Christopher M. Bishop

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Object RecognitionA Statistical Learning
Perspective

• Christopher M. Bishop

Microsoft Research, Cambridge
Sicily, 2003
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Question 1

• Will visual category recognition be solved by an
  architecture based on classification of feature
  vectors using advanced learning algorithms?
• No
• large number of classes
• many degrees of freedom of variability
  (geometric, photometric, ...)
• transformations are highly non-linear in the
  pixel values(objects live on non-linear
  manifolds)
• occlusion
• expensive to provide detailed labelling of
  training data

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Question 2

• If we want to achieve a human like capacity to
  recognise 1000s of visual categories, learning
  from a few examples, what will move us forward
  most significantly?
• Large training sets
• algorithms which can effectively utilize lots of
  unlabelled/partially labelled data
• But should the models be generative or
  discriminative?

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Generative vs. Discriminative Models

• Generative approach separately model
  class-conditional densities and priorsthen
  evaluate posterior probabilities using Bayes
  theorem
• Discriminative approaches
• model posterior probabilities directly
• just predict class label (no inference stage)

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Generative vs. Discriminative
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Advantages of Knowing Posterior Probabilities

• No re-training if loss matrix changes
• inference hard, decision stage is easy
• Reject option dont make decision when largest
  probability is less than threshold
• Compensating for skewed class priors
• Combining models
• e.g. independent measurements

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Unlabelled Data
Class 2
Test point
Class 1
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Unlabelled Data
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Generative Methods

• ? Relatively straightforward to characterize
  invariances
• ? They can handle partially labelled data
• ? They wastefully model variability which is
  unimportant for classification
• ? They scale badly with the number of classes and
  the number of invariant transformations (slow on
  test data)

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Discriminative Methods

• ? They use the flexibility of the model in
  relevant regions of input space
• ? They can be extremely fast once trained
• ? They interpolate between training examples, and
  hence can fail if novel inputs are presented
• ? They dont easily handle compositionality (e.g.
  faces can have glasses and/or moutaches and/or
  hats)

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Hybrid Approaches

• Generatively inspired models, trained
  discriminatively
• state of the art in speech recognition
• hidden Markov model handles time-warp invariances
• parameters determined by maximum mutual
  information not maximum likelihood