机器学习笔记----线性规划--练习作业

http://openclassroom.stanford.edu/MainFolder/DocumentPage.php?course=MachineLearning&doc=exercises/ex2/ex2.html

练习1 的作业：

我使用的 Octave ，

Understanding $J(\theta)$

We'd like to understand better what gradient descent has done, and visualize the relationship between the parameters $\theta \in {\mathbb R}^2$ and $J(\theta)$ . In this problem, we'll plot $J(\theta)$ as a 3D surface plot. (When applying learning algorithms, we don't usually try to plot $J(\theta)$ since usually $\theta \in {\mathbb R}^n$ is very high-dimensional so that we don't have any simple way to plot or visualize $J(\theta)$ . But because the example here uses a very low dimensional $\theta \in {\mathbb R}^2$ , we'll plot $J(\theta)$ to gain more intuition about linear regression.) Recall that the formula for $J(\theta)$ is

$\begin{displaymath} J(\theta)=\frac{1}{2m}\sum_{i=1}^{m}\left(h_{\theta}(x^{(i)})-y^{(i)}\right)^{2} \nonumber \end{displaymath}$

程序如下：

x = load('C:/Users/samsung/Desktop/ex2Data/ex2x.dat');
y = load('C:/Users/samsung/Desktop/ex2Data/ex2y.dat');
m=  length(y);
x = [ones(m,1),x];
J_vals = zeros(100,100);
theta0_vals = linspace(-3,3,100);
theta1_vals = linspace(-1,1,100);
for i =1:length(theta0_vals)
for j = 1:length(theta1_vals)
t=[theta0_vals(i);theta1_vals(j)];
J_vals(i,j) = (x*t - y)'*(x*t-y)/(2*m);
end
end
J_vals = J_vals';
figure;
surf(theta0_vals, theta1_vals, J_vals);
 
xlabel('\theta_0'); ylabel('\theta_1');

练习 2 ：

x = load('C:/Users/samsung/Desktop/ex2Data/ex2x.dat');
y = load('C:/Users/samsung/Desktop/ex2Data/ex2y.dat');

figure % open a new figure window
plot(x, y, 'o');
ylabel('Height in meters');
xlabel('Age in years');
theta = [0;0];
alfa = 0.07;
m  =  length(y);
x = [ones(m,1),x];
 ##temp  = x(:,2)' *(x*theta -y)/m * alfa;
#for i = 1:1500
#theta =theta -  x' *(x*theta -y)/ m * alfa;
#end   ##z这里的循环使用了 梯度下降迭代法，求出 theta  
theta = inv(x'*x)*x'*y;   ##是同一公式，计算速度快

hold on % Plot new data without clearing old plot
plot(x(:,2), x*theta, '-')
 % remember that x is now a matrix with 2 columns
 % and the second column contains the time info
legend('Training data', 'Linear regression')

机器学习笔记----线性规划--练习作业

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