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机器学习(coursera 斯坦福)第九周编程作业

Preface

本文是机器学习第九周部分课程内容,以及编程作业答案记录,完整题目以及代码见github


estimateGaussian.m

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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)

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


end

selectThreshold.m

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


end

cofiCostFunc.m

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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));

X_grad = ((X * Theta') .* R - Y .* R) * Theta + lambda .* X;
Theta_grad = ((X * Theta') .* R - Y .* R)' * X + lambda .* Theta;


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

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

end

参考 

Coursera—machine learning(Andrew Ng)第九周编程作业
matlab中repmat函数的用法

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