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Bayesian field theory /
| Clasificación: | Libro Electrónico |
|---|---|
| Autor principal: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Baltimore, Md. :
Johns Hopkins University Press,
2003.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Contents; List of Figures; List of Tables; List of Numerical Case Studies; Acknowledgments; 1 Introduction; 2 Bayesian framework; 2.1 Bayesian models; 2.1.1 Independent, dependent, and hidden variables; 2.1.2 Energies, free energies, and errors; 2.1.3 Bayes' theorem: Posterior, prior, and likelihood; 2.1.4 Predictive density and learning; 2.1.5 Mutual information and learning; 2.1.6 Maximum A Posteriori Approximation (MAP); 2.1.7 Normalization, non-negativity, and specific priors; 2.1.8 Numerical case study: A fair coin?; 2.2 Bayesian decision theory; 2.2.1 Loss and risk.
- 2.2.2 Loss functions for approximation2.2.3 General loss functions and unsupervised learning; 2.2.4 Log-loss and Maximum A Posteriori Approximation; 2.2.5 Empirical risk minimization; 2.2.6 Interpretations of Occam's razor; 2.2.7 Approaches to empirical learning; 2.3 A priori information; 2.3.1 Controlled, measured, and structural priors; 2.3.2 Noise induced priors; 3 Gaussian prior factors; 3.1 Gaussian prior factor for log-likelihoods; 3.1.1 Lagrange multipliers: Error functional E(L); 3.1.2 Normalization by parameterization: Error functional E(g); 3.1.3 The Hessians H[sub(L)], H[sub(g)].
- 3.2 Gaussian prior factor for likelihoods3.2.1 Lagrange multipliers: Error functional E(P); 3.2.2 Normalization by parameterization: Error functional E(z); 3.2.3 The Hessians H[sub(P)], H[sub(z)]; 3.3 Quadratic density estimation and empirical risk minimization; 3.4 Numerical case study: Density estimation with Gaussian specific priors; 3.5 Gaussian prior factors for general field; 3.5.1 The general case; 3.5.2 Square root of P; 3.5.3 Distribution functions; 3.6 Covariances and invariances; 3.6.1 Approximate invariance; 3.6.2 Infinitesimal translations; 3.6.3 Approximate periodicity.
- 3.6.4 Approximate fractals3.7 Non-zero means; 3.8 Regression; 3.8.1 Gaussian regression; 3.8.2 Exact predictive density; 3.8.3 Gaussian mixture regression (cluster regression); 3.8.4 Support vector machines and regression; 3.8.5 Numerical case study: Approximately invariant regression (AIR); 3.9 Classification; 4 Parameterizing likelihoods: Variational methods; 4.1 General likelihood parameterizations; 4.2 Gaussian priors for likelihood parameters; 4.3 Linear trial spaces; 4.4 Linear regression; 4.5 Mixture models; 4.6 Additive models; 4.7 Product ansatz; 4.8 Decision trees.
- 4.9 Projection pursuit4.10 Neural networks; 5 Parameterizing priors: Hyperparameters; 5.1 Quenched and annealed prior normalization; 5.2 Saddle point approximations and hyperparameters; 5.2.1 Joint MAP; 5.2.2 Stepwise MAP; 5.2.3 Pointwise approximation; 5.2.4 Marginal posterior and empirical Bayes; 5.2.5 Some variants of stationarity equations; 5.3 Adapting prior, means; 5.3.1 General considerations; 5.3.2 Density estimation and nonparametric boosting; 5.3.3 Unrestricted variation; 5.3.4 Regression; 5.4 Adapting prior covariances; 5.4.1 General case; 5.4.2 Automatic relevance detection.