Coursera机器学习-Week 2-编程作业:Linear Regression

记得上一次学这门课程就是卡到了这里才做不下去的，因为那时候看着英文文档就头大~~~

这次折腾了好久终于搞定了这些个作业，想想就扎心，英文成了我最大的瓶颈！因为文档看得不是特别懂，光如何提交都搞了好久才搞定。

这次作业都是完善一些函数，本身不难，如果你看懂了视频以及英文文档的话~~~

1 warmUpExercise.m

将给定代码插入即可，就是完善一个生成 5∗5 单位矩阵。

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

2.1 plotData.m

这个部分是给定一个数据集进行二维平面的画图，设置一下画图的符号及横纵轴的标记（暂且这么叫吧）。

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

2.2.3 computeCost.m

计算一下误差。

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 = 0;

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta
%               You should set J to the cost.

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

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

end

2.2.4 gradientDescent.m

梯度下降算法，对 θ0 与 θ1 进行更新。

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, 1);

for iter = 1: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.
    %

    delta = (1 / m) * (X' * (X * theta - y));
    theta = theta - alpha .* delta;

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

    % Save the cost J in every iteration    
    J_history(iter) = computeCost(X, y, theta);

end

end

3.1 featureNormalize.m

由上述单个变量的线性回归变为多个变量的线性回归，对房屋的价格进行预测，这里需要计算标准差。

function [X_norm, mu, sigma] = featureNormalize(X)
%FEATURENORMALIZE Normalizes the features in X 
%   FEATURENORMALIZE(X) returns a normalized version of X where
%   the mean value of each feature is 0 and the standard deviation
%   is 1. This is often a good preprocessing step to do when
%   working with learning algorithms.

% You need to set these values correctly
X_norm = X;
mu = zeros(1, size(X, 2));
sigma = zeros(1, size(X, 2));

% ====================== YOUR CODE HERE ======================
% Instructions: First, for each feature dimension, compute the mean
%               of the feature and subtract it from the dataset,
%               storing the mean value in mu. Next, compute the 
%               standard deviation of each feature and divide
%               each feature by it's standard deviation, storing
%               the standard deviation in sigma. 
%
%               Note that X is a matrix where each column is a 
%               feature and each row is an example. You need 
%               to perform the normalization separately for 
%               each feature. 
%
% Hint: You might find the 'mean' and 'std' functions useful.
%       

for i = 1 : size(X, 2)

    mu(1, i) = mean(X(:, i));
    sigma(1, i) = std(X(:, i)) + eps;
    X_norm(:, i) = (X_norm(:, i) - mu(1, i)) ./ sigma(1, i);

end

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

end

3.2 computeCostMulti.m

可以直接拿单变量线性回归的相关代码用，因为道理都是一样的。

function J = computeCostMulti(X, y, theta)
%COMPUTECOSTMULTI Compute cost for linear regression with multiple variables
%   J = COMPUTECOSTMULTI(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 = 0;

% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost of a particular choice of theta
%               You should set J to the cost.

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

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

end

3.2 gradientDescentMulti.m

同上。

function [theta, J_history] = gradientDescentMulti(X, y, theta, alpha, num_iters)
%GRADIENTDESCENTMULTI Performs gradient descent to learn theta
%   theta = GRADIENTDESCENTMULTI(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, 1);

for iter = 1: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 (computeCostMulti) and gradient here.
    %

    delta = (1 / m) * (X' * (X * theta - y));
    theta = theta - alpha .* delta;

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

    % Save the cost J in every iteration    
    J_history(iter) = computeCostMulti(X, y, theta);

end

end

3.3 normalEqn.m

利用正规方程计算 θ=(XTX)−1XTy 。

function [theta] = normalEqn(X, y)
%NORMALEQN Computes the closed-form solution to linear regression 
%   NORMALEQN(X,y) computes the closed-form solution to linear 
%   regression using the normal equations.

theta = zeros(size(X, 2), 1);

% ====================== YOUR CODE HERE ======================
% Instructions: Complete the code to compute the closed form solution
%               to linear regression and put the result in theta.
%

% ---------------------- Sample Solution ----------------------

theta = pinv(X' * X) * X' * y;

% -------------------------------------------------------------

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

end

结果

亲测，都可以提交通过检测。