apunkt/PageIndex
1
0
Fork 0
mirror of https://github.com/VectifyAI/PageIndex.git synced 2026-04-25 16:16:22 +02:00
Code Issues Projects Releases Packages Wiki Activity Actions 2
PageIndex/examples/documents/results/PRML_structure.json

1847 lines
48 KiB
JSON
Raw Normal View History

add node id, node summary and doc summary
2025-04-03 13:35:38 +08:00
{
"doc_name": "PRML.pdf",
"structure": [
{
"title": "Preface",
"start_index": 1,
"end_index": 6,
"node_id": "0000"
},
{
"title": "Preface",
"start_index": 7,
"end_index": 10,
"node_id": "0001"
},
{
"title": "Mathematical notation",
"start_index": 11,
"end_index": 13,
"node_id": "0002"
},
{
"title": "Contents",
"start_index": 13,
"end_index": 20,
"node_id": "0003"
},
{
"title": "Introduction",
"start_index": 21,
"end_index": 24,
"nodes": [
{
"title": "Example: Polynomial Curve Fitting",
"start_index": 24,
"end_index": 32,
"node_id": "0005"
},
{
"title": "Probability Theory",
"start_index": 32,
"end_index": 37,
"nodes": [
{
"title": "Probability densities",
"start_index": 37,
"end_index": 39,
"node_id": "0007"
},
{
"title": "Expectations and covariances",
"start_index": 39,
"end_index": 41,
"node_id": "0008"
},
{
"title": "Bayesian probabilities",
"start_index": 41,
"end_index": 44,
"node_id": "0009"
},
{
"title": "The Gaussian distribution",
"start_index": 44,
"end_index": 48,
"node_id": "0010"
},
{
"title": "Curve fitting re-visited",
"start_index": 48,
"end_index": 50,
"node_id": "0011"
},
{
"title": "Bayesian curve fitting",
"start_index": 50,
"end_index": 52,
"node_id": "0012"
}
],
"node_id": "0006"
},
{
"title": "Model Selection",
"start_index": 52,
"end_index": 53,
"node_id": "0013"
},
{
"title": "The Curse of Dimensionality",
"start_index": 53,
"end_index": 58,
"node_id": "0014"
},
{
"title": "Decision Theory",
"start_index": 58,
"end_index": 59,
"nodes": [
{
"title": "Minimizing the misclassification rate",
"start_index": 59,
"end_index": 61,
"node_id": "0016"
},
{
"title": "Minimizing the expected loss",
"start_index": 61,
"end_index": 62,
"node_id": "0017"
},
{
"title": "The reject option",
"start_index": 62,
"end_index": 62,
"node_id": "0018"
},
{
"title": "Inference and decision",
"start_index": 62,
"end_index": 66,
"node_id": "0019"
},
{
"title": "Loss functions for regression",
"start_index": 66,
"end_index": 68,
"node_id": "0020"
}
],
"node_id": "0015"
},
{
"title": "Information Theory",
"start_index": 68,
"end_index": 75,
"nodes": [
{
"title": "Relative entropy and mutual information",
"start_index": 75,
"end_index": 78,
"node_id": "0022"
}
],
"node_id": "0021"
}
],
"node_id": "0004"
},
{
"title": "Exercises",
"start_index": 78,
"end_index": 87,
"node_id": "0023"
},
{
"title": "Probability Distributions",
"start_index": 87,
"end_index": 88,
"nodes": [
{
"title": "Binary Variables",
"start_index": 88,
"end_index": 91,
"nodes": [
{
"title": "The beta distribution",
"start_index": 91,
"end_index": 94,
"node_id": "0026"
}
],
"node_id": "0025"
},
{
"title": "Multinomial Variables",
"start_index": 94,
"end_index": 96,
"nodes": [
{
"title": "The Dirichlet distribution",
"start_index": 96,
"end_index": 98,
"node_id": "0028"
}
],
"node_id": "0027"
},
{
"title": "The Gaussian Distribution",
"start_index": 98,
"end_index": 105,
"nodes": [
{
"title": "Conditional Gaussian distributions",
"start_index": 105,
"end_index": 108,
"node_id": "0030"
},
{
"title": "Marginal Gaussian distributions",
"start_index": 108,
"end_index": 110,
"node_id": "0031"
},
{
"title": "Bayes\u2019 theorem for Gaussian variables",
"start_index": 110,
"end_index": 113,
"node_id": "0032"
},
{
