Andrew Ng机器学习week6(Regularized Linear Regression and Bias/Variance)编程习题

linearRegCostFunction.m

function [J, grad] = linearRegCostFunction(X, y, theta, lambda)%LINEARREGCOSTFUNCTION Compute cost and gradient for regularized linear %regression with multiple variables%   [J, grad] = LINEARREGCOSTFUNCTION(X, y, theta, lambda) computes the %   cost of using theta as the parameter for linear regression to fit the %   data points in X and y. Returns the cost in J and the gradient in grad% Initialize some useful valuesm = 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 and gradient of regularized linear %               regression for a particular choice of theta.%%               You should set J to the cost and grad to the gradient.%predictions = X * theta;sqrErrors = (predictions - y) .^ 2;theta_r = [0;theta(2:end)];J = 1 / (2 * m) * sum(sqrErrors) + lambda / (2 * m) * sum(theta_r .^ 2);grad = X' * (predictions - y) / m + theta_r * lambda / m;% =========================================================================grad = grad(:);end

learningCurve.m

function [error_train, error_val] = ...    learningCurve(X, y, Xval, yval, lambda)%LEARNINGCURVE Generates the train and cross validation set errors needed %to plot a learning curve%   [error_train, error_val] = ...%       LEARNINGCURVE(X, y, Xval, yval, lambda) returns the train and%       cross validation set errors for a learning curve. In particular, %       it returns two vectors of the same length - error_train and %       error_val. Then, error_train(i) contains the training error for%       i examples (and similarly for error_val(i)).%%   In this function, you will compute the train and test errors for%   dataset sizes from 1 up to m. In practice, when working with larger%   datasets, you might want to do this in larger intervals.%% Number of training examplesm = size(X, 1);% You need to return these values correctlyerror_train = zeros(m, 1);error_val   = zeros(m, 1);% ====================== YOUR CODE HERE ======================% Instructions: Fill in this function to return training errors in %               error_train and the cross validation errors in error_val. %               i.e., error_train(i) and %               error_val(i) should give you the errors%               obtained after training on i examples.%% Note: You should evaluate the training error on the first i training%       examples (i.e., X(1:i, :) and y(1:i)).%%       For the cross-validation error, you should instead evaluate on%       the _entire_ cross validation set (Xval and yval).%% Note: If you are using your cost function (linearRegCostFunction)%       to compute the training and cross validation error, you should %       call the function with the lambda argument set to 0. %       Do note that you will still need to use lambda when running%       the training to obtain the theta parameters.%% Hint: You can loop over the examples with the following:%%       for i = 1:m%           % Compute train/cross validation errors using training examples %           % X(1:i, :) and y(1:i), storing the result in %           % error_train(i) and error_val(i)%           ....%           %       end%% ---------------------- Sample Solution ----------------------for i = 1:m  theta = trainLinearReg([ones(i,1), X(1:i,:)], y(1:i), lambda);  error_train(i) = linearRegCostFunction([ones(i,1), X(1:i,:)], y(1:i), theta, 0);  error_val(i) = linearRegCostFunction([ones(size(Xval,1),1), Xval], yval, theta, 0);end% -------------------------------------------------------------% =========================================================================end

polyFeatures.m

function [X_poly] = polyFeatures(X, p)%POLYFEATURES Maps X (1D vector) into the p-th power%   [X_poly] = POLYFEATURES(X, p) takes a data matrix X (size m x 1) and%   maps each example into its polynomial features where%   X_poly(i, :) = [X(i) X(i).^2 X(i).^3 ...  X(i).^p];%% You need to return the following variables correctly.X_poly = zeros(numel(X), p);% ====================== YOUR CODE HERE ======================% Instructions: Given a vector X, return a matrix X_poly where the p-th %               column of X contains the values of X to the p-th power.%% for i = 1:p  X_poly(:,i) = X .^ i;end% =========================================================================end

validationCurve.m

function [lambda_vec, error_train, error_val] = ...    validationCurve(X, y, Xval, yval)%VALIDATIONCURVE Generate the train and validation errors needed to%plot a validation curve that we can use to select lambda%   [lambda_vec, error_train, error_val] = ...%       VALIDATIONCURVE(X, y, Xval, yval) returns the train%       and validation errors (in error_train, error_val)%       for different values of lambda. You are given the training set (X,%       y) and validation set (Xval, yval).%% Selected values of lambda (you should not change this)lambda_vec = [0 0.001 0.003 0.01 0.03 0.1 0.3 1 3 10]';% You need to return these variables correctly.error_train = zeros(length(lambda_vec), 1);error_val = zeros(length(lambda_vec), 1);% ====================== YOUR CODE HERE ======================% Instructions: Fill in this function to return training errors in %               error_train and the validation errors in error_val. The %               vector lambda_vec contains the different lambda parameters %               to use for each calculation of the errors, i.e, %               error_train(i), and error_val(i) should give %               you the errors obtained after training with %               lambda = lambda_vec(i)%% Note: You can loop over lambda_vec with the following:%%       for i = 1:length(lambda_vec)%           lambda = lambda_vec(i);%           % Compute train / val errors when training linear %           % regression with regularization parameter lambda%           % You should store the result in error_train(i)%           % and error_val(i)%           ....%           %       end%%for i = 1:length(lambda_vec)  theta = trainLinearReg(X, y, lambda_vec(i));  error_train(i) = linearRegCostFunction(X, y, theta, 0);  error_val(i) = linearRegCostFunction(Xval, yval, theta, 0);end% =========================================================================end