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Andrew Ng机器学习week9(Anomaly Detection and Recommender Systems)编程习题
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 = 1/m * sum(X);
sigma2 = 1/m * sum((X - repmat(mu, m, 1)).^2);% =============================================================endselectThreshold.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 predictionspredictions = (pval < epsilon);fp = sum((predictions == 1) & (yval == 0));fn = sum((predictions == 0) & (yval == 1));tp = sum((predictions == 1) & (yval == 1));prec = tp / (tp + fp);rec = tp / (tp + fn);F1 = 2 * prec * rec / (prec + rec);% =============================================================if F1 > bestF1bestF1 = F1;bestEpsilon = epsilon;end
endend
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
%J = (1/2).*sum(sum(((X*Theta').*R-Y.*R).^2))+(lambda./2.*sum(sum(Theta.^2)))+(lambda./2.*sum(sum(X.^2)));
% Only predict rating X*Theta' if user has rated (i.e. R=1)X_grad = (((X*Theta').*R*Theta-Y.*R*Theta)+lambda.*X);
Theta_grad = ((X'*((X*Theta').*R)-X'*(Y.*R)))'+lambda.*Theta;% Alternative according to exercise handout
%[r,c]=size(R);
%for i=1:r
% idx = find(R(i,:)==1);
% Theta_temp = Theta(idx,:);
% Y_temp = Y(i,idx);
% X_grad(i,:) = (X(i,:)*Theta_temp'-Y_temp)*Theta_temp;
%end% For Theta_grad, similar approach to X_grad% =============================================================grad = [X_grad(:); Theta_grad(:)];end
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