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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 18 of 22.

IndexAll notes

02-02-409Expected Value (Mean)Probability and statisticsDiscrete random variables (DRVs)02-02-410Probability Mass Function (PMF)Probability and statisticsDiscrete random variables (DRVs)02-02-411VarianceProbability and statisticsDiscrete random variables (DRVs)02-02-412Variance (Linearity)Probability and statisticsDiscrete random variables (DRVs)02-02-413Central Limit TheoremProbability and statisticsSampling and limit theorems 02-02-414Random Sampling (i.i.d. samples)Probability and statisticsSampling and limit theorems 02-02-415Sampling Distribution of the MeanProbability and statisticsSampling and limit theorems 02-02-416Marginal Likelihood (Evidence)Machine learningBayesian linear regression (BLR)02-02-417Parameter PosteriorMachine learningBayesian linear regression (BLR)02-02-418Parameter PriorMachine learningBayesian linear regression (BLR)02-02-419Posterior CovarianceMachine learningBayesian linear regression (BLR)02-02-420Posterior Mean (MAP)Machine learningBayesian linear regression (BLR)02-02-421Posterior Predictive DistributionMachine learningBayesian linear regression (BLR)02-02-422Cross-Entropy Loss (Binary)Machine learningClassification loss functions 02-02-423K-Means Objective, Within-Cluster Sum of Squares, WCSSMachine learningClustering algorithms 02-02-424Infinite Step Function (Constraint Penalty)Machine learningContinuous optimisation for ML constraints 02-02-425PSD Verification via Rayleigh QuotientMachine learningContinuous optimisation for ML constraints 02-02-426Quadratic Programming Matrix FormulationMachine learningContinuous optimisation for ML constraints 02-02-427Latent Variable Expected Log-LikelihoodMachine learningDensity estimation: Gaussian mixture models (GMM)02-02-428Log-Likelihood ObjectiveMachine learningDensity estimation: Gaussian mixture models (GMM)02-02-429Mixture DensityMachine learningDensity estimation: Gaussian mixture models (GMM)02-02-430Data CenteringMachine learningDimensionality reduction: principal component analysis (PCA)02-02-431Eigenvector Equation (Principal Axes)Machine learningDimensionality reduction: principal component analysis (PCA)02-02-432Low-Rank Approximation (SVD)Machine learningDimensionality reduction: principal component analysis (PCA)