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