# Post Categories

## Meta

• ### First Post, An Explication

A solemn oath to the reader… An oath I will surely forget and fail to uphold. Take it as you will

## General

• ### First Post, An Explication

A solemn oath to the reader… An oath I will surely forget and fail to uphold. Take it as you will

## Mathematics

• ### The sequential shooters

There are N people indexed by $1,..,N$ (because down with the zero-indexers! Long live Peano!) standing in a circle. They’re standing such that $i$ is between $i-1$ and $i+1$ (unless $i \in{1,N}$, for obvious reasons).

Then starting with $1$ and going around the circle in turn, each person shoots the person directly to their left. This stops when there’s...

# Background

If you’ve ever read any papers referring to quantile regression (QR), you undoubtedly have read “MSE yields means, MAE yields medians, and QR yields quantiles”. But what they hell does that even mean? Like not just hand-wavy bullshit, but really, what does that mean? After all, these are just loss functions and therefore don’t yield anything at all....

• ### Let's Cover The Fundamental Group (pt 1)

Munkres saves the day and explains the fundamental secrets behind the most invariant of groups!

• ### Let's Cover Homotopy (an apologetic revisionary tale)

Munkres will surely save us our trespasses this once, but NEVER AGAIN!

• ### Let's Cover Homology (pt 1)

What does topology have to do with data?! And what is this topology thing anyway?

• ### A dirty little ditty on Finite Automata

A basic yet formal introduction to Finite Automata and how strings act on them.

• ### What's in a language?

The basics of the theory of formal languages

## Probability

• ### Probability -- A Measure Theoretic Approach

We cover probability from a measure theoretic approach

## Statistics

• ### Decomposition of Autoregressive Models

We discuss the decomposition of AR models into components, and how eigenvalues are involved (because they always are).

• ### Markov Chain Monte Carlo

Markov Chain Monte Carlo is a tool for sampling otherwise intractible distributions. In this post, we’ll go through some descriptions, reasoning, and examples therein.

• ### Linear Regression -- The Basics

Linear Regression is the bedrock of Machine Learning. We cover the basics therein, some theory involved, and give some relevant examples.

## Theorem-of-the-day

• ### Let's talk Homotopy and Algebra

Just a little dip into homotopy via the Fundamental Theorem of Algebra

## Finance

• ### A little geometric walk down risk model lane

Let’s talk about the geometry of risk models

## Riddle

• ### The Sequential Doors and The Data Science Analogue

This post is going to be something of a combination riddle and blog post.

# The setup

There are $N$ doors indexed by $1,..,N$ along a wall and they’re all closed. Then for each $i\in{1,2,\dots,N}$, you toggle every $i$ door. So at first ($i = 1$) you toggle every door. Then $i=2$ you toggle every second door – the even...