Geometry of Diversity and Determinantal Point Processes ...

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iraq iraqi killed baghdad arab marines deaths forces social tax security democrats rove accounts owen nominees senate democrats judicial filibusters israel palestinian iraqi israeli gaza abbas baghdad pope vatican church parkinson Jan 08 Jan 28 Feb 17 Mar 09 Mar 29 Apr 18 May 08 May 28 Jun 17 Feb 24: Parkinson’s Disease Increases Risks to Pope Feb 26: Pope’s Health Raises Questions About His Ability to Lead Mar 13: Pope Returns Home After 18 Days at Hospital Apr 01: Pope’s Condition Worsens as World Prepares for End of Papacy Apr 02: Pope, Though Gravely Ill, Utters Thanks for Prayers Apr 18: Europeans Fast Falling Away from Church Apr 20: In Developing World, Choice [of Pope] Met with Skepticism May 18: Pope Sends Message with Choice of Name
Dynamic topic model hotel kitchen casa inches post shade monica closet mets rangers dodgers delgado martinez astacio angels mientkiewicz social security accounts retirement benefits tax workers 401 payroll palestinian israel baghdad palestinians sunni korea gaza israeli cancer heart breast women disease aspirin risk study Jan 08 Jan 28 Feb 17 Mar 09 Mar 29 Apr 18 May 08 May 28 Jun 17 [Blei & Lafferty, 2006]
Page 1 and 2:
Geometry of Diversity and Determina
Page 3 and 4:
Eichner & Ferrari BMVC09
Page 5 and 6:
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
Page 29 and 30:
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
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
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 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
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