Making the Right Moves: Guiding α-Expansion using Local Primal-Dual Gaps
1
Making the Right Moves: Guiding α-Expansion using Local Primal- Dual Gaps Dhruv Batra (TTI Chicago), Pushmeet Kohli (Microsoft Research Cambridge) MAP Inference in MRFs Expansion Algorithm Primal-Dual Interpretation of Expansion Local Primal-Dual Gap (LPDG) Algorithm Results More Results Graph Structure MAP Inference Variables Node / Edge Potentials Energy / Cost Function Current Soln 2-Label Problem + GC New Soln Loop over α α-Expansion α Traditional Loop: LPDG Loop: Adaptive Re-ordering of Labels leads to Massive Speed-ups! LP Relaxations [Schlesinger ‘76; Wainwright et al. ’05; Komodakis et al. ‘05] Primal LP Dual LP Normalization Marginalization Lagrangian Multipliers Local Primal-Dual Gap Interpretation Proposed Label Scores LPDG-crisp LPDG-deficit LPDG-tradeoff LPDG Full Sweep LPDG Partial Sweep Ordering of Expanded Labels Move Number Classical Expansions Our Guided Expansions 1 Airplane Car 2 Bicycle Person 3 Bird Motorbike 4 Boat Train 5 Bottle Airplane 1 Airplane Sheep 2 Bicycle Dog 3 Bird Bird 4 Boat Cow 5 Bottle Cat 1 Airplane Airplane 2 Bicycle Bird 3 Bird Dog 4 Boat TV 5 Bottle Train LPDG correlated with decrease in energy! Cuts Runtime by ~50% Partial Sweeps Effect of Initialization
description
Making the Right Moves: Guiding α-Expansion using Local Primal-Dual Gaps Dhruv Batra (TTI Chicago), Pushmeet Kohli (Microsoft Research Cambridge). Primal-Dual Interpretation of Expansion. Algorithm. More Results. MAP Inference in MRFs. LPDG Full Sweep. LP Relaxations. - PowerPoint PPT Presentation
Transcript of Making the Right Moves: Guiding α-Expansion using Local Primal-Dual Gaps
Making the Right Moves: Guiding α-Expansion using Local Primal-Dual GapsDhruv Batra (TTI Chicago), Pushmeet Kohli (Microsoft Research Cambridge)
MAP Inference in MRFs
Expansion Algorithm
Primal-Dual Interpretation of Expansion
Local Primal-Dual Gap (LPDG)
Algorithm
Results
More Results
Graph Structure
MAP Inference
Variables Node / Edge Potentials
Energy / Cost Function
Current Soln 2-Label Problem + GC New Soln
Loop over α
α-Expansionα
Traditional Loop:
LPDG Loop:
Adaptive Re-ordering of Labels leads to Massive Speed-ups!
LP Relaxations [Schlesinger ‘76; Wainwright et al. ’05; Komodakis et al. ‘05]
Primal LP Dual LP
NormalizationNormalization
MarginalizationMarginalization
LagrangianLagrangian
MultipliersMultipliers
Local Primal-Dual Gap
Interpretation
Proposed Label Scores
LPDG-crisp
LPDG-deficit
LPDG-tradeoff
LPDG Full Sweep
LPDG Partial Sweep
Ordering of Expanded Labels
Move Number
Classical Expansions
Our Guided Expansions
1 Airplane Car
2 Bicycle Person
3 Bird Motorbike
4 Boat Train
5 Bottle Airplane
1 Airplane Sheep
2 Bicycle Dog
3 Bird Bird
4 Boat Cow
5 Bottle Cat
1 Airplane Airplane
2 Bicycle Bird
3 Bird Dog
4 Boat TV
5 Bottle Train
LPDG correlated with decrease in energy!
Cuts Runtime by ~50%
Partial Sweeps Effect of Initialization
![arXiv:1008.5107v1 [astro-ph.CO] 30 Aug 2010 · blind ALFALFA catalog are new HI detections and many are altogether new redshifts, indicating that the conven- tional wisdom guiding](https://static.fdocument.org/doc/165x107/5c67dbce09d3f2ff5a8c9179/arxiv10085107v1-astro-phco-30-aug-2010-blind-alfalfa-catalog-are-new-hi.jpg)
![THE IRREDUCIBLE COMPONENTS OF THE PRIMAL COHOMOLOGY …eizadi/papers/Simplicity... · 2020. 2. 10. · Mori and Mukai [MM83] showed that is dominant. The ppav (A;) with singular theta](https://static.fdocument.org/doc/165x107/613120501ecc51586944897d/the-irreducible-components-of-the-primal-cohomology-eizadipaperssimplicity.jpg)
