Geometry of Diversity and Determinantal Point Processes ...

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k-DPP sampling • Need new PHASE ONE to pick |J| = k • No longer independent: • Once we pick one, can only pick k-1 more
k-DPP sampling • Solution: recursion on elementary symmetric polynomials: e N k = ∑ J∈{1,...,N} |J|=k ∏ n∈J λ n • Runtime <strong>of</strong> new PHASE ONE is O(Nk) • PHASE TWO is unchanged
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Geometry of Diversity and Determina
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Eichner & Ferrari BMVC09
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Human pose estimation: what’s so
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Human pose estimation: what’s so
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Local signal is weak = true right e
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Graphical Models vs. Tyranny of Sma
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Accuracy of Wrist Localization 90 8
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The Catch • Problem: inference ex
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A distribution over sets of poses?
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Image search: “jaguar” Relevanc
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Summarization
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Graphical models?
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Graphical models? 0/1 sentence i
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Graphical models?
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Determinantal point processes (DPPs
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Determinantal point processes Quali
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Discrete point process • N items
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Independent point process • Each
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Feature function g on items in Y
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Feature function g on items in Y
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L = L ij = g(i) ⊤ g(j)
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Determinantal point process L = P(Y
Page 53 and 54: Determinantal point process • Giv
Page 55 and 56: Determinantal point process • Giv
Page 57 and 58: DPP inference • Normalization: P(
Page 59 and 60: DPP inference • Marginals: P(A Y
Page 61 and 62: P(A Y ) = det(K A )
Page 63 and 64: P(A Y ) = det(K A ) P(i Y ) = det(K
Page 65 and 66: Point process samples Independent D
Page 67 and 68: L =
Page 69 and 70: L = L ij = q(i) (i) (j)q(j)
Page 71 and 72: L = L ij = q(i) (i) (j)q(j) q(i)
Page 73 and 74: q(i) (i) Vol 2 P({i, j}) q(j) (j)
Page 75 and 76: q(i) (i) Vol 2 P({i, j}) q(j) (j) I
Page 77 and 78: Quality vs. diversity • Intuitive
Page 79 and 80: Quality vs. diversity • Intuitive
Page 81 and 82: Eigendecomposition N∑ L = λ n v
Page 83 and 84: 1 2 3 4 5 6 v 4 v 6 v 1 v 2 v 3 v 5
Page 85 and 86: Elementary DPP v 1 v 2 v 3 v 5 P {2
Page 87 and 88: Key insight Every DPP is a “facto
Page 89 and 90: ∑ P ∝ 1 2 3 4 5 6 J⊆{1,...,N}
Page 91 and 92: Choose elementary DPP P J PHASE ONE
Page 93 and 94: Sampling algorithm Choose elementar
Page 95 and 96: Consequences • Phase one determin
Page 97 and 98: What if we need exactly k diverse i
Page 99 and 100: k-DPPs • Simple idea: condition D
Page 101 and 102: k-DPP ∑ P ∝ λ n J⊆{1,...,N}
Page 103: ∑ P ∝ λ n J⊆{1,...,N} P J
Page 107 and 108: Quality features • Dubbed the “
Page 109 and 110: Quality features 2. Pizza Hut has r
Page 111 and 112: Quality features Mean similarity 2.
Page 113 and 114: Diversity features • φ fixed to
Page 115 and 116: Diversity features • φ fixed to
Page 117 and 118: System ROUGE-1F ROUGE-1R R-SU4F Beg
Page 119 and 120: System ROUGE-1F ROUGE-1R R-SU4F Beg
Page 121 and 122: ? ? ? ?
Page 123 and 124: Y Y Y I""""""""really""""""""love""
Page 125 and 126: Structured DPPs • Exponentially m
Page 127 and 128: 1. Factorization • Quality scores
Page 129 and 130: 1. Factorization • Quality scores
Page 131 and 132: Quality
Page 133 and 134: Quality x x
Page 135 and 136: Diversity
Page 137 and 138: Diversity Low diversity
Page 139 and 140: Diversity Low diversity High divers
Page 141 and 142: 2. Dual representation Φ Q Q Φ
Page 143 and 144: 2. Dual representation L = C = 2 N
Page 145 and 146: 2. Dual representation L = C = 2 N
Page 147 and 148: 3. Second-order message passing
Page 149 and 150: 3. Second-order message passing •
Page 151: Multiple-pose estimation
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Pose accuracy Overall F Arms F 1 1
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News happens Apr 3: Instagram reach
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News happens Apr 9: Facebook buys I
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News happens
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iraq iraqi killed baghdad arab mari
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hotel kitchen casa inches post shad
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Scale • ~35,000 articles per six
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Scale • ~35,000 articles per six
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Results: Human summaries & Turk rat
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Results: Human summaries & Turk rat
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k-SDPPs vs. Tyranny of Small Decisi
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• DPPs capture global, negative c
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