"title": "Maximum likelihood for the Gaussian",
"start_index": 113,
"end_index": 114,
"node_id": "0033"
},
{
"title": "Sequential estimation",
"start_index": 114,
"end_index": 117,
"node_id": "0034"
},
{
"title": "Bayesian inference for the Gaussian",
"start_index": 117,
"end_index": 122,
"node_id": "0035"
},
{
"title": "Student\u2019s t-distribution",
"start_index": 122,
"end_index": 125,
"node_id": "0036"
},
{
"title": "Periodic variables",
"start_index": 125,
"end_index": 130,
"node_id": "0037"
},
{
"title": "Mixtures of Gaussians",
"start_index": 130,
"end_index": 133,
"node_id": "0038"
}
],
"node_id": "0029"
},
{
"title": "The Exponential Family",
"start_index": 133,
"end_index": 136,
"nodes": [
{
"title": "Maximum likelihood and sufficient statistics",
"start_index": 136,
"end_index": 137,
"node_id": "0040"
},
{
"title": "Conjugate priors",
"start_index": 137,
"end_index": 137,
"node_id": "0041"
},
{
"title": "Noninformative priors",
"start_index": 137,
"end_index": 140,
"node_id": "0042"
}
],
"node_id": "0039"
},
{
"title": "Nonparametric Methods",
"start_index": 140,
"end_index": 142,
"nodes": [
{
"title": "Kernel density estimators",
"start_index": 142,
"end_index": 144,
"node_id": "0044"
},
{
"title": "Nearest-neighbour methods",
"start_index": 144,
"end_index": 147,
"node_id": "0045"
}
],
"node_id": "0043"
}
],
"node_id": "0024"
},
{
"title": "Exercises",
"start_index": 147,
"end_index": 156,
"node_id": "0046"
},
{
"title": "Linear Models for Regression",
"start_index": 157,
"end_index": 158,
"nodes": [
{
"title": "Linear Basis Function Models",
"start_index": 158,
"end_index": 160,
"nodes": [
{
"title": "Maximum likelihood and least squares",
"start_index": 160,
"end_index": 163,
"node_id": "0049"
},
{
"title": "Geometry of least squares",
"start_index": 163,
"end_index": 163,
"node_id": "0050"
},
{
"title": "Sequential learning",
"start_index": 163,
"end_index": 164,
"node_id": "0051"
},
{
"title": "Regularized least squares",
"start_index": 164,
"end_index": 166,
"node_id": "0052"
},
{
"title": "Multiple outputs",
"start_index": 166,
"end_index": 167,
"node_id": "0053"
}
],
"node_id": "0048"
},
{
"title": "The Bias-Variance Decomposition",
"start_index": 167,
"end_index": 172,
"node_id": "0054"
},
{
"title": "Bayesian Linear Regression",
"start_index": 172,
"end_index": 172,
"nodes": [
{
"title": "Parameter distribution",
"start_index": 172,
"end_index": 176,
"node_id": "0056"
},
{
"title": "Predictive distribution",
"start_index": 176,
"end_index": 179,
"node_id": "0057"
},
{
"title": "Equivalent kernel",
"start_index": 179,
"end_index": 181,
"node_id": "0058"
}
],
"node_id": "0055"
},
{
"title": "Bayesian Model Comparison",
"start_index": 181,
"end_index": 185,
"node_id": "0059"
},
{
"title": "The Evidence Approximation",
"start_index": 185,
"end_index": 186,
"nodes": [
{
"title": "Evaluation of the evidence function",
"start_index": 186,
"end_index": 188,
"node_id": "0061"
},
{
"title": "Maximizing the evidence function",
"start_index": 188,
"end_index": 190,
"node_id": "0062"
},
{
"title": "Effective number of parameters",
"start_index": 190,
"end_index": 192,
"node_id": "0063"
}
],
"node_id": "0060"
},
{
"title": "Limitations of Fixed Basis Functions",
"start_index": 192,
"end_index": 193,
"node_id": "0064"
}
],
"node_id": "0047"
},
{
"title": "Exercises",
"start_index": 193,
"end_index": 199,
"node_id": "0065"
},
{
"title": "Linear Models for Classification",
"start_index": 199,
"end_index": 201,
"nodes": [
{
"title": "Discriminant Functions",
"start_index": 201,
"end_index": 201,
"nodes": [
{
