2.X 编程作业 with One Variable(基础成绩部分)

Warm-up Exercise 10/10

点击查看【bilibili】

function A = warmUpExercise()
%WARMUPEXERCISE Example function in octave
%   A = WARMUPEXERCISE() is an example function that returns the 5x5 identity matrix
A = [];
% ============= YOUR CODE HERE ==============
% Instructions: Return the 5x5 identity matrix 
%               In octave, we return values by defining which variables
%               represent the return values (at the top of the file)
%               and then set them accordingly. 
A = eye(5);
% ===========================================
end

随后在命令行中输入submit()，根据提示输入Email和Token即可提交！

Computing Cost(for One Variable) 40/40

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以下加入到plotData.m中，完成plotData()函数

plot(x, y, 'rx', 'MarkerSize', 10); % 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

以下在命令行中输入

data = load('ex1data1.txt');% 读取训练集
X = data(:,1);
y = data(:,2);
plotData(X,y);                % 绘制训练集的图像
m = length(X);                % m就是训练集的size
X = [ones(m,1), data(:,1)];    % 给训练集增加一列1对应θ0
theta = zeros(2,1);            % 2 * 1 注意，已经定义了列向量θ，不用再转置
iterations = 1500;            % 迭代次数
alpha = 0.01;                % 学习速率

以下加入到computeCost.m中，完成computeCost()函数

h = X * theta;
J = 1 / (2 * m) * sum((h - y) .^ 2);

X——————————————m*2 matrix——————第一列全是1(x{0})第二列是x{1}

theta———————————2*1 matrix——————两个参数\theta{1},\theta{2}

h = X * theta————-m*1 matrix——————第i行对应h(x^{(i)})

sum((h - y) .^ 2)—-a scalar value——-求出各行(h(x^{(i)}) - y{(i)}){2}再相加

最后，得到J是一个标量，代表预测值和实际值之间的误差

测试并提交

computeCost(X,y,[-1;2])    % 54.2425
submit()

Gradient Descent (for One Variable) 50/50

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本次程序中可以作如下简化计算

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以下加入到gradientDescent.m中

theta = theta - alpha / m * (X' * (X * theta - y));

测试并提交

theta = gradientDescent(X, y, theta, alpha, iterations);
hold on;
plot(X(:,2), X * theta, '-')
legend('Training data', 'Linear regression')
submit()

到此为止，编程作业含成绩部分已完成（100/100）

下面是关于J(\theta_{0},\theta{1})的可视化

Feature normalization 0/0