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annotate toolboxes/distance_learning/mlr/separationOracle/separationOraclePrecAtK.m @ 0:e9a9cd732c1e tip

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first hg version after svn
author wolffd
date Tue, 10 Feb 2015 15:05:51 +0000
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wolffd@0 1 function [Y, Loss] = separationOraclePrecAtK(q, D, pos, neg, k)
wolffd@0 2 %
wolffd@0 3 % [Y,Loss] = separationOraclePrecAtK(q, D, pos, neg, k)
wolffd@0 4 %
wolffd@0 5 % q = index of the query point
wolffd@0 6 % D = the current distance matrix
wolffd@0 7 % pos = indices of relevant results for q
wolffd@0 8 % neg = indices of irrelevant results for q
wolffd@0 9 % k = length of the list to consider
wolffd@0 10 %
wolffd@0 11 % Y is a permutation 1:n corresponding to the maximally
wolffd@0 12 % violated constraint
wolffd@0 13 %
wolffd@0 14 % Loss is the loss for Y, in this case, 1-Prec@k(Y)
wolffd@0 15
wolffd@0 16
wolffd@0 17 % First, sort the documents in descending order of W'Phi(q,x)
wolffd@0 18 % Phi = - (X(q) - X(x)) * (X(q) - X(x))'
wolffd@0 19
wolffd@0 20 % Sort the positive documents
wolffd@0 21 ScorePos = - D(pos,q);
wolffd@0 22 [Vpos, Ipos] = sort(full(ScorePos'), 'descend');
wolffd@0 23 Ipos = pos(Ipos);
wolffd@0 24
wolffd@0 25 % Sort the negative documents
wolffd@0 26 ScoreNeg = -D(neg,q);
wolffd@0 27 [Vneg, Ineg] = sort(full(ScoreNeg'), 'descend');
wolffd@0 28 Ineg = neg(Ineg);
wolffd@0 29
wolffd@0 30 % Now, solve the DP for the interleaving
wolffd@0 31
wolffd@0 32 numPos = length(pos);
wolffd@0 33 numNeg = length(neg);
wolffd@0 34 n = numPos + numNeg;
wolffd@0 35
wolffd@0 36 cVpos = cumsum(Vpos);
wolffd@0 37 cVneg = cumsum(Vneg);
wolffd@0 38
wolffd@0 39
wolffd@0 40 % If we don't have enough positive (or negative) examples, scale k down
wolffd@0 41 k = min([k, numPos, numNeg]);
wolffd@0 42
wolffd@0 43 % Algorithm:
wolffd@0 44 % For each precision score in 0, 1/k, 2/k, ... 1
wolffd@0 45 % Calculate maximum discriminant score for that precision level
wolffd@0 46 Precision = (0:(1/k):1)';
wolffd@0 47 Discriminant = zeros(k+1, 1);
wolffd@0 48 NegsBefore = zeros(numPos, k+1);
wolffd@0 49
wolffd@0 50 % For 0 precision, all positives go after the first k negatives
wolffd@0 51
wolffd@0 52 NegsBefore(:,1) = k + binarysearch(Vpos, Vneg(k+1:end));
wolffd@0 53
wolffd@0 54 Discriminant(1) = Vpos * (numNeg - 2 * NegsBefore(:,1)) + numPos * cVneg(end) ...
wolffd@0 55 - 2 * sum(cVneg(NegsBefore((NegsBefore(:,1) > 0),1)));
wolffd@0 56
wolffd@0 57
wolffd@0 58
wolffd@0 59 % For precision (a-1)/k, swap the (a-1)'th positive doc
wolffd@0 60 % into the top (k-a) negative docs
wolffd@0 61
wolffd@0 62 for a = 2:(k+1)
wolffd@0 63 NegsBefore(:,a) = NegsBefore(:,a-1);
wolffd@0 64
wolffd@0 65 % We have a-1 positives, and k - (a-1) negatives
wolffd@0 66 NegsBefore(a-1, a) = binarysearch(Vpos(a-1), Vneg(1:(k-a+1)));
wolffd@0 67
wolffd@0 68 % There were NegsBefore(a-1,a-1) negatives before (a-1)
wolffd@0 69 % Now there are NegsBefore(a,a-1)
wolffd@0 70 Discriminant(a) = Discriminant(a-1) ...
wolffd@0 71 + 2 * (NegsBefore(a-1,a-1) - NegsBefore(a-1,a)) * Vpos(a-1);
wolffd@0 72
wolffd@0 73 if NegsBefore(a-1,a-1) > 0
wolffd@0 74 Discriminant(a) = Discriminant(a) + 2 * cVneg(NegsBefore(a-1,a-1));
wolffd@0 75 end
wolffd@0 76 if NegsBefore(a-1,a) > 0
wolffd@0 77 Discriminant(a) = Discriminant(a) - 2 * cVneg(NegsBefore(a-1,a));
wolffd@0 78 end
wolffd@0 79 end
wolffd@0 80
wolffd@0 81 % Normalize discriminant scores
wolffd@0 82 Discriminant = Discriminant / (numPos * numNeg);
wolffd@0 83 [s, x] = max(Discriminant - Precision);
wolffd@0 84
wolffd@0 85 % Now we know that there are x-1 relevant docs in the max ranking
wolffd@0 86 % Construct Y from NegsBefore(x,:)
wolffd@0 87
wolffd@0 88 Y = nan * ones(n,1);
wolffd@0 89 Y((1:numPos)' + NegsBefore(:,x)) = Ipos;
wolffd@0 90 Y(isnan(Y)) = Ineg;
wolffd@0 91
wolffd@0 92 % Compute loss for this list
wolffd@0 93 Loss = 1 - Precision(x);
wolffd@0 94 end
wolffd@0 95