Geometry of Diversity and Determinantal Point Processes ...

More documents

Recommendations

Info

Scale • ~35,000 articles per six month time period • About 10 360 possible sets <strong>of</strong> threads • D = 36,356-dimensional diversity features • Naively, each second-order message is 200 TB • Using r<strong>and</strong>om projections to approximate volumes We show need only log(# articles) projections
Results: Human summaries & Turk ratings System k-means DTM k-SDPP Rouge1 16.5 14.7 17.2 Rouge2 0.69 0.75 0.89 Rouge-SU4 3.76 3.44 3.98 Coherence 2.73 3.19 3.31
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
Page 7 and 8:
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 13 and 14:
Page 15 and 16:
Page 17 and 18:
Accuracy of Wrist Localization 90 8
Page 19 and 20:
The Catch • Problem: inference ex
Page 21 and 22:
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
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 and 78:
Quality vs. diversity • Intuitive
Page 79 and 80:
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
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 170 and 171: 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
show all

Geometry of Diversity and Determinantal Point Processes ...

You also want an ePaper? Increase the reach of your titles

Delete template?

Save as template?