The content here-in has been influenced by Mung Chiang’s Networked Life and Introduction to Algorithms by CLRS.
Bayesian
This page is for the closed form solutions (where they exist) and approximation solutions to Regularised Regressions.
We will also understand that regularisation is sensible artifact once we consider its MAP (maximum a posteriori) derivation.
This page pairs well with Statistics.
Elements of Probability Theory
Definition
(Random Experiment, Sample Space, Events)
A random experiment has uncertain outcomes. The sample space \(S\) is the set of all possible outcomes. An event \(E\) is a subset of \(S\). The certain event is \(S\); the impossible event is \(\varnothing\).
Definition
(Probability Measure (Kolmogorov Axioms))
A probability space \((S,\mathcal{F},P)\) consists of a sample space \(S\), a \(\sigma\)-algebra \(\mathcal{F}\subseteq 2^S\), and a function \(P:\mathcal{F}\to[0,1]\) such that: