# 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

## Computational biology

RNA-seq: the basics

On cell types and cell states

Three strategies for cataloging cell types

## Graphs

Graph convolutional neural networks

The graph Laplacian

## Probabilistic models

Gaussian mixture models

Variational autoencoders

## 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