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Part 2: Unsupervised Learning Machine Learning Techniques  for Computer Vision Microsoft Research Cambridge ECCV 2004, Prague Christopher M. Bishop
Overview of Part 2 ,[object Object],[object Object],[object Object],[object Object],[object Object]
The Gaussian Distribution ,[object Object],[object Object],mean covariance
Gaussian Mixtures ,[object Object],[object Object]
Example: Mixture of 3 Gaussians
Maximum Likelihood for the GMM ,[object Object],[object Object],[object Object]
EM Algorithm  –  Informal Derivation
EM Algorithm  –  Informal Derivation ,[object Object]
EM Algorithm  –  Informal Derivation ,[object Object]
EM Algorithm  –  Informal Derivation ,[object Object],[object Object]
Old Faithful Data Set Duration of eruption (minutes) Time between eruptions (minutes)
 
 
 
 
 
 
Latent Variable View of EM ,[object Object],[object Object],[object Object],[object Object]
Latent Variable View of EM ,[object Object],[object Object],[object Object],[object Object]
Incomplete and Complete Data complete incomplete
Latent Variable Viewpoint
Latent Variable Viewpoint  ,[object Object],[object Object],[object Object],[object Object]
Graphical Representation of GMM
Latent Variable View of EM ,[object Object],[object Object],[object Object],[object Object],[object Object]
Posterior Probabilities (colour coded)
Over-fitting in Gaussian Mixture Models ,[object Object],[object Object]
Cross Validation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Bayesian Mixture of Gaussians ,[object Object],[object Object]
Data Set Size ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Variational Inference ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
General View of Variational Inference ,[object Object],[object Object],[object Object]
Variational Lower Bound
Factorized Approximation ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
 
Lower Bound ,[object Object],[object Object],[object Object]
Illustration: Univariate Gaussian ,[object Object],[object Object],[object Object]
Initial Configuration
After Updating
After Updating
Converged Solution
Variational Mixture of Gaussians ,[object Object],[object Object]
Variational Equations for GMM
Lower Bound for GMM
VIBES ,[object Object]
ML Limit ,[object Object]
Bound vs. K for Old Faithful Data
Bayesian Model Complexity
Sparse Bayes for Gaussian Mixture ,[object Object],[object Object],[object Object],[object Object],[object Object]
 
 
Summary: Variational Gaussian Mixtures ,[object Object],[object Object],[object Object],[object Object]
Continuous Latent Variables ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
Probabilistic PCA ,[object Object],[object Object],[object Object],PCA factor analysis
Probabilistic PCA ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]
EM for PCA
EM for PCA
EM for PCA
EM for PCA
EM for PCA
EM for PCA
EM for PCA
Bayesian PCA ,[object Object],[object Object],[object Object],ML PCA Bayesian PCA
Non-linear Manifolds ,[object Object]
Bayesian Mixture of BPCA Models
 
Flexible Sprites ,[object Object],[object Object],[object Object],[object Object],[object Object]
 
Transformed Component Analysis ,[object Object],[object Object],[object Object],[object Object]
 
Bayesian Constellation Model ,[object Object],[object Object],[object Object]
Bayesian Constellation Model
Summary of Part 2 ,[object Object],[object Object],[object Object],[object Object],[object Object],[object Object],[object Object]

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Part 2: Unsupervised Learning Machine Learning Techniques