斯坦福大学(吴恩达) 机器学习课后习题详解 第九周 编程题 异常检测与推荐系统

作业 下载 地址：https://download.csdn.net/download/wwangfabei1989/10326175

1. estimateGaussian.m 

 

function [mu sigma2] = estimateGaussian(X)
%ESTIMATEGAUSSIAN This function estimates the parameters of a 
%Gaussian distribution using the data in X
%   [mu sigma2] = estimateGaussian(X), 
%   The input X is the dataset with each n-dimensional data point in one row
%   The output is an n-dimensional vector mu, the mean of the data set
%   and the variances sigma^2, an n x 1 vector
% 


% Useful variables
[m, n] = size(X);


% You should return these values correctly
mu = zeros(n, 1);
sigma2 = zeros(n, 1);


% ====================== YOUR CODE HERE ======================
% Instructions: Compute the mean of the data and the variances
%               In particular, mu(i) should contain the mean of
%               the data for the i-th feature and sigma2(i)
%               should contain variance of the i-th feature.
%




mu=(mean(X))';


sigma2=(var(X,1))';














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




end

 

2. selectThreshold.m 

function [bestEpsilon bestF1] = selectThreshold(yval, pval)
%SELECTTHRESHOLD Find the best threshold (epsilon) to use for selecting
%outliers
%   [bestEpsilon bestF1] = SELECTTHRESHOLD(yval, pval) finds the best
%   threshold to use for selecting outliers based on the results from a
%   validation set (pval) and the ground truth (yval).
%


bestEpsilon = 0;
bestF1 = 0;
F1 = 0;


stepsize = (max(pval) - min(pval)) / 1000;
for epsilon = min(pval):stepsize:max(pval)
    
    % ====================== YOUR CODE HERE ======================
    % Instructions: Compute the F1 score of choosing epsilon as the
    %               threshold and place the value in F1. The code at the
    %               end of the loop will compare the F1 score for this
    %               choice of epsilon and set it to be the best epsilon if
    %               it is better than the current choice of epsilon.
    %               
    % Note: You can use predictions = (pval < epsilon) to get a binary vector
    %       of 0's and 1's of the outlier predictions
     
     predictions=(pval < epsilon);
     
     tp=sum((predictions==1)&(yval==1));
     
     fp=sum((predictions==1)&(yval==0));
     
     fn=sum((predictions==0)&(yval==1));
     
     prec=tp/(tp+fp);
     rec=tp/(tp+fn);
     F1=2*prec*rec/(prec+rec);    






















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


    if F1 > bestF1
       bestF1 = F1;
       bestEpsilon = epsilon;
    end
end


end

3.cofiCostFunc.m 

function [J, grad] = cofiCostFunc(params, Y, R, num_users, num_movies, ...
                                  num_features, lambda)
%COFICOSTFUNC Collaborative filtering cost function
%   [J, grad] = COFICOSTFUNC(params, Y, R, num_users, num_movies, ...
%   num_features, lambda) returns the cost and gradient for the
%   collaborative filtering problem.
%


% Unfold the U and W matrices from params
X = reshape(params(1:num_movies*num_features), num_movies, num_features);
Theta = reshape(params(num_movies*num_features+1:end), ...
                num_users, num_features);


            
% You need to return the following values correctly
J = 0;
X_grad = zeros(size(X));
Theta_grad = zeros(size(Theta));


% ====================== YOUR CODE HERE ======================
% Instructions: Compute the cost function and gradient for collaborative
%               filtering. Concretely, you should first implement the cost
%               function (without regularization) and make sure it is
%               matches our costs. After that, you should implement the 
%               gradient and use the checkCostFunction routine to check
%               that the gradient is correct. Finally, you should implement
%               regularization.
%
% Notes: X - num_movies  x num_features matrix of movie features
%        Theta - num_users  x num_features matrix of user features
%        Y - num_movies x num_users matrix of user ratings of movies
%        R - num_movies x num_users matrix, where R(i, j) = 1 if the 
%            i-th movie was rated by the j-th user
%
% You should set the following variables correctly:
%
%        X_grad - num_movies x num_features matrix, containing the 
%                 partial derivatives w.r.t. to each element of X
%        Theta_grad - num_users x num_features matrix, containing the 
%                     partial derivatives w.r.t. to each element of Theta
%


temp=X*Theta'-Y;


J=sum((temp.^2)(R==1))/2;


 X_grad=(temp.*R)*Theta;
 Theta_grad=((temp.*R)'*X); 


 J=J+sum((Theta.^2)(:))*lambda/2+sum((X.^2)(:))*lambda/2;
 
 X_grad=X_grad+lambda*X;
 
 Theta_grad=Theta_grad+lambda*Theta;






















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


grad = [X_grad(:); Theta_grad(:)];


end

知乎： https://zhuanlan.zhihu.com/albertwang

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