"title": "Two classes",
"start_index": 201,
"end_index": 202,
"node_id": "0068"
},
{
"title": "Multiple classes",
"start_index": 202,
"end_index": 204,
"node_id": "0069"
},
{
"title": "Least squares for classification",
"start_index": 204,
"end_index": 206,
"node_id": "0070"
},
{
"title": "Fisher\u2019s linear discriminant",
"start_index": 206,
"end_index": 209,
"node_id": "0071"
},
{
"title": "Relation to least squares",
"start_index": 209,
"end_index": 211,
"node_id": "0072"
},
{
"title": "Fisher\u2019s discriminant for multiple classes",
"start_index": 211,
"end_index": 212,
"node_id": "0073"
},
{
"title": "The perceptron algorithm",
"start_index": 212,
"end_index": 216,
"node_id": "0074"
}
],
"node_id": "0067"
},
{
"title": "Probabilistic Generative Models",
"start_index": 216,
"end_index": 218,
"nodes": [
{
"title": "Continuous inputs",
"start_index": 218,
"end_index": 220,
"node_id": "0076"
},
{
"title": "Maximum likelihood solution",
"start_index": 220,
"end_index": 222,
"node_id": "0077"
},
{
"title": "Discrete features",
"start_index": 222,
"end_index": 222,
"node_id": "0078"
},
{
"title": "Exponential family",
"start_index": 222,
"end_index": 223,
"node_id": "0079"
}
],
"node_id": "0075"
},
{
"title": "Probabilistic Discriminative Models",
"start_index": 223,
"end_index": 224,
"nodes": [
{
"title": "Fixed basis functions",
"start_index": 224,
"end_index": 225,
"node_id": "0081"
},
{
"title": "Logistic regression",
"start_index": 225,
"end_index": 227,
"node_id": "0082"
},
{
"title": "Iterative reweighted least squares",
"start_index": 227,
"end_index": 229,
"node_id": "0083"
},
{
"title": "Multiclass logistic regression",
"start_index": 229,
"end_index": 230,
"node_id": "0084"
},
{
"title": "Probit regression",
"start_index": 230,
"end_index": 232,
"node_id": "0085"
},
{
"title": "Canonical link functions",
"start_index": 232,
"end_index": 232,
"node_id": "0086"
}
],
"node_id": "0080"
},
{
"title": "The Laplace Approximation",
"start_index": 233,
"end_index": 236,
"nodes": [
{
"title": "Model comparison and BIC",
"start_index": 236,
"end_index": 237,
"node_id": "0088"
}
],
"node_id": "0087"
},
{
"title": "Bayesian Logistic Regression",
"start_index": 237,
"end_index": 237,
"nodes": [
{
"title": "Laplace approximation",
"start_index": 237,
"end_index": 238,
"node_id": "0090"
},
{
"title": "Predictive distribution",
"start_index": 238,
"end_index": 240,
"node_id": "0091"
}
],
"node_id": "0089"
}
],
"node_id": "0066"
},
{
"title": "Exercises",
"start_index": 240,
"end_index": 245,
"node_id": "0092"
},
{
"title": "Neural Networks",
"start_index": 245,
"end_index": 247,
"nodes": [
{
"title": "Feed-forward Network Functions",
"start_index": 247,
"end_index": 251,
"nodes": [
{
"title": "Weight-space symmetries",
"start_index": 251,
"end_index": 252,
"node_id": "0095"
}
],
"node_id": "0094"
},
{
"title": "Network Training",
"start_index": 252,
"end_index": 256,
"nodes": [
{
"title": "Parameter optimization",
"start_index": 256,
"end_index": 257,
"node_id": "0097"
},
{
"title": "Local quadratic approximation",
"start_index": 257,
"end_index": 259,
"node_id": "0098"
},
{
"title": "Use of gradient information",
"start_index": 259,
"end_index": 260,
"node_id": "0099"
},
{
"title": "Gradient descent optimization",
"start_index": 260,
"end_index": 261,
"node_id": "0100"
}
],
"node_id": "0096"
},
{
"title": "Error Backpropagation",
"start_index": 261,
"end_index": 262,
"nodes": [
{
"title": "Evaluation of error-function derivatives",
"start_index": 262,
"end_index": 265,
"node_id": "0102"
},
{
"title": "A simple example",
"start_index": 265,
"end_index": 266,
"node_id": "0103"
},
{
"title": "Efficiency of backpropagation",
"start_index": 266,
"end_index": 267,
"node_id": "0104"
},
{
"title": "The Jacobian matrix",
"start_index": 267,
"end_index": 269,
"node_id": "0105"
}
],
"node_id": "0101"
},
{
"title": "The Hessian Matrix",
"start_index": 269,
"end_index": 270,
"nodes": [
{
"title": "Diagonal approximation",
"start_index": 270,
"end_index": 271,
"node_id": "0107"
},
{
"title": "Outer product approximation",
"start_index": 271,
"end_index": 272,
"node_id": "0108"
},
{
"title": "Inverse Hessian",
"start_index": 272,
"end_index": 272,
"node_id": "0109"
},
{
"title": "Finite differences",
"start_index": 272,
"end_index": 273,
"node_id": "0110"
},
{
"title": "Exact evaluation of the Hessian",
"start_index": 273,
"end_index": 274,
"node_id": "0111"
},
{
"title": "Fast multiplication by the Hessian",
"start_index": 274,
"end_index": 276,
"node_id": "0112"
}
],
"node_id": "0106"
},
{
"title": "Regularization in Neural Networks",
"start_index": 276,
"end_index": 277,
"nodes": [
{
"title": "Consistent Gaussian priors",
"start_index": 277,
"end_index": 279,
"node_id": "0114"
},
{
"title": "Early stopping",
"start_index": 279,
"end_index": 281,
"node_id": "0115"
},
{
"title": "Invariances",
"start_index": 281,
"end_index": 283,
"node_id": "0116"
},
{
"title": "Tangent propagation",
"start_index": 283,
"end_index": 285,
"node_id": "0117"
},
{
"title": "Training with transformed data",
"start_index": 285,
"end_index": 287,
"node_id": "0118"
},
{
"title": "Convolutional networks",
"start_index": 287,
"end_index": 289,
"node_id": "0119"
},
{
"title": "Soft weight sharing",
"start_index": 289,
"end_index": 292,
"node_id": "0120"
}
],
"node_id": "0113"
},
{
"title": "Mixture Density Networks",
"start_index": 292,
"end_index": 297,
"node_id": "0121"
},
{
"title": "Bayesian Neural Networks",
"start_index": 297,
"end_index": 298,
"nodes": [
{
"title": "Posterior parameter distribution",
"start_index": 298,
"end_index": 300,
"node_id": "0123"
},
{
"title": "Hyperparameter optimization",
"start_index": 300,
"end_index": 301,
"node_id": "0124"
},
{
"title": "Bayesian neural networks for classification",
"start_index": 301,
"end_index": 304,
"node_id": "0125"
}
],
"node_id": "0122"
}
],
"node_id": "0093"
},
{
"title": "Exercises",
"start_index": 304,
"end_index": 311,
"node_id": "0126"
},
{
"title": "Kernel Methods",
"start_index": 311,
"end_index": 313,
"nodes": [
{
"title": "Dual Representations",
"start_index": 313,
"end_index": 314,
"node_id": "0128"
},
{
"title": "Constructing Kernels",
"start_index": 314,
"end_index": 319,
"node_id": "0129"
},
{
"title": "Radial Basis Function Networks",
"start_index": 319,
"end_index": 321,
"nodes": [
{
"title": "Nadaraya-Watson model",
"start_index": 321,
"end_index": 323,
"node_id": "0131"
}
],
"node_id": "0130"
},
{
"title": "Gaussian Processes",
"start_index": 323,
"end_index": 324,
"nodes": [
{
"title": "Linear regression revisited",
"start_index": 324,
"end_index": 326,
"node_id": "0133"
},
{
"title": "Gaussian processes for regression",
"start_index": 326,
"end_index": 331,
"node_id": "0134"
},
{
"title": "Learning the hyperparameters",
"start_index": 331,
"end_index": 332,
"node_id": "0135"
},
{
"title": "Automatic relevance determination",
"start_index": 332,
"end_index": 333,
"node_id": "0136"
},
{
"title": "Gaussian processes for classification",
"start_index": 333,
"end_index": 335,
"node_id": "0137"
},
{
"title": "Laplace approximation",
"start_index": 335,
"end_index": 339,
"node_id": "0138"
},
{
