机器学习预测octave代码

    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 values
    m = length(y); % number of training examples
    J_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/m*X'*((X*theta)-y);
    J_history(iter)=computeCost(X,y,theta);//代价函数中间变量J的计算，上面等式计算theta的过程已经算出J的偏导
    
    % ============================================================
    
    % Save the cost J in every iteration    
    
    end

    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 values
    m = 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 = 1/(2*m)*sum(((X*theta)-y).^2);
    
    
    
    % =========================================================================
    
    end

    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 values
    m = length(y); % number of training examples
    J_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/m*X'*((X*theta)-y);
    % ============================================================
    
    % Save the cost J in every iteration    
    J_history(iter) = computeCostMulti(X, y, theta);
    
    end
    
    end

    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 correctly
    X_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.
    %       
    
    mu = mean(X_norm);
    sigma = std(X_norm);
    X_norm(:,1) = (X_norm(:,1)-mu(1))/sigma(1);
    X_norm(:,2) = (X_norm(:,2)-mu(2))/sigma(2);
    
    
    
    
    
    
    
    % ============================================================
    
    end