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02-02Notes

A working library of the mathematics behind the analysis.

524 notes in 7 areas, from notation to machine learning. Each takes one formula: what it says, a small worked example, and code that runs. Revised in place. Page 19 of 22.

IndexAll notes

02-02-433Projection (Encoding)Machine learningDimensionality reduction: principal component analysis (PCA)02-02-434Reconstruction (Decoding)Machine learningDimensionality reduction: principal component analysis (PCA)02-02-435Residual Error (Truncated Eigenvalues)Machine learningDimensionality reduction: principal component analysis (PCA)02-02-436Sample Covariance MatrixMachine learningDimensionality reduction: principal component analysis (PCA)02-02-437E-Step (Responsibilities)Machine learningExpectation–maximisation (EM) for GMMs 02-02-438Effective Component SizeMachine learningExpectation–maximisation (EM) for GMMs 02-02-439M-Step (Covariance Update)Machine learningExpectation–maximisation (EM) for GMMs 02-02-440M-Step (Means Update)Machine learningExpectation–maximisation (EM) for GMMs 02-02-441M-Step (Weights Update)Machine learningExpectation–maximisation (EM) for GMMs 02-02-442Feature Matrix (Phi) FormulationMachine learningLinear regression and maximum likelihood estimation (MLE)02-02-443Gradient of Least-Squares LossMachine learningLinear regression and maximum likelihood estimation (MLE)02-02-444Least-Squares Objective (Empirical Risk)Machine learningLinear regression and maximum likelihood estimation (MLE)02-02-445Maximum Likelihood Reconstruction (Orthogonal Projection)Machine learningLinear regression and maximum likelihood estimation (MLE)02-02-446Normal Equations (MLE Solution)Machine learningLinear regression and maximum likelihood estimation (MLE)02-02-447Ridge Regression Solution (L₂ Penalty)Machine learningLinear regression and maximum likelihood estimation (MLE)02-02-448General Neural Network Layer MappingMachine learningLogistic regression and neural networks 02-02-449Logistic Sigmoid (Transfer/Activation Function)Machine learningLogistic regression and neural networks 02-02-450AccuracyMachine learningModel evaluation metrics 02-02-451Coefficient of Determination (R²)Machine learningModel evaluation metrics 02-02-452F1-Score (Harmonic Mean)Machine learningModel evaluation metrics 02-02-453Mean Absolute Error (MAE)Machine learningModel evaluation metrics 02-02-454PrecisionMachine learningModel evaluation metrics 02-02-455Recall, SensitivityMachine learningModel evaluation metrics 02-02-456Akaike Information Criterion (AIC)Machine learningModel selection and information criteria