本章目录
4 Gaussian models 97
4.1 Introduction 97
4.1.1 Notation 97
4.1.2 Basics 97
4.1.3 MLE for an MVN 99
4.1.4 Maximum entropy derivation of the Gaussian * 101
4.2 Gaussian discriminant analysis 101
4.2.1 Quadratic discriminant analysis (QDA) 102
4.2.2 Linear discriminant analysis (LDA) 103
4.2.3 Two-class LDA 104
4.2.4 MLE for discriminant analysis 106
4.2.5 Strategies for preventing overfitting 106
4.2.6 Regularized LDA * 107
4.2.7 Diagonal LDA 108
4.2.8 Nearest shrunken centroids classifier * 109
4.3 Inference in jointly Gaussian distributions 110
4.3.1 Statement of the result 111
4.3.2 Examples 111
4.3.3 Information form 115
4.3.4 Proof of the result * 116
4.4 Linear Gaussian systems 119
4.4.1 Statement of the result 119
4.4.2 Examples 120
4.4.3 Proof of the result * 124
4.5 Digression: The Wishart distribution * 125
4.5.1 Inverse Wishart distribution 126
4.5.2 Visualizing the Wishart distribution * 127
4.6 Inferring the parameters of an MVN 127
4.6.1 Posterior distribution of μ 128
4.6.2 Posterior distribution of Σ * 128
4.6.3 Posterior distribution of μ and Σ * 132
4.6.4 Sensor fusion with unknown precisions * 138
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