Coursera: Machine Learning (Week 9) [Assignment Solution] - Andrew NG

 Recommended Courses:

1. Coursera: Machine Learning
2. Google Data Analytics Professional Certificate.

 1.Anomaly detection and recommender systems 

Don't just copy paste the code for the sake of completion. 

Make sure you understand the code first.

In this exercise, you will implement the anomaly detection algorithm and apply it to detect failing servers on a network. In the second part, you will use collaborative filtering to build a recommender system for movies. Before starting on the programming exercise, we strongly recommend watching the video lectures and completing the review questions for the associated topics.

It consist of the following files:

• ex8.m - Octave/MATLAB script for first part of exercise
• ex8 cofi.m - Octave/MATLAB script for second part of exercise
• ex8data1.mat - First example Dataset for anomaly detection
• ex8data2.mat - Second example Dataset for anomaly detection
• ex8 movies.mat - Movie Review Dataset
• ex8 movieParams.mat - Parameters provided for debugging
• multivariateGaussian.m - Computes the probability density function for a Gaussian distribution
• visualizeFit.m - 2D plot of a Gaussian distribution and a dataset
• checkCostFunction.m - Gradient checking for collaborative filtering
• computeNumericalGradient.m - Numerically compute gradients
• fmincg.m - Function minimization routine (similar to fminunc)
• loadMovieList.m - Loads the list of movies into a cell-array
• movie ids.txt - List of movies
• normalizeRatings.m - Mean normalization for collaborative filtering
• submit.m - Submission script that sends your solutions to our servers
• [*] estimateGaussian.m - Estimate the parameters of a Gaussian distribution with a diagonal covariance matrix
• [*] selectThreshold.m - Find a threshold for anomaly detection
• [*] cofiCostFunc.m - Implement the cost function for collaborative filtering
• 
  

* indicates files you will need to complete

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-mu').^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);     % m x 1 
      
      tp = sum((cvPredictions == 1) & (yval == 1)); % m x 1
      fp = sum((cvPredictions == 1) & (yval == 0)); % m x 1
      fn = sum((cvPredictions == 0) & (yval == 1)); % m x 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 :

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));            % Nm x n
  Theta_grad = zeros(size(Theta));    % Nu x n
  
  % ====================== 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
  %
  
  %% %%%%% WORKING: Without Regularization %%%%%%%%%%
  Error = (X*Theta') - Y;
  
  J = (1/2)*sum(sum(Error.^2.*R));
  
  X_grad = (Error.*R)*Theta;   % Nm x n
  Theta_grad = (Error.*R)'*X;  % Nu x n
  
  %% %%%%% WORKING: With Regularization
  Reg_term_theta = (lambda/2)*sum(sum(Theta.^2));
  Reg_term_x = (lambda/2)*sum(sum(X.^2));
  
  J = J + Reg_term_theta + Reg_term_x;
  
  X_grad = X_grad + lambda*X;             % Nm x n
  Theta_grad = Theta_grad + lambda*Theta; % Nu x n
  
  % =============================================================
  
  grad = [X_grad(:); Theta_grad(:)];

end

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