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

Deep learning

Graph convolutional neural networks
Variational autoencoders

Graphs

The graph Laplacian

Probabilistic models

Gaussian mixture models

Algorithms for statistical inference

Expectation-maximization: theory and intuition
Variational inference
Blackbox variational inference via the reparameterization gradient

The evidence lower bound

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

The calculus of variations

Functionals and functional derivatives