/
Mean field approximation for CRF inference Mean field approximation for CRF inference

Mean field approximation for CRF inference - PowerPoint Presentation

trish-goza
trish-goza . @trish-goza
Follow
416 views
Uploaded On 2016-05-29

Mean field approximation for CRF inference - PPT Presentation

CRF Inference Problem CRF over variables CRF distribution MAP inference MPM maximum posterior marginals inference Other notation Unnormalized distribution Variational distribution ID: 339894

updates inference field crf inference updates crf field distribution potentials comparison belief propagation objective local variational higher order expectations

Share:

Link:

Embed:

Download Presentation from below link

Download Presentation The PPT/PDF document "Mean field approximation for CRF inferen..." is the property of its rightful owner. Permission is granted to download and print the materials on this web site for personal, non-commercial use only, and to display it on your personal computer provided you do not modify the materials and that you retain all copyright notices contained in the materials. By downloading content from our website, you accept the terms of this agreement.


Presentation Transcript

Slide1

Mean field approximation for CRF inference

Slide2

CRF Inference Problem

CRF over variables:

CRF distribution:

MAP inference:MPM (maximum posterior marginals) inference:Slide3

Other notation

Unnormalized

distribution

Variational distributionExpectationEntropySlide4

Variational Inference

Inference => minimize KL-divergence

General Objective FunctionSlide5

Mean field approximation

Variational

distribution => product of independent

marginals:Expectations:Entropy:Slide6

Mean field objective

ObjectiveSlide7

Local optimality conditions

Lagrangian

Setting derivatives to 0 gives conditions for local optimalitySlide8

Coordinate ascent

Sequential coordinate ascent

Initialize

Q_i’s to uniform distributionFor i = 1...N, update vector Q_i by summing expectations over all cliques involving X_i (while fixing all Q_j

, j!=i)Parallel updates algorithmAs above, but perform updates in step 2 for all

Q_i’s in parrallel (i.e. Generating Q^1, Q^2...)Slide9

Comparison with belief propagation

Objective

Factored energy functional

Local polytope Slide10

Comparison with belief propagation

Message updates:

Extracting beliefs (after convergence):Slide11

Comparison with belief propagation

- = => Bethe free energy for

pairwise

graphsBethe cluster graphs:

General:

Pairwise

:Slide12

Mean field updates

Updates in dense CRF (

Krahenbuhl

NIPS ’11)Evaluate using filtering =Slide13

Higher-order potentials

Pattern-based potentials

P^n

-Potts potentialsSlide14

Higher-order potentials

Co-occurrence potentials

L

(X) = set of labels present in X{Y_1,...Y_L} = set of binary latent variables