"title": "Connection to neural networks",
"start_index": 339,
"end_index": 340,
"node_id": "0139"
}
],
"node_id": "0132"
}
],
"node_id": "0127"
},
{
"title": "Exercises",
"start_index": 340,
"end_index": 344,
"node_id": "0140"
},
{
"title": "Sparse Kernel Machines",
"start_index": 345,
"end_index": 346,
"nodes": [
{
"title": "Maximum Margin Classifiers",
"start_index": 346,
"end_index": 351,
"nodes": [
{
"title": "Overlapping class distributions",
"start_index": 351,
"end_index": 356,
"node_id": "0143"
},
{
"title": "Relation to logistic regression",
"start_index": 356,
"end_index": 358,
"node_id": "0144"
},
{
"title": "Multiclass SVMs",
"start_index": 358,
"end_index": 359,
"node_id": "0145"
},
{
"title": "SVMs for regression",
"start_index": 359,
"end_index": 364,
"node_id": "0146"
},
{
"title": "Computational learning theory",
"start_index": 364,
"end_index": 365,
"node_id": "0147"
}
],
"node_id": "0142"
},
{
"title": "Relevance Vector Machines",
"start_index": 365,
"end_index": 365,
"nodes": [
{
"title": "RVM for regression",
"start_index": 365,
"end_index": 369,
"node_id": "0149"
},
{
"title": "Analysis of sparsity",
"start_index": 369,
"end_index": 373,
"node_id": "0150"
},
{
"title": "RVM for classification",
"start_index": 373,
"end_index": 377,
"node_id": "0151"
}
],
"node_id": "0148"
}
],
"node_id": "0141"
},
{
"title": "Exercises",
"start_index": 377,
"end_index": 379,
"node_id": "0152"
},
{
"title": "Graphical Models",
"start_index": 379,
"end_index": 380,
"nodes": [
{
"title": "Bayesian Networks",
"start_index": 380,
"end_index": 382,
"nodes": [
{
"title": "Example: Polynomial regression",
"start_index": 382,
"end_index": 385,
"node_id": "0155"
},
{
"title": "Generative models",
"start_index": 385,
"end_index": 386,
"node_id": "0156"
},
{
"title": "Discrete variables",
"start_index": 386,
"end_index": 390,
"node_id": "0157"
},
{
"title": "Linear-Gaussian models",
"start_index": 390,
"end_index": 392,
"node_id": "0158"
}
],
"node_id": "0154"
},
{
"title": "Conditional Independence",
"start_index": 392,
"end_index": 393,
"nodes": [
{
"title": "Three example graphs",
"start_index": 393,
"end_index": 398,
"node_id": "0160"
},
{
"title": "D-separation",
"start_index": 398,
"end_index": 403,
"node_id": "0161"
}
],
"node_id": "0159"
},
{
"title": "Markov Random Fields",
"start_index": 403,
"end_index": 403,
"nodes": [
{
"title": "Conditional independence properties",
"start_index": 403,
"end_index": 404,
"node_id": "0163"
},
{
"title": "Factorization properties",
"start_index": 404,
"end_index": 407,
"node_id": "0164"
},
{
"title": "Illustration: Image de-noising",
"start_index": 407,
"end_index": 410,
"node_id": "0165"
},
{
"title": "Relation to directed graphs",
"start_index": 410,
"end_index": 413,
"node_id": "0166"
}
],
"node_id": "0162"
},
{
"title": "Inference in Graphical Models",
"start_index": 413,
"end_index": 414,
"nodes": [
{
"title": "Inference on a chain",
"start_index": 414,
"end_index": 418,
"node_id": "0168"
},
{
"title": "Trees",
"start_index": 418,
"end_index": 419,
"node_id": "0169"
},
{
"title": "Factor graphs",
"start_index": 419,
"end_index": 422,
"node_id": "0170"
},
{
"title": "The sum-product algorithm",
"start_index": 422,
"end_index": 431,
"node_id": "0171"
},
{
"title": "The max-sum algorithm",
"start_index": 431,
"end_index": 436,
"node_id": "0172"
},
{
"title": "Exact inference in general graphs",
"start_index": 436,
"end_index": 437,
"node_id": "0173"
},
{
"title": "Loopy belief propagation",
"start_index": 437,
"end_index": 438,
"node_id": "0174"
},
{
"title": "Learning the graph structure",
