Notes

I do not have a deep formal background in the mathematical topics used in computational biology and I have found it helpful to create clean, organized notes in order to solidify my understanding. It occurred to me that these notes may be useful to others, so I will periodically post them here. There may be errors in these notes. Let me know if you find anything that can be improved.

Miscellaneous topics

Supremums and infimums
The binomial theorem
Sigmoid functions

Linear algebra

Vector spaces
Normed vector spaces
Dot product
Linear transformations
Matrices
Matrix-vector multiplication
Matrices as linear transformations
Matrix multiplication
Inverse matrices

Probability

Sigma-algebras
Measure
Measurable functions
Probability spaces
Variance
Intuition into covariance

Information theory

Self-information
Perplexity

Probabilistic modeling

Common distributions

Poisson

Inference

Evidence lower bound
Variational inference
Mean field variational inference
Expectation-maximization
Psuedocounts  

Binary classification

Logistic regression

The logistic regression model

Ensemble methods

AdaBoost

Regression

Squared loss
Ordinary least squares