1. Introduction
    1. example: polynomial curve fitting
    2. probability theory
    3. model selection
    4. the curse of dimensionality
    5. decision theory
    6. information theory
  2. Probability Distribution
    1. binary variables
    2. multinomial variables
    3. the gaussian distribution
    4. the exponential family
    5. nonparametric methods
  3. Linear Models for Regression
    1. linear basis function models
    2. the bias-variance decomposition
    3. bayesian linear regression
    4. bayesian model comparison
    5. the evidence approximation
    6. limitations of fixed basis functions
  4. Linear Models for Classification
    1. discriminant functions
    2. probabilistic generative models
    3. probabilistic discriminative models
    4. the laplace approximation
    5. bayseian logistic regression
  5. Neural Networks
    1. feed-forward network functions
    2. network training
    3. error backpropagation
    4. the hessian matrix
    5. regularization in neural networks
    6. mixture density networks
    7. bayesian neural networks
  6. Kernel Methods
    1. dual representation
    2. constructing kernels
    3. radial basis function networks
    4. gaussian processes
  7. Sparse Kernal Machines
    1. maximum margin classifiers
    2. relevance vector machines
  8. Graphical Models
    1. bayesian networks
    2. conditional independence
    3. markov random fields
    4. inference in graphical models
  9. Mixture Models and EM
    1. k-means clustering
    2. mixtures of gaussians
    3. an alternative view of em
    4. the em algorithm in general
  10. Approximate Inference
    1. variational inference
    2. illustration: variational mixture of gaussians
    3. variational linear regression
    4. exponential family distributions
    5. local variational methods
    6. variational logistic regression
    7. expectiation propagation
  11. Sampling Methods
    1. basic sampling algorithms
    2. markov chain monte carlo
    3. gibbs sampling
    4. slice sampling
    5. the hybrid monte carlo algorithm
    6. estimating the partition function
  12. Continuous Latent Variables
    1. principal component analysis
    2. probabilistic PCA
    3. kernel PCA
    4. nonlinear latent variable models
  13. Sequential Data
    1. markov models
    2. hidden markov models
    3. linear dynamical systems
  14. Combining Models
    1. bayesian model averaging
    2. committees
    3. boosting
    4. tree-based models
    5. conditional mixture models