"start_index": 438,
"end_index": 438,
"node_id": "0175"
}
],
"node_id": "0167"
}
],
"node_id": "0153"
},
{
"title": "Exercises",
"start_index": 438,
"end_index": 443,
"node_id": "0176"
},
{
"title": "Mixture Models and EM",
"start_index": 443,
"end_index": 444,
"nodes": [
{
"title": "K-means Clustering",
"start_index": 444,
"end_index": 448,
"nodes": [
{
"title": "Image segmentation and compression",
"start_index": 448,
"end_index": 450,
"node_id": "0179"
}
],
"node_id": "0178"
},
{
"title": "Mixtures of Gaussians",
"start_index": 450,
"end_index": 452,
"nodes": [
{
"title": "Maximum likelihood",
"start_index": 452,
"end_index": 455,
"node_id": "0181"
},
{
"title": "EM for Gaussian mixtures",
"start_index": 455,
"end_index": 459,
"node_id": "0182"
}
],
"node_id": "0180"
},
{
"title": "An Alternative View of EM",
"start_index": 459,
"end_index": 461,
"nodes": [
{
"title": "Gaussian mixtures revisited",
"start_index": 461,
"end_index": 463,
"node_id": "0184"
},
{
"title": "Relation to K-means",
"start_index": 463,
"end_index": 464,
"node_id": "0185"
},
{
"title": "Mixtures of Bernoulli distributions",
"start_index": 464,
"end_index": 468,
"node_id": "0186"
},
{
"title": "EM for Bayesian linear regression",
"start_index": 468,
"end_index": 470,
"node_id": "0187"
}
],
"node_id": "0183"
},
{
"title": "The EM Algorithm in General",
"start_index": 470,
"end_index": 475,
"node_id": "0188"
}
],
"node_id": "0177"
},
{
"title": "Exercises",
"start_index": 475,
"end_index": 480,
"node_id": "0189"
},
{
"title": "Approximate Inference",
"start_index": 481,
"end_index": 482,
"nodes": [
{
"title": "Variational Inference",
"start_index": 482,
"end_index": 484,
"nodes": [
{
"title": "Factorized distributions",
"start_index": 484,
"end_index": 486,
"node_id": "0192"
},
{
"title": "Properties of factorized approximations",
"start_index": 486,
"end_index": 490,
"node_id": "0193"
},
{
"title": "Example: The univariate Gaussian",
"start_index": 490,
"end_index": 493,
"node_id": "0194"
},
{
"title": "Model comparison",
"start_index": 493,
"end_index": 494,
"node_id": "0195"
}
],
"node_id": "0191"
},
{
"title": "Illustration: Variational Mixture of Gaussians",
"start_index": 494,
"end_index": 495,
"nodes": [
{
"title": "Variational distribution",
"start_index": 495,
"end_index": 501,
"node_id": "0197"
},
{
"title": "Variational lower bound",
"start_index": 501,
"end_index": 502,
"node_id": "0198"
},
{
"title": "Predictive density",
"start_index": 502,
"end_index": 503,
"node_id": "0199"
},
{
"title": "Determining the number of components",
"start_index": 503,
"end_index": 505,
"node_id": "0200"
},
{
"title": "Induced factorizations",
"start_index": 505,
"end_index": 506,
"node_id": "0201"
}
],
"node_id": "0196"
},
{
"title": "Variational Linear Regression",
"start_index": 506,
"end_index": 506,
"nodes": [
{
"title": "Variational distribution",
"start_index": 506,
"end_index": 508,
"node_id": "0203"
},
{
"title": "Predictive distribution",
"start_index": 508,
"end_index": 509,
"node_id": "0204"
},
{
"title": "Lower bound",
"start_index": 509,
"end_index": 510,
"node_id": "0205"
}
],
"node_id": "0202"
},
{
"title": "Exponential Family Distributions",
"start_index": 510,
"end_index": 511,
"nodes": [
{
"title": "Variational message passing",
"start_index": 511,
"end_index": 512,
"node_id": "0207"
}
],
"node_id": "0206"
},
{
"title": "Local Variational Methods",
"start_index": 513,
"end_index": 518,
"node_id": "0208"
},
{
"title": "Variational Logistic Regression",
"start_index": 518,
"end_index": 518,
"nodes": [
{
"title": "Variational posterior distribution",
