Daniel@0: function [Y, Loss] = separationOraclePrecAtK(q, D, pos, neg, k)
Daniel@0: %
Daniel@0: %   [Y,Loss]  = separationOraclePrecAtK(q, D, pos, neg, k)
Daniel@0: %
Daniel@0: %   q   = index of the query point
Daniel@0: %   D   = the current distance matrix
Daniel@0: %   pos = indices of relevant results for q
Daniel@0: %   neg = indices of irrelevant results for q
Daniel@0: %   k   = length of the list to consider
Daniel@0: %
Daniel@0: %   Y is a permutation 1:n corresponding to the maximally
Daniel@0: %   violated constraint
Daniel@0: %
Daniel@0: %   Loss is the loss for Y, in this case, 1-Prec@k(Y)
Daniel@0: 
Daniel@0: 
Daniel@0:     % First, sort the documents in descending order of W'Phi(q,x)
Daniel@0:     % Phi = - (X(q) - X(x)) * (X(q) - X(x))'
Daniel@0:     
Daniel@0:     % Sort the positive documents
Daniel@0:     ScorePos        = - D(pos,q);
Daniel@0:     [Vpos, Ipos]    = sort(full(ScorePos'), 'descend');
Daniel@0:     Ipos            = pos(Ipos);
Daniel@0:     
Daniel@0:     % Sort the negative documents
Daniel@0:     ScoreNeg        = -D(neg,q);
Daniel@0:     [Vneg, Ineg]    = sort(full(ScoreNeg'), 'descend');
Daniel@0:     Ineg            = neg(Ineg);
Daniel@0: 
Daniel@0:     % Now, solve the DP for the interleaving
Daniel@0: 
Daniel@0:     numPos  = length(pos);
Daniel@0:     numNeg  = length(neg);
Daniel@0:     n       = numPos + numNeg;
Daniel@0: 
Daniel@0:     cVpos           = cumsum(Vpos);
Daniel@0:     cVneg           = cumsum(Vneg);
Daniel@0: 
Daniel@0: 
Daniel@0:     % If we don't have enough positive (or negative) examples, scale k down
Daniel@0:     k = min([k, numPos, numNeg]);
Daniel@0: 
Daniel@0:     % Algorithm:
Daniel@0:     %   For each precision score in 0, 1/k, 2/k, ... 1
Daniel@0:     %       Calculate maximum discriminant score for that precision level
Daniel@0:     Precision       = (0:(1/k):1)';
Daniel@0:     Discriminant    = zeros(k+1, 1);
Daniel@0:     NegsBefore      = zeros(numPos, k+1);
Daniel@0: 
Daniel@0:     % For 0 precision, all positives go after the first k negatives
Daniel@0: 
Daniel@0:     NegsBefore(:,1) = k + binarysearch(Vpos, Vneg(k+1:end));
Daniel@0: 
Daniel@0:     Discriminant(1) = Vpos * (numNeg - 2 * NegsBefore(:,1)) + numPos * cVneg(end) ...
Daniel@0:                     - 2 * sum(cVneg(NegsBefore((NegsBefore(:,1) > 0),1)));
Daniel@0: 
Daniel@0: 
Daniel@0: 
Daniel@0:     % For precision (a-1)/k, swap the (a-1)'th positive doc
Daniel@0:     %   into the top (k-a) negative docs
Daniel@0: 
Daniel@0:     for a = 2:(k+1)
Daniel@0:         NegsBefore(:,a) = NegsBefore(:,a-1);
Daniel@0: 
Daniel@0:         % We have a-1 positives, and k - (a-1) negatives
Daniel@0:         NegsBefore(a-1, a) = binarysearch(Vpos(a-1), Vneg(1:(k-a+1)));
Daniel@0: 
Daniel@0:         % There were NegsBefore(a-1,a-1) negatives before (a-1)
Daniel@0:         % Now there are NegsBefore(a,a-1)
Daniel@0:         Discriminant(a) = Discriminant(a-1) ...
Daniel@0:                         + 2 * (NegsBefore(a-1,a-1) - NegsBefore(a-1,a)) * Vpos(a-1);
Daniel@0: 
Daniel@0:         if NegsBefore(a-1,a-1) > 0
Daniel@0:             Discriminant(a) = Discriminant(a) + 2 * cVneg(NegsBefore(a-1,a-1));
Daniel@0:         end
Daniel@0:         if NegsBefore(a-1,a) > 0
Daniel@0:             Discriminant(a) = Discriminant(a) - 2 * cVneg(NegsBefore(a-1,a));
Daniel@0:         end
Daniel@0:     end
Daniel@0: 
Daniel@0:     % Normalize discriminant scores
Daniel@0:     Discriminant    = Discriminant / (numPos * numNeg);
Daniel@0:     [s, x]          = max(Discriminant - Precision);
Daniel@0: 
Daniel@0:     % Now we know that there are x-1 relevant docs in the max ranking
Daniel@0:     % Construct Y from NegsBefore(x,:)
Daniel@0: 
Daniel@0:     Y = nan * ones(n,1);
Daniel@0:     Y((1:numPos)' + NegsBefore(:,x)) = Ipos;
Daniel@0:     Y(isnan(Y))                     = Ineg;
Daniel@0: 
Daniel@0:     % Compute loss for this list
Daniel@0:     Loss        = 1 - Precision(x);
Daniel@0: end
Daniel@0: