Exercises – ML Study Notes

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.
%

XwithoutMean = zeros(m,n);
expandmu = zeros(m,n);
mu = (sum(X) * 1/m)’;
expandmu = repmat(mu’, m , 1);
sigma2 = 1/m * sum( (X-expandmu).^2 );
% =============================================================
end

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
cvPredictions = pval < epsilon;

truePositives = sum( (cvPredictions == 1) & ( yval == 1));
falsePositives = sum( (cvPredictions == 1) & (yval == 0));
trueNegatives = sum( (cvPredictions == 0) & (yval == 0));
falseNegatives = sum( (cvPredictions == 0) & (yval == 1));
prec = truePositives / (truePositives + falsePositives);
rec = truePositives / (truePositives + falseNegatives);
F1 = 2 * prec * rec / (prec + rec);
% =============================================================

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

end

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
%
OtX = (X * Theta’) – Y;
J_temp = (OtX).^2;
J = sum(J_temp(R==1)) * 1/2;