Variational Bayesian methods

Contents:

• Introduction
• Bayesian inference
  • Probability Theory
  • Inference
• Variational Bayesian approximation
  • Minimizing Kullback-Leibler divergence
  • Mean-field, fixed form
  • Variational Bayesian expectation maximization algorithm
• Variational message passing
• Stochastic variational inference
• Non-conjugate methods
  • Lower bounding
  • Numerical integration
  • Conjugate exponential family interpretation
  • Tilted VB
  • Other methods
• Riemannian conjugate gradient learning
  • Riemannian manifold
  • Algorithm
• Improving optimization
  • Deterministic annealing
  • Parameter expansion
  • Pattern searches
• Gaussian processes
  • Gaussian process regression
  • Variational sparse approximation
  • Uncertain inputs
  • Stochastic inference
  • Variational approximation of hyperparameters? Elsewhere?
  • GP-LVM?
  • Deep GPs?
• Markov models
  • Smoothing in HMM
  • Smoothing in LSSM
  • Gaussian Markov random fields
• General black-box framework
  • “Black box”
  • Variational approximation as linear regression
  • Gradient-based approximation
• Inference model