【matlab】stanford线性回归，logistic regression 实验

1、找到衡量误差的函数costFunction

2、拟合参数theta，使costFunction最小。用梯度下降，迭代n次，迭代更新theta，让costFunction减小

3、找到了合适的参数theta，进行预测

一、linear regression

computeCost：

for i=1:m
    h = X(i,:) * theta;
    J = J + (h - y(i))^2;
end
J = J / (2*m);

梯度下降过程，拟合参数theta

for iter = 1:num_iters

    sum = zeros(size(theta,1),1);
    for j = 1:size(theta,1)
        for i = 1:m
            h = X(i,:) * theta;
            sum(j) = sum(j) + (h - y(i))*X(i,j);
        end
        % theta(j) = theta(j) - alpha * sum / m; 
        %go wrong! simultaneously update theta
    end
    
    theta = theta - sum .* alpha ./ m;

    % Save the cost J in every iteration    
    J_history(iter) = computeCostMulti(X, y, theta);

end

二、Logistic Regression

costFunction

function [J, grad] = costFunctionReg(theta, X, y, lambda)
%COSTFUNCTIONREG Compute cost and gradient for logistic regression with regularization
%   J = COSTFUNCTIONREG(theta, X, y, lambda) computes the cost of using
%   theta as the parameter for regularized logistic regression and the
%   gradient of the cost w.r.t. to the parameters. 

% Initialize some useful values
m = length(y); % number of training examples

% You need to return the following variables correctly 
J = 0;
grad = zeros(size(theta));


for i=1:m
    J = J - y(i)*log(h_fun(X(i,:), theta)) - (1-y(i))*log(1-h_fun(X(i,:),theta));
end
J = J / m;
reg = 0;
for j=2:size(theta)
    reg = reg + theta(j)^2;
end
reg = reg * lambda /(2*m);
J = J + reg;

for i=1:m
    grad(1) = grad(1) + (h_fun(X(i,:),theta) - y(i))*X(i,1);
end
grad(1) = grad(1) / m;
for j=2:size(theta)
    for i=1:m
        grad(j) = grad(j) + (h_fun(X(i,:),theta) - y(i)) * X(i,j) + lambda*theta(j)/m;
    end
    grad(j) = grad(j) / m;
end


end

参数拟合

% Initialize fitting parameters
initial_theta = zeros(size(X, 2), 1);

% Set regularization parameter lambda to 1 (you should vary this)
lambda = 0;

% Set Options
options = optimset('GradObj', 'on', 'MaxIter', 400);

% Optimize
[theta, J, exit_flag] = ...
    fminunc(@(t)(costFunctionReg(t, X, y, lambda)), initial_theta, options);