markov random fields & conditional random fields
DESCRIPTION
Markov Random Fields & Conditional Random Fields. John Winn MSR Cambridge. Road map. Markov Random Fields What they are Uses in vision/object recognition Advantages Difficulties Conditional Random Fields What they are Further difficulties. 12. 23. X 1. X 2. X 3. 234. X 4. - PowerPoint PPT PresentationTRANSCRIPT
Markov Random Fields & Conditional Random Fields
John WinnMSR Cambridge
Road map
Markov Random Fields What they are Uses in vision/object recognition Advantages Difficulties
Conditional Random Fields What they are Further difficulties
Markov Random Fields
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Examples of use in vision Grid-shaped MRFs for pixel labelling e.g.
segmentation
MRFs (e.g. stars) over part positions for pictorial structures/constellation models.
Advantages Probabilistic model:
Captures uncertainty No ‘irreversible’ decisions Iterative reasoning Principled fusing of different cues
Undirected model Allows ‘non-causal’ relationships (soft constraints)
Efficient algorithms:inference now practical for MRFs with millions variables – can be applied to raw pixels.
Maximum Likelihood Learning
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Sufficient statisticsof data
Expected model sufficient statistics
Difficulty I: Inference
Exact inference intractable except in a few cases e.g. small models
Must resort to approximate methods Loopy belief propagation MCMC sampling Alpha expansion (MAP solution only)
Difficulty II: Learning
Gradient descent – vulnerable to local minima Slow – must perform expensive inference at each
iteration. Can stop inference early…
Contrastive divergence Piecewise training + variants
Need fast + accurate methods
Difficulty III: Large cliques For images, we want to look at patches not pairs of
pixels. Therefore would like to use large cliques. Cost of inference (memory and CPU) typically
exponential in clique size.
Example: Field of Experts, Black + Roth Training: contrastive divergence
over a week on a cluster of 50+ machines Test: Gibbs sampling
very slow?
Other MRF issues…
Local minima when performing inference in high-dimensional latent spaces
MRF models often require making inaccurate independence assumptions about the observations.
Conditional Random Fields
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Examples of use in vision Grid-shaped CRFs for pixel labelling
(e.g. segmentation), using boosted classifiers.
Difficulty IV: CRF Learning
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Expected sufficient statistics given the image
Difficulty V: Scarcity of labels
CRF is a conditional model – needs labels. Labels are expensive + increasingly hard to
define. Labels are also inherently lower dimensional than
the data and hence support learning fewer parameters than generative models.