Informal notes

These are some notes I've created to help undestand different subjects in mathematics. This page is continuously expanding.

Machine learning

Logistic Regression and Cross Entropy

Logistic regression is log-linear, and is derived from the cross entropy.

Two-step ARMA estimation

This short article describes a technique for estimating ARMA model parameters.

Stochastic processes

Derivation of Brownian Motion from the Random Walk

I derive Brownian Motion from first principles Random Walk. This interesting derivation shows how discrete random walks relate to diffusion processes.

Derivative of Brownian Motion is White Gaussian Noise

This derives White Gaussian Noise as the derivative of Brownian Motion. This is enormously important in Ito calculus and stochastic differential equations.

Signal processing

A Friendly Introduction to Fourier Analysis

This derives the Fourier transform from the Fourier series, with an emphasis on intuitive continuity between these tools. The last part of the article I show how within a Hilbert space formulation all of this is very simple.