Contents

• Contents
• Introduction
• Bayesian framework
  • Basic model and notations
  • Bayesian decision theory
  • Maximum A Posteriori Approximation
  • Normalization, non-negativity, and specific priors
  • Empirical risk minimization
  • Interpretations of Occam's razor
  • A priori information and a posteriori control
• Gaussian prior factors
  • Gaussian prior factor for log-probabilities
  • Gaussian prior factor for probabilities
  • General Gaussian prior factors
  • Covariances and invariances
  • Non-zero means
  • Quadratic density estimation and empirical risk minimization
  • Regression
  • Classification
  • Inverse quantum mechanics
• Parameterizing likelihoods: Variational methods
  • General parameterizations
  • Gaussian priors for parameters
  • Linear trial spaces
  • Mixture models
  • Additive models
  • Product ansatz
  • Decision trees
  • Projection pursuit
  • Neural networks
• Parameterizing priors: Hyperparameters
  • Prior normalization
  • Adapting prior means
  • Adapting prior covariances
  • Exact posterior for hyperparameters
  • Integer hyperparameters
  • Local hyperfields
• Non-Gaussian prior factors
  • Mixtures of Gaussian prior factors
  • Prior mixtures for density estimation
  • Prior mixtures for regression
  • Local mixtures
  • Non-quadratic potentials
• Iteration procedures: Learning
  • Numerical solution of stationarity equations
  • Learning matrices
  • Initial configurations and kernel methods
  • Numerical examples
• Bibliography
• About this document ...