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Markov Random Fields & Conditional Random FieldsPowerPoint Presentation

Markov Random Fields & Conditional Random Fields

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Markov Random Fields & Conditional Random Fields

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Markov Random Fields & Conditional Random Fields

John WinnMSR Cambridge

- Markov Random Fields
- What they are
- Uses in vision/object recognition
- Advantages
- Difficulties

- Conditional Random Fields
- What they are
- Further difficulties

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- Grid-shaped MRFs for pixel labelling e.g. segmentation

- MRFs (e.g. stars) over part positions for pictorial structures/constellation models.

- 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.

Sufficient statisticsof data

Expected model sufficient statistics

- 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)

- 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

- 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 divergenceover a week on a cluster of 50+ machines
- Test: Gibbs samplingvery slow?

- Local minima when performing inference in high-dimensional latent spaces
- MRF models often require making inaccurate independence assumptions about the observations.

Lafferty et al., 2001

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- Grid-shaped CRFs for pixel labelling (e.g. segmentation), using boosted classifiers.

Sufficient statisticsof labels given the image

Expected sufficient statistics given the image

- 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.