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| "title": "Preface", | |
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| { | |
| "title": "Preface", | |
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| { | |
| "title": "Mathematical notation", | |
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| { | |
| "title": "Contents", | |
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| }, | |
| { | |
| "title": "Introduction", | |
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| { | |
| "title": "Example: Polynomial Curve Fitting", | |
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| "end_index": 32, | |
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| { | |
| "title": "Probability Theory", | |
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| { | |
| "title": "Probability densities", | |
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| { | |
| "title": "Expectations and covariances", | |
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| { | |
| "title": "Bayesian probabilities", | |
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| "node_id": "0009" | |
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| { | |
| "title": "The Gaussian distribution", | |
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| "end_index": 48, | |
| "node_id": "0010" | |
| }, | |
| { | |
| "title": "Curve fitting re-visited", | |
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| "end_index": 50, | |
| "node_id": "0011" | |
| }, | |
| { | |
| "title": "Bayesian curve fitting", | |
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| { | |
| "title": "Model Selection", | |
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| "end_index": 53, | |
| "node_id": "0013" | |
| }, | |
| { | |
| "title": "The Curse of Dimensionality", | |
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| "end_index": 58, | |
| "node_id": "0014" | |
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| { | |
| "title": "Decision Theory", | |
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| "end_index": 59, | |
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| { | |
| "title": "Minimizing the misclassification rate", | |
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| "end_index": 61, | |
| "node_id": "0016" | |
| }, | |
| { | |
| "title": "Minimizing the expected loss", | |
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| "end_index": 62, | |
| "node_id": "0017" | |
| }, | |
| { | |
| "title": "The reject option", | |
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| "end_index": 62, | |
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| { | |
| "title": "Inference and decision", | |
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| { | |
| "title": "Loss functions for regression", | |
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| "node_id": "0015" | |
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| { | |
| "title": "Information Theory", | |
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| { | |
| "title": "Relative entropy and mutual information", | |
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| "node_id": "0021" | |
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| { | |
| "title": "Exercises", | |
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| "node_id": "0023" | |
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| { | |
| "title": "Probability Distributions", | |
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| { | |
| "title": "Binary Variables", | |
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| { | |
| "title": "The beta distribution", | |
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| "node_id": "0025" | |
| }, | |
| { | |
| "title": "Multinomial Variables", | |
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| "end_index": 96, | |
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| { | |
| "title": "The Dirichlet distribution", | |
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| "node_id": "0027" | |
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| { | |
| "title": "The Gaussian Distribution", | |
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| { | |
| "title": "Conditional Gaussian distributions", | |
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| { | |
| "title": "Marginal Gaussian distributions", | |
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| "node_id": "0031" | |
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| { | |
| "title": "Bayes\u2019 theorem for Gaussian variables", | |
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| { | |
| "title": "Maximum likelihood for the Gaussian", | |
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| { | |
| "title": "Sequential estimation", | |
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| { | |
| "title": "Bayesian inference for the Gaussian", | |
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| { | |
| "title": "Student\u2019s t-distribution", | |
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| { | |
| "title": "Periodic variables", | |
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| "title": "Mixtures of Gaussians", | |
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| { | |
| "title": "The Exponential Family", | |
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| "title": "Maximum likelihood and sufficient statistics", | |
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| "title": "Conjugate priors", | |
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| { | |
| "title": "Noninformative priors", | |
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| "title": "Kernel density estimators", | |
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| { | |
| "title": "Nearest-neighbour methods", | |
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| { | |
| "title": "Exercises", | |
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| { | |
| "title": "Linear Models for Regression", | |
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| "title": "Linear Basis Function Models", | |
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| "title": "Maximum likelihood and least squares", | |
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| "title": "Geometry of least squares", | |
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| "title": "Multiple outputs", | |
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| "title": "The Bias-Variance Decomposition", | |
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| { | |
| "title": "Bayesian Linear Regression", | |
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| "title": "Predictive distribution", | |
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| { | |
| "title": "Equivalent kernel", | |
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| "title": "Bayesian Model Comparison", | |
