# Blog posts

A blog containing tutorials, notes, and insights on topics in math, statistics, machine learning, computational biology, and pedagogy. To view posts in the order that they were published, click here.

## Miscellaneous

True understanding is “seeing” in 3D

Intrinsic dimensionality

The overloaded equals sign

The binomial theorem

## Computational biology

RNA-seq: the basics

Median-ratio normalization for bulk RNA-seq data

On cell types and cell states

Three strategies for cataloging cell types

Assessing the utility of data visualizations based on dimensionality reduction

## Deep learning

Graph convolutional neural networks

Variational autoencoders

## Graphs

## Probabilistic models

## Algorithms for statistical inference

Expectation-maximization: theory and intuition

Variational inference

Blackbox variational inference via the reparameterization gradient

## Quantities related to probabilistic models

## Probability

Demystifying measure-theoretic probability theory (part 1: probability spaces)

Demystifying measure-theoretic probability theory (part 2: random variables)

Demystifying measure-theoretic probability theory (part 3: expectation)

Visualizing covariance

## Information theory

What is information? (Foundations of information theory: Part 1)

Information entropy (Foundations of information theory: Part 2)

Shannon’s Source Coding Theorem (Foundations of information theory: Part 3)

Perplexity: a more intuitive measure of uncertainty than entropy

## Linear algebra

Vector spaces

Span and linear independence

Normed vector spaces

Introducing matrices

Matrix-vector multiplication

Matrices as functions

Matrices characterize linear transformations

Matrix multiplication

Invertible matrices

Vector spaces induced by matrices: column, row, and null spaces

Reasoning about systems of linear equations using linear algebra

Row reduction with elementary matrices

Deriving the formula for the determinant

What determinants tell us about linear transformations

The invertible matrix theorem