【Coursera-Machine Learning】自用1

目录

前言

一、进度

二、基本内容

1.ML定义

2.Supervised/Unsupervised Learning定义

3.Hypothesis Function

4.Cost Function

 5.Hypothesis Function 和 Cost Function的关系

6.Gradient Descent

7.Feature Scaling

8.Normal Equation

 9.作业

总结

前言

大学没干过什么事，最近被推荐了coursera，尝试开发一下自己在Machine Learning上的兴趣。

咱就不鸽一次，看看能不能学完

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一、进度

第一周、第二周（36%）

二、基本内容 1.ML定义

关于E、T、P三者的关系 

2.Supervised/Unsupervised Learning定义

1.Classification（Supervised）

2.Regression（Supervised）

3.Clustering（Unsupervised）

个人理解区别在于有无训练集，能预判给出想要的结果。以该题为例：

3.Hypothesis Function

就是估计函数，前两课学习的都是简单的预估函数，例如

4.Cost Function

核心公式，用于计算损失函数，是关于的函数

 5.Hypothesis Function 和 Cost Function的关系

以图为例，假设=0，则一个取定值的hypothesis function会对应到cost function图像的一点。可以看到对于图中的例子，取1时损失最小

 

6.Gradient Descent

 两个核心公式，一个是定义式，一个是表达式

一般使用后面已经求完偏导的式子来迭代。

基本思路：对于所有初值给定的θ，进行迭代，每迭代一次，每个θ都会进行修改，修改的过程是根据损失函数决定的。有点像之前学过的Simulated Annealing的意思

为学习率。不可以过大或者过小（过大就会反向求解，过小效率过低）特别注意的是，在类似二次函数的图像中通过gradient descent，刚开始的时候斜率比较大，所以求偏导的值会比较大，那么θ就会更快的靠近最优解，所以不需要实时变化。

再进行迭代的时候要注意先给出求完偏导后的该部分的值矩阵：

 然后再将所有θ值同时更新（后面的代码作业就在这里出现了问题）

7.Feature Scaling

 我们可以修改所有的样本值，使得计算的结果放在等高线图里更为平均

8.Normal Equation

 先有一个我觉得极其优美的公式，第一期看到的时候真的受到了震撼：

 

 然后的核心式子就是以下式子：

 以该样本为例：

注意第一列需要手动加上一列1，然后对于给出的样本矩阵和结果向量，就能用Normal Equation进行求解了。Angrew提到有可能XTX是不可逆的可能性，那就要注意样本值会不会有线性相关的存在，比如一个x是圆的半径，另一个x是圆的面积。这就可能导致XTX不可逆。

至于什么时候用Gradient Descent，什么时候用Normal Equation，当样本矩阵的维数过大的时候，就不适合用Normal Equation，计算时间过长。但是Gradient Descent什么时候都可以用。 

 9.作业

值得注意的就是第六块的同时更新θ值部分。有一道题我之前写的是：

可以很明显看到，每一次的迭代我的θ减去的值都在改变。而事实上allparameter向量的值是不能改编的。

参考他人资料后改的写法是：

 直接用矩阵进行运算，而我的思路还停留在数组:(

最后备份一下作业：

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

end

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

end

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.
%
mu=mean(X);
sigma=std(X)
X_norm=(X-mu)./sigma;
% ============================================================

end

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

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

end

end

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

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

end

end

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

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

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总结

别鸽，继续 : )

Andrew Ng赛高