Statistics

General statistics
  1. Random variables as vectors
  2. Covariance matrix, its determinant, Mahalanobis distance
  3. Sample statistics: moments, order statistics, extreme value theory
  4. Important distributions: normal (inflection pt, rot. invar., Gaussian process, etc.), nomial
  5. Important distributions: poisson (derivation, indep to memoryless), geometric, exponential, gamma
  6. Important distributions: beta, Dirichlet
  7. Important distributions: t
  8. Distribution of means with non-vanishing variance: intuition for the Cauchy distribution
  9. Insight into PGFs, MGFs
  10. Bayesian stuff, overfitting, bias-variance decomposition [1]
  11. Relationship between median and absolute error/absolute deviation in regression, Lasso, Tikhonov regularisation, Generalised SVD [1][2][3]
  12. OLD: Convolutions, generating functions and the central limit theorem
Random processes
Time series...

ARIMA/differential equations, characteristic functions intuition, ambit stochastics

Markov chains, random walks, martingales

Data mining
Regression, classification, PCA, convolutional filters/edge detection...

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