Download - Tighter Relaxations for MAP-MRF Inference: A Local Primal-Dual Gap based Separation Algorithm
Tighter Relaxations for MAP-MRF Inference: A Local Primal-Dual Gap based Separation AlgorithmDhruv Batra (TTI-Chicago), Sebastian Nowozin (Microsoft Research Cambridge), Pushmeet Kohli (Microsoft Research Cambridge)
LP-Relaxations for MAP Inference in MRFs Tighter LPs and Cluster Pursuit
Graph Structure
MAP Inference LP Relaxations
[Wainwright et al. ‘08, Sontag et al. ‘07]
Reparameterization
Cluster Pursuit
What’s a good cluster score?
[Sontag et al. UAI ’08] Lower-bound on improvement in Dual
[Werner CVPR ’08] Try each cluster and check improvement [Komodakis et al. ECCV ‘08]
PROPOSED: A surrogate score -- Efficiently computable -- Correlated with increase in Dual -- Motivated by LP duality Complimentary Slackness
Local Primal-Dual Gap
Complimentary Slackness Conditions
Local Primal-Dual Gap
Properties -- Positive -- Sums to current Primal-Dual Gap -- Slackness property
Results
Markov Random Fields
Variables Factors / Cliques
Energy / Cost Function
Pairwise MRF
Primal LP Dual LP
NormalizationNormalization
MarginalizationMarginalization
LagrangianLagrangian
MultipliersMultipliers
Controls Tightness of LPControls Tightness of LP
Original Factor Incoming Messages Outgoing Messages
Primal Dual
Original Image Noisy Blurry Image Pairwise LP Soln Triplet LP Soln
Dual vs. Iterations Dual vs. Time Primal-Dual Gap vs. Time
-- Synthetic experiments; Stereo; Image De-convolulation