Contents

• List of abbreviations
• List of symbols
• Introduction
  • Problem setting
  • Aim of the thesis
  • Structure of the thesis
  • Contributions of the thesis
  
  
• Mathematical preliminaries of time series modelling
  • Theory
    • Dynamical systems
    • Linear systems
    • Nonlinear systems and chaos
    • Tools for time series analysis
  • Practical considerations
    • Delay coordinates in practice
    • Prediction algorithms
  
  
• Bayesian methods for data analysis
  • Bayesian statistics
    • Constructing probabilistic models
    • Hierarchical models
    • Conjugate priors
  • Posterior approximations
    • Model selection
    • Stochastic approximations
    • Laplace approximation
    • EM algorithm
  • Ensemble learning
    • Information theoretic approach
  
  
• Building blocks of the model
  • Hidden Markov models
    • Markov chains
    • Hidden states
    • Continuous observations
    • Learning algorithms
  • Nonlinear state-space models
    • Linear models
    • Extension from linear to nonlinear
    • Multilayer perceptrons
    • Nonlinear factor analysis
    • Learning algorithms
  • Previous hybrid models
    • Switching state-space models
    • Other hidden Markov model hybrids
  
  
• The model
  • Bayesian continuous density hidden Markov model
    • The model
    • The approximating posterior distribution
  • Bayesian nonlinear state-space model
    • The generative model
    • The probabilistic model
    • The approximating posterior distribution
  • Combining the two models
    • The structure of the model
    • The approximating posterior distribution
  
  
• The algorithm
  • Learning algorithm for the continuous density hidden Markov model
    • Evaluating the cost function
    • Optimising the cost function
  • Learning algorithm for the nonlinear state-space model
    • Evaluating the cost function
    • Optimising the cost function
    • Learning procedure
    • Continuing learning with new data
  • Learning algorithm for the switching model
    • Evaluating and optimising the cost function
    • Learning procedure
    • Learning with known state sequence
  
  
• Experimental results
  • Speech data
    • Preprocessing
    • Properties of the data set
  • Comparison with other models
    • The experimental setting
    • The results
  • Segmentation of annotated data
    • The training procedure
    • The results
  
  
• Discussion
• Standard probability distributions
  • Normal distribution
  • Dirichlet distribution
  
  
• Probabilistic computations for MLP networks
• Bibliography
• About this document ...