Graphical Models

https://en.wikipedia.org/wiki/Bayesian_network bayesian networks directed edges express conditional rpobablity. Hopefully acyclic. https://en.wikipedia.org/wiki/Graphical_model graphical models https://en.wikipedia.org/wiki/Markov_random_field

Statistics

student’s t chi squared p value

I should have more to say here? Probability Experimental design Hypothesis testing Goodness of fit metrices Bayes rules Regularization Bayes rule and regularization can be seen to be related. Regularization corresponds to a prior that the values of your parameters aren’t going to be ridiculous. A Gaussian prior and guassian distrubtion of error

$e^{ -\frac{\eps^2}{\sigma^2} }$ $y_j = \eps_j + \sum a_i f_i(x_j)$

Machine learning

Cumulants Paradoxes

Measure theory stochastic calculus

Combinatorics

Markov decision processes Monte carlo algos las vegas algos

Bayesian

bayesian vs freqeuntist Priors as regularization

Distributions

Gaussian Poisson Binomial

Information

Entropy Mackay https://www.inference.org.uk/itprnn/book.pdf Information Theory, Inference, and Learning Algorithms https://www.youtube.com/watch?v=BCiZc0n6COY&ab_channel=JakobFoerster

Mathematical

https://en.wikipedia.org/wiki/Cox%27s_theorem

from z3 import *
E = Sort("Event")
P = Function("P", E, RealSort())

# Proof system for probability theory?

https://en.wikipedia.org/wiki/Probability_axioms Kolmogorov axioms

Sets and probability. You need to know an ambient space X to be working in.

https://en.wikipedia.org/wiki/Probabilistic_logic

Law of Total Probability $P(A) = \sum P(A \cap B_i) = \sum P(A | B_i) P(B_i)$ if $B_i$ is a partition of the sample space

https://en.wikipedia.org/wiki/Law_of_total_expectation

Central limit theorem

Markov bound Chernoff bound

Discrete math / combinatorics