1 / 14

Mean field approximation for CRF inference

Mean field approximation for CRF inference. CRF Inference Problem. CRF over variables: CRF distribution: MAP inference: MPM (maximum posterior marginals ) inference:. Other notation. Unnormalized distribution Variational distribution Expectation Entropy. Variational Inference.

sileas
Download Presentation

Mean field approximation for CRF inference

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Mean field approximation for CRF inference

  2. CRF Inference Problem • CRF over variables: • CRF distribution: • MAP inference: • MPM (maximum posterior marginals) inference:

  3. Other notation • Unnormalized distribution • Variational distribution • Expectation • Entropy

  4. Variational Inference • Inference => minimize KL-divergence • General Objective Function

  5. Mean field approximation • Variational distribution => product of independent marginals: • Expectations: • Entropy:

  6. Mean field objective • Objective

  7. Local optimality conditions • Lagrangian • Setting derivatives to 0 gives conditions for local optimality

  8. Coordinate ascent • Sequential coordinate ascent • Initialize Q_i’s to uniform distribution • For 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 algorithm • As above, but perform updates in step 2 for all Q_i’s in parrallel (i.e. Generating Q^1, Q^2...)

  9. Comparison with belief propagation • Objective • Factored energy functional • Local polytope

  10. Comparison with belief propagation • Message updates: • Extracting beliefs (after convergence):

  11. Comparison with belief propagation • - = => Bethe free energy for pairwise graphs • Bethe cluster graphs: General: Pairwise:

  12. Mean field updates • Updates in dense CRF (Krahenbuhl NIPS ’11) • Evaluate using filtering • =

  13. Higher-order potentials • Pattern-based potentials • P^n-Potts potentials

  14. Higher-order potentials • Co-occurrence potentials • L(X) = set of labels present in X • {Y_1,...Y_L} = set of binary latent variables

More Related