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Introduction
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Bayesian Field Theory Nonparametric
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Bayesian Field Theory Nonparametric
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 ...
Joerg_Lemm 2001-01-21