Geometry of Diversity and Determinantal Point Processes ...

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Quality vs. diversity • Intuitive and natural tradeoff • Log-linear quality model: q(i) =exp(θ ⊤ f(i)) • Optimize by maximum likelihood • Can find global optimum in O(N 3 )
Quality vs. diversity • Intuitive and natural tradeoff • Log-linear quality model: q(i) =exp(θ ⊤ f(i)) • Optimize by maximum likelihood • Can find global optimum in O(N 3 ) • Don’t yet know how to learn diversity efficiently (a natural parametrization is NP-hard)
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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:
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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
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
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: 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 and 104: ∑ P ∝ λ n J⊆{1,...,N} P J
Page 105 and 106: k-DPP sampling • Solution: recurs
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
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1. Factorization • Quality scores
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Quality
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Quality x x
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Diversity
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Diversity Low diversity
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Diversity Low diversity High divers
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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
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3. Second-order message passing
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3. Second-order message passing •
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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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