here.    %    theta = theta - alpha * (X' * (X * theta - y)) / m;    % ============================================================    % Save the cost J in every iteration        J_history(iter) = computeCostMulti(X, y, theta);endend

7、Normal Equations

function [theta] = normalEqn(X, y)%NORMALEQN Computes the closed-form solution to linear regression %   NORMALEQN(X,y) computes the closed-form solution to linear %   regression using the normal equations.theta = zeros(size(X, 2), 1);% ====================== YOUR CODE HERE ======================% Instructions: Complete the code to compute the closed form solution%               to linear regression and put the result in theta.%theta = pinv(X' * X) * X' * y;% ---------------------- Sample Solution ----------------------% -------------------------------------------------------------% ============================================================end