"start_index": 518,
"end_index": 520,
"node_id": "0210"
},
{
"title": "Optimizing the variational parameters",
"start_index": 520,
"end_index": 522,
"node_id": "0211"
},
{
"title": "Inference of hyperparameters",
"start_index": 522,
"end_index": 525,
"node_id": "0212"
}
],
"node_id": "0209"
},
{
"title": "Expectation Propagation",
"start_index": 525,
"end_index": 531,
"nodes": [
{
"title": "Example: The clutter problem",
"start_index": 531,
"end_index": 533,
"node_id": "0214"
},
{
"title": "Expectation propagation on graphs",
"start_index": 533,
"end_index": 537,
"node_id": "0215"
}
],
"node_id": "0213"
}
],
"node_id": "0190"
},
{
"title": "Exercises",
"start_index": 537,
"end_index": 542,
"node_id": "0216"
},
{
"title": "Sampling Methods",
"start_index": 543,
"end_index": 546,
"nodes": [
{
"title": "Basic Sampling Algorithms",
"start_index": 546,
"end_index": 546,
"nodes": [
{
"title": "Standard distributions",
"start_index": 546,
"end_index": 548,
"node_id": "0219"
},
{
"title": "Rejection sampling",
"start_index": 548,
"end_index": 550,
"node_id": "0220"
},
{
"title": "Adaptive rejection sampling",
"start_index": 550,
"end_index": 552,
"node_id": "0221"
},
{
"title": "Importance sampling",
"start_index": 552,
"end_index": 554,
"node_id": "0222"
},
{
"title": "Sampling-importance-resampling",
"start_index": 554,
"end_index": 556,
"node_id": "0223"
},
{
"title": "Sampling and the EM algorithm",
"start_index": 556,
"end_index": 556,
"node_id": "0224"
}
],
"node_id": "0218"
},
{
"title": "Markov Chain Monte Carlo",
"start_index": 557,
"end_index": 559,
"nodes": [
{
"title": "Markov chains",
"start_index": 559,
"end_index": 561,
"node_id": "0226"
},
{
"title": "The Metropolis-Hastings algorithm",
"start_index": 561,
"end_index": 562,
"node_id": "0227"
}
],
"node_id": "0225"
},
{
"title": "Gibbs Sampling",
"start_index": 562,
"end_index": 566,
"node_id": "0228"
},
{
"title": "Slice Sampling",
"start_index": 566,
"end_index": 568,
"node_id": "0229"
},
{
"title": "The Hybrid Monte Carlo Algorithm",
"start_index": 568,
"end_index": 568,
"nodes": [
{
"title": "Dynamical systems",
"start_index": 568,
"end_index": 572,
"node_id": "0231"
},
{
"title": "Hybrid Monte Carlo",
"start_index": 572,
"end_index": 574,
"node_id": "0232"
}
],
"node_id": "0230"
},
{
"title": "Estimating the Partition Function",
"start_index": 574,
"end_index": 576,
"node_id": "0233"
}
],
"node_id": "0217"
},
{
"title": "Exercises",
"start_index": 576,
"end_index": 579,
"node_id": "0234"
},
{
"title": "Continuous Latent Variables",
"start_index": 579,
"end_index": 581,
"nodes": [
{
"title": "Principal Component Analysis",
"start_index": 581,
"end_index": 581,
"nodes": [
{
"title": "Maximum variance formulation",
"start_index": 581,
"end_index": 583,
"node_id": "0237"
},
{
"title": "Minimum-error formulation",
"start_index": 583,
"end_index": 585,
"node_id": "0238"
},
{
"title": "Applications of PCA",
"start_index": 585,
"end_index": 589,
"node_id": "0239"
},
{
"title": "PCA for high-dimensional data",
"start_index": 589,
"end_index": 590,
"node_id": "0240"
}
],
"node_id": "0236"
},
{
"title": "Probabilistic PCA",
"start_index": 590,
"end_index": 594,
"nodes": [
{
"title": "Maximum likelihood PCA",
"start_index": 594,
"end_index": 597,
"node_id": "0242"
},
{
"title": "EM algorithm for PCA",
"start_index": 597,
"end_index": 600,
"node_id": "0243"
},
{
"title": "Bayesian PCA",
"start_index": 600,
"end_index": 603,
"node_id": "0244"
},
{
"title": "Factor analysis",
"start_index": 603,
"end_index": 606,
"node_id": "0245"
}
],
"node_id": "0241"
},
{
