Geometry of Diversity and Determinantal Point Processes ...

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Scale • ~35,000 articles per six month time period
Scale • ~35,000 articles per six month time period • About 10 360 possible sets <strong>of</strong> threads • D = 36,356-dimensional diversity features
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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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Page 15 and 16:
Page 17 and 18:
Accuracy of Wrist Localization 90 8
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The Catch • Problem: inference ex
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Page 23 and 24:
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}
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Choose elementary DPP P J PHASE ONE
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Sampling algorithm Choose elementar
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Consequences • Phase one determin
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What if we need exactly k diverse i
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k-DPPs • Simple idea: condition D
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k-DPP ∑ P ∝ λ n J⊆{1,...,N}
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∑ P ∝ λ n J⊆{1,...,N} P J
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k-DPP sampling • Solution: recurs
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Quality features • Dubbed the “
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Quality features 2. Pizza Hut has r
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Quality features Mean similarity 2.
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Diversity features • φ fixed to
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Diversity features • φ fixed to
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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
Page 158 and 159: Pose accuracy Overall F Arms F 1 1
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
Page 166 and 167: iraq iraqi killed baghdad arab mari
Page 168 and 169: hotel kitchen casa inches post shad
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
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