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| "title": "The Evidence Approximation", | |
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| "title": "Evaluation of the evidence function", | |
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| { | |
| "title": "Effective number of parameters", | |
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| "title": "Limitations of Fixed Basis Functions", | |
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| "title": "Exercises", | |
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| { | |
| "title": "Linear Models for Classification", | |
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| "title": "Discriminant Functions", | |
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| "title": "Multiple classes", | |
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| "title": "Least squares for classification", | |
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| { | |
| "title": "Fisher\u2019s linear discriminant", | |
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| { | |
| "title": "Relation to least squares", | |
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| "title": "Fisher\u2019s discriminant for multiple classes", | |
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| "title": "Probabilistic Generative Models", | |
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| { | |
| "title": "Iterative reweighted least squares", | |
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| "title": "Canonical link functions", | |
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| { | |
| "title": "The Laplace Approximation", | |
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| "title": "Bayesian Logistic Regression", | |
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| "title": "Neural Networks", | |
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| { | |
| "title": "A simple example", | |
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| "title": "Efficiency of backpropagation", | |
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| "title": "Training with transformed data", | |
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| "title": "Maximum likelihood PCA", | |
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| { | |
| "title": "EM algorithm for PCA", | |
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| "title": "Nonlinear Latent Variable Models", | |
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| "title": "Autoassociative neural networks", | |
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| { | |
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| }, | |
| { | |
| "title": "Sequential Data", | |
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| { | |
| "title": "Markov Models", | |
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| { | |
| "title": "Hidden Markov Models", | |
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| { | |
| "title": "Maximum likelihood for the HMM", | |
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| "title": "The forward-backward algorithm", | |
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| "title": "The sum-product algorithm for the HMM", | |
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| "title": "Extensions of the hidden Markov model", | |
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| "title": "Linear Dynamical Systems", | |
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| "title": "Inference in LDS", | |
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| { | |
| "title": "Learning in LDS", | |
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| { | |
| "title": "Extensions of LDS", | |
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| "node_id": "0264" | |
| }, | |
| { | |
| "title": "Particle filters", | |
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| "node_id": "0261" | |
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| "node_id": "0252" | |
| }, | |
| { | |
| "title": "Exercises", | |
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| "end_index": 672, | |
| "node_id": "0266" | |
| }, | |
| { | |
| "title": "Combining Models", | |
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| "title": "Bayesian Model Averaging", | |
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| { | |
| "title": "Committees", | |
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| "end_index": 677, | |
| "node_id": "0269" | |
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| { | |
| "title": "Boosting", | |
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| { | |
| "title": "Minimizing exponential error", | |
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| "title": "Error functions for boosting", | |
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| "end_index": 683, | |
| "node_id": "0272" | |
| } | |
| ], | |
| "node_id": "0270" | |
| }, | |
| { | |
| "title": "Tree-based Models", | |
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| "end_index": 686, | |
| "node_id": "0273" | |
| }, | |
| { | |
| "title": "Conditional Mixture Models", | |
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| "end_index": 687, | |
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| { | |
| "title": "Mixtures of linear regression models", | |
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| { | |
| "title": "Mixtures of logistic models", | |
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| "end_index": 692, | |
| "node_id": "0276" | |
| }, | |
| { | |
| "title": "Mixtures of experts", | |
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| "end_index": 694, | |
| "node_id": "0277" | |
| } | |
| ], | |
| "node_id": "0274" | |
| } | |
| ], | |
| "node_id": "0267" | |
| }, | |
| { | |
| "title": "Exercises", | |
| "start_index": 694, | |
| "end_index": 696, | |
| "node_id": "0278" | |
| }, | |
| { | |
| "title": "Appendix A Data Sets", | |
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| "end_index": 704, | |
| "node_id": "0279" | |
| }, | |
| { | |
| "title": "Appendix B Probability Distributions", | |
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| "end_index": 714, | |
| "node_id": "0280" | |
| }, | |
| { | |
| "title": "Appendix C Properties of Matrices", | |
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| "end_index": 722, | |
| "node_id": "0281" | |
| }, | |
| { | |
| "title": "Appendix D Calculus of Variations", | |
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| "end_index": 726, | |
| "node_id": "0282" | |
| }, | |
| { | |
| "title": "Appendix E Lagrange Multipliers", | |
| "start_index": 727, | |
| "end_index": 730, | |
| "node_id": "0283" | |
| }, | |
| { | |
| "title": "References", | |
| "start_index": 731, | |
| "end_index": 749, | |
| "node_id": "0284" | |
| }, | |
| { | |
| "title": "Index", | |
| "start_index": 749, | |
| "end_index": 758, | |
| "node_id": "0285" | |
| } | |
| ] | |
| } |