"title": "Kernel PCA",
"start_index": 606,
"end_index": 610,
"node_id": "0246"
},
{
"title": "Nonlinear Latent Variable Models",
"start_index": 611,
"end_index": 611,
"nodes": [
{
"title": "Independent component analysis",
"start_index": 611,
"end_index": 612,
"node_id": "0248"
},
{
"title": "Autoassociative neural networks",
"start_index": 612,
"end_index": 615,
"node_id": "0249"
},
{
"title": "Modelling nonlinear manifolds",
"start_index": 615,
"end_index": 619,
"node_id": "0250"
}
],
"node_id": "0247"
}
],
"node_id": "0235"
},
{
"title": "Exercises",
"start_index": 619,
"end_index": 624,
"node_id": "0251"
},
{
"title": "Sequential Data",
"start_index": 625,
"end_index": 627,
"nodes": [
{
"title": "Markov Models",
"start_index": 627,
"end_index": 630,
"node_id": "0253"
},
{
"title": "Hidden Markov Models",
"start_index": 630,
"end_index": 635,
"nodes": [
{
"title": "Maximum likelihood for the HMM",
"start_index": 635,
"end_index": 638,
"node_id": "0255"
},
{
"title": "The forward-backward algorithm",
"start_index": 638,
"end_index": 645,
"node_id": "0256"
},
{
"title": "The sum-product algorithm for the HMM",
"start_index": 645,
"end_index": 647,
"node_id": "0257"
},
{
"title": "Scaling factors",
"start_index": 647,
"end_index": 649,
"node_id": "0258"
},
{
"title": "The Viterbi algorithm",
"start_index": 649,
"end_index": 651,
"node_id": "0259"
},
{
"title": "Extensions of the hidden Markov model",
"start_index": 651,
"end_index": 655,
"node_id": "0260"
}
],
"node_id": "0254"
},
{
"title": "Linear Dynamical Systems",
"start_index": 655,
"end_index": 658,
"nodes": [
{
"title": "Inference in LDS",
"start_index": 658,
"end_index": 662,
"node_id": "0262"
},
{
"title": "Learning in LDS",
"start_index": 662,
"end_index": 664,
"node_id": "0263"
},
{
"title": "Extensions of LDS",
"start_index": 664,
"end_index": 665,
"node_id": "0264"
},
{
"title": "Particle filters",
"start_index": 665,
"end_index": 666,
"node_id": "0265"
}
],
"node_id": "0261"
}
],
"node_id": "0252"
},
{
"title": "Exercises",
"start_index": 666,
"end_index": 672,
"node_id": "0266"
},
{
"title": "Combining Models",
"start_index": 673,
"end_index": 674,
"nodes": [
{
"title": "Bayesian Model Averaging",
"start_index": 674,
"end_index": 675,
"node_id": "0268"
},
{
"title": "Committees",
"start_index": 675,
"end_index": 677,
"node_id": "0269"
},
{
"title": "Boosting",
"start_index": 677,
"end_index": 679,
"nodes": [
{
"title": "Minimizing exponential error",
"start_index": 679,
"end_index": 681,
"node_id": "0271"
},
{
"title": "Error functions for boosting",
"start_index": 681,
"end_index": 683,
"node_id": "0272"
}
],
"node_id": "0270"
},
{
"title": "Tree-based Models",
"start_index": 683,
"end_index": 686,
"node_id": "0273"
},
{
"title": "Conditional Mixture Models",
"start_index": 686,
"end_index": 687,
"nodes": [
{
"title": "Mixtures of linear regression models",
"start_index": 687,
"end_index": 690,
"node_id": "0275"
},
{
"title": "Mixtures of logistic models",
"start_index": 690,
"end_index": 692,
"node_id": "0276"
},
{
"title": "Mixtures of experts",
"start_index": 692,
"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",
"start_index": 697,
"end_index": 704,
"node_id": "0279"
},
{
"title": "Appendix B Probability Distributions",
"start_index": 705,
"end_index": 714,
"node_id": "0280"
},
{
"title": "Appendix C Properties of Matrices",
"start_index": 715,
"end_index": 722,
"node_id": "0281"
},
{
"title": "Appendix D Calculus of Variations",
"start_index": 723,
"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"
}
]
}
Reference in a new issue Copy permalink