Coursera machine learning week 9 assignment answers – Andrew Ng

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

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

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