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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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Graphical Models vs. Tyranny of Sma
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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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Graphical Models vs. Tyranny of Sma
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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
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Determinantal point process • Giv
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Determinantal point process • Giv
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DPP inference • Normalization: P(
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DPP inference • Marginals: P(A Y
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P(A Y ) = det(K A )
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P(A Y ) = det(K A ) P(i Y ) = det(K
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Point process samples Independent D
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L =
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L = L ij = q(i) (i) (j)q(j)
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L = L ij = q(i) (i) (j)q(j) q(i)
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q(i) (i) Vol 2 P({i, j}) q(j) (j)
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q(i) (i) Vol 2 P({i, j}) q(j) (j) I
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Quality vs. diversity • Intuitive
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Quality vs. diversity • Intuitive
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Eigendecomposition N∑ L = λ n v
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1 2 3 4 5 6 v 4 v 6 v 1 v 2 v 3 v 5
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Elementary DPP v 1 v 2 v 3 v 5 P {2
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Key insight Every DPP is a “facto
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∑ P ∝ 1 2 3 4 5 6 J⊆{1,...,N}
- Page 91 and 92: Choose elementary DPP P J PHASE ONE
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- 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 and 104: ∑ P ∝ λ n J⊆{1,...,N} P J
- Page 105 and 106: k-DPP sampling • Solution: recurs
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- Page 109 and 110: Quality features 2. Pizza Hut has r
- Page 111 and 112: Quality features Mean similarity 2.
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- 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: 2. Dual representation Φ Q Q Φ
- 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 •
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- Page 160 and 161: News happens Apr 3: Instagram reach
- Page 162 and 163: News happens Apr 9: Facebook buys I
- Page 164 and 165: News happens
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- Page 168 and 169: hotel kitchen casa inches post shad
- Page 170 and 171: Scale • ~35,000 articles per six
- Page 172 and 173: Scale • ~35,000 articles per six
- Page 174 and 175: Results: Human summaries & Turk rat
- Page 176 and 177: Results: Human summaries & Turk rat
- Page 178 and 179: k-SDPPs vs. Tyranny of Small Decisi
- Page 180 and 181: • DPPs capture global, negative c