Week2 Programming Assignment: Linear Regression

这是我Andrew NG的Week2的第一次编程作业，这其中有一些我所学到的东西，以博客的形式记录，随笔。

收获：

  • 矩阵运算可以替代循环。

内容包括

  1. univariate下
    • univariate任务下一个demo：
    • 数据集绘制为图像
    • 损失函数计算
    • 梯度下降
  2. multivariate任务下
    • 损失函数代码，梯度下降代码与上述一致（实用矩阵和向量化，从一开始就兼容了多变量的情况）
    • normal equation替代梯度下降计算参数　　
  3. 提交结果
  4. 分数
 1 function A = warmUpExercise()
 2 %WARMUPEXERCISE Example function in octave
 3 %   A = WARMUPEXERCISE() is an example function that returns the 5x5 identity matrix
 4 
 5 A = [];
 6 % ============= YOUR CODE HERE ==============
 7 % Instructions: Return the 5x5 identity matrix 
 8 %               In octave, we return values by defining which variables
 9 %               represent the return values (at the top of the file)
10 %               and then set them accordingly. 
11 A=eye(5);
12 % ===========================================
13 end

 

运行效果

 

 1 function plotData(x, y)
 2 %PLOTDATA Plots the data points x and y into a new figure 
 3 %   PLOTDATA(x,y) plots the data points and gives the figure axes labels of
 4 %   population and profit.
 5 
 6 figure; % open a new figure window
 7 
 8 % ====================== YOUR CODE HERE ======================
 9 % Instructions: Plot the training data into a figure using the 
10 %               "figure" and "plot" commands. Set the axes labels using
11 %               the "xlabel" and "ylabel" commands. Assume the 
12 %               population and revenue data have been passed in
13 %               as the x and y arguments of this function.
14 %
15 % Hint: You can use the 'rx' option with plot to have the markers
16 %       appear as red crosses. Furthermore, you can make the
17 %       markers larger by using plot(..., 'rx', 'MarkerSize', 10);
18 
19 
20 plot(x, y, 'rx', 'MarkerSize', 10); % Plot the data
21 ylabel('Profit in $10,000s'); % Set the y?axis label
22 xlabel('Population of City in 10,000s'); % Set the x?axis label
23 % ============================================================
24 
25 end

运行效果

 

 

 

 1 function J = computeCost(X, y, theta)
 2 %COMPUTECOST Compute cost for linear regression
 3 %   J = COMPUTECOST(X, y, theta) computes the cost of using theta as the
 4 %   parameter for linear regression to fit the data points in X and y
 5 
 6 % Initialize some useful values
 7 m = length(y); % number of training examples
 8 
 9 % You need to return the following variables correctly 
10 J = 0;
11 
12 % ====================== YOUR CODE HERE ======================
13 % Instructions: Compute the cost of a particular choice of theta
14 %               You should set J to the cost.
15 h_theta = X*theta;
16 sum_vector =ones(1,m);
17 J=sum_vector*((h_theta-y).^2)/(2*m);
18 
19 
20 
21 % =========================================================================
22 
23 end

运行效果

 

 1 function [theta, J_history] = gradientDescent(X, y, theta, alpha, num_iters)
 2 %GRADIENTDESCENT Performs gradient descent to learn theta
 3 %   theta = GRADIENTDESCENT(X, y, theta, alpha, num_iters) updates theta by 
 4 %   taking num_iters gradient steps with learning rate alpha
 5 
 6 % Initialize some useful values
 7 m = length(y); % number of training examples
 8 J_history = zeros(num_iters, 1);
 9 
10 for iter = 1:num_iters
11 
12     % ====================== YOUR CODE HERE ======================
13     % Instructions: Perform a single gradient step on the parameter vector
14     %               theta. 
15     %
16     % Hint: While debugging, it can be useful to print out the values
17     %       of the cost function (computeCost) and gradient here.
18     %
19     h_theta = X*theta;
20     errors_vector=h_theta-y;
21     theta_change = (X'*errors_vector)*alpha/(m);
22     theta=theta-theta_change;
23     % ============================================================
24     
25     % Save the cost J in every iteration    
26     J_history(iter) = computeCost(X, y, theta);
27 
28 end
29 
30 end

运行效果

 

 

 

 进行数据拟合并预测

 

 损失函数三维立体图像

等高线

 

 1 function [theta] = normalEqn(X, y)
 2 %NORMALEQN Computes the closed-form solution to linear regression 
 3 %   NORMALEQN(X,y) computes the closed-form solution to linear 
 4 %   regression using the normal equations.
 5 
 6 theta = zeros(size(X, 2), 1);
 7 
 8 % ====================== YOUR CODE HERE ======================
 9 % Instructions: Complete the code to compute the closed form solution
10 %               to linear regression and put the result in theta.
11 %
12 
13 % ---------------------- Sample Solution ----------------------
14 
15 
16 theta=pinv(X'*X)*X'*y;
17 
18 % -------------------------------------------------------------
19 
20 
21 % ============================================================
22 
23 end

 

 

computeCostMulti和gradientDescentMulti与上面univariate一致

 

最终结果

 1 >> submit
 2 == Submitting solutions | Linear Regression with Multiple Variables...
 3 Use token from last successful submission (yuhang.tao.email@gmail.com)? (Y/n): Y
 4 == 
 5 ==                                   Part Name |     Score | Feedback
 6 ==                                   --------- |     ----- | --------
 7 ==                            Warm-up Exercise |  10 /  10 | Nice work!
 8 ==           Computing Cost (for One Variable) |  40 /  40 | Nice work!
 9 ==         Gradient Descent (for One Variable) |  50 /  50 | Nice work!
10 ==                       Feature Normalization |   0 /   0 | Nice work!
11 ==     Computing Cost (for Multiple Variables) |   0 /   0 | Nice work!
12 ==   Gradient Descent (for Multiple Variables) |   0 /   0 | Nice work!
13 ==                            Normal Equations |   0 /   0 | Nice work!
14 ==                                   --------------------------------
15 ==                                             | 100 / 100 | 
16 ==

Coursera上不对选做题加分

posted @ 2020-01-06 13:22  TimeIsChoice  阅读(333)  评论(0)  编辑  收藏  举报