吴恩达机器学习-ex1-Linear Regression

知识点：

这个博主总结的很好，还强调了重点，对于回顾和写代码都有不少帮助，十分感谢：Linear Regression 知识点总结

 

作业：

这个过程中加深了对知识点的理解，代码出错想不通的时候，自己又重新推导了一遍公式，看了一些别人的博客，发现不少博客总结的很棒，比如开头的那篇。

主要是通过梯度下降法，找到使代价函数 J 最小的参数值。代码主要部分添加了注释，方便日后回顾。

• 单变量线性回归：

 导入数据：

%% ======================= Part 2: Plotting =======================
fprintf('Plotting Data ...\n')
data = load('ex1data1.txt');
X = data(:, 1); y = data(:, 2);
m = length(y);      % number of training examples

% Plot Data
% Note: You have to complete the code in plotData.m 
plotData(X, y);

fprintf('Program paused. Press enter to continue.\n');
pause;

其中，plotData函数如下：（作图）

function plotData(x, y)
%PLOTDATA Plots the data points x and y into a new figure 
%   PLOTDATA(x,y) plots the data points and gives the figure axes labels of
%   population and profit.

figure; % open a new figure window

% ====================== YOUR CODE HERE ======================
% Instructions: Plot the training data into a figure using the 
%               "figure" and "plot" commands. Set the axes labels using
%               the "xlabel" and "ylabel" commands. Assume the 
%               population and revenue data have been passed in
%               as the x and y arguments of this function.
%
% Hint: You can use the 'rx' option with plot to have the markers
%       appear as red crosses. Furthermore, you can make the
%       markers larger by using plot(..., 'rx', 'MarkerSize', 10);

plot(x, y, 'rx', 'MarkerSize', 10);
xlabel('Population of city in 10,000s');
ylabel('Profit in $10,000s');

% ============================================================

end

运行效果：

 代价函数和梯度下降：

%% =================== Part 3: Cost and Gradient descent ===================

X = [ones(m, 1), data(:,1)];         % Add a column of ones to x      
%为每个数据集 增加特征一个点 X0 == 1，使得参数theta(0)也和矩阵X有关。此时有n+1个特征和n个变量（theta）

theta = zeros(2, 1); % initialize fitting parameters    theta(0)和theta(1)


% Some gradient descent settings
iterations = 1500;                %指定迭代次数
alpha = 0.01;                        %学习率

%%==========================测试不同theta，损失函数的计算结果不同======================

fprintf('\nTesting the cost function ...\n')
% compute and display initial cost                theta给初始值的时候，损失函数的值
J = computeCost(X, y, theta);
fprintf('With theta = [0 ; 0]\nCost computed = %f\n', J);
fprintf('Expected cost value (approx) 32.07\n');

% further testing of the cost function            更改theta，损失函数的值
J = computeCost(X, y, [-1 ; 2]);
fprintf('\nWith theta = [-1 ; 2]\nCost computed = %f\n', J);
fprintf('Expected cost value (approx) 54.24\n');

fprintf('Program paused. Press enter to continue.\n');
pause;


%%============================梯度下降函数============================

fprintf('\nRunning Gradient Descent ...\n')
% run gradient descent
theta = gradientDescent(X, y, theta, alpha, iterations);     
%其中调用了损失函数computeCost

%%============================显示找到最佳的参数theta========================

% print theta