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

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
Reasoning about systems of linear equations using linear algebra

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

The calculus of variations

Functionals and functional derivatives

The evidence lower bound

Algorithms for statistical inference

Expectation-maximization: theory and intuition
Variational inference

Probabilistic models

Gaussian mixture models

Algorithms for clustering

Gaussian mixture models

Graph theory

The graph Laplacian