Geometry of Diversity and Determinantal Point Processes ...

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Human pose estimation: what’s so hard? intrinsic'scale' varia,ons' ligh%ng' varia%on' pose%% varia*on%
Human pose estimation: what’s so hard? intrinsic'scale' varia,ons' ligh%ng' varia%on' pose%% varia*on% foreshortening+
Page 1 and 2: Geometry of Diversity and Determina
Page 3 and 4: Eichner & Ferrari BMVC09
Page 5: Human pose estimation: what’s so
Page 9 and 10: Local signal is weak = true right e
Page 11 and 12: Graphical Models vs. Tyranny of Sma
Page 17 and 18: Accuracy of Wrist Localization 90 8
Page 19 and 20: The Catch • Problem: inference ex
Page 23 and 24: A distribution over sets of poses?
Page 25 and 26: Image search: “jaguar” Relevanc
Page 27 and 28: Summarization
Page 29 and 30: Graphical models?
Page 31 and 32: Graphical models? 0/1 sentence i
Page 33 and 34: Graphical models?
Page 35 and 36: Determinantal point processes (DPPs
Page 37 and 38: Determinantal point processes Quali
Page 39 and 40: Discrete point process • N items
Page 41 and 42: Independent point process • Each
Page 43 and 44: Feature function g on items in Y
Page 45 and 46: Feature function g on items in Y
Page 49 and 50: L = L ij = g(i) ⊤ g(j)
Page 51 and 52: 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
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Point process samples Independent D
Page 67 and 68:
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
Page 79 and 80:
Quality vs. diversity • Intuitive
Page 81 and 82:
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
Page 95 and 96:
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
Page 101 and 102:
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
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System ROUGE-1F ROUGE-1R R-SU4F Beg
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? ? ? ?
Page 123 and 124:
Y Y Y I""""""""really""""""""love""
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Structured DPPs • Exponentially m
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1. Factorization • Quality scores
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1. Factorization • Quality scores
Page 131 and 132:
Quality
Page 133 and 134:
Quality x x
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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
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2. Dual representation L = C = 2 N
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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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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 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
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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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