必做：
[*] warmUpExercise.m - Simple example function in Octave/MATLAB
[*] plotData.m - Function to display the dataset
[*] computeCost.m - Function to compute the cost of linear regression
[*] gradientDescent.m - Function to run gradient descent
1.warmUpExercise.m
A = eye();
2.plotData.m
plot(x, y, 'rx', 'MarkerSize', ); % Plot the data
ylabel('Profit in $10,000s'); % Set the y-axis label
xlabel('Population of City in 10,000s'); % Set the x-axis label
3.computeCost.m
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 = ; % ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta
% You should set J to the cost. H = X*theta-y;
J = (1/(2*m))*sum(H.*H); % ========================================================================= end
公式：
注意matlab中 .* 的用法。
4.gradientDescent.m
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, ); for iter = :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. H = X*theta-y;
theta(1)=theta(1)-alpha*(1/m)*sum(H.*X(:,1));
theta(2)=theta(2)-alpha*(1/m)*sum(H.*X(:,2)); % ============================================================ % Save the cost J in every iteration
J_history(iter) = computeCost(X, y, theta); end end
单变量梯度下降
对函数J(θ)求偏导
即 H.*X(:,1)
θi向着梯度最小的方向减少,alpha为步长。
theta(i)=theta(i)-alpha*(1/m)*sum(H.*X(:,i));