Brian Zhang's blog

Statistics and other topics

Recent posts

Apr 12, 2025 · 1 min read
Motivating Problems in Math What are mathematical achievements that are useful for motivating the study of mathematics?
Sep 19, 2022 · 3 min read
A Regularization Proof Investigating behavior of a function minimum as we add regularization.
Feb 4, 2020 · 1 min read
On NumPy Multithreading Two notes. First, numpy supports multithreading, and this can give you a speed boost in multicore environments! Second, multithreading can hurt performance when you're running multiple Python / numpy processes at once.
Oct 25, 2019 · 2 min read
Fast Hierarchical Clustering Using fastcluster O(N^2) routines for the most commonly used types of clustering.
Sep 28, 2019 · 4 min read
Software Engineering Tools Across 4 Languages Over the past two years, I've found myself getting more interested in abstract math as well as software engineering. Compared to machine learning, which can be a pretty heuristic science (think about the process of writing tests for machine learning code), both math and computer science tend to be built on modular components, each with a precise, testable description.
Jan 22, 2019 · 9 min read
Subtle Observations on Range Queries For my current research, I've had to read Kelleher et al.'s excellent msprime paper (2016) for simulating genetic sequences under the coalescent with recombination. A small trick that is used in their algorithm is the data structure of a Fenwick tree or binary indexed tree. Since I also have a side interest in competitive programming (mainly through USACO and Project Euler), I took a bit more time to learn this data structure.
Oct 24, 2018 · 8 min read
Missing Heritability and Microaggressions Missing heritability is like microaggressions: many seemingly insignificant effects can add up.
Jul 10, 2018 · 14 min read
Random Graphs and Giant Components This post will introduce some of the ideas behind random graphs, a very exciting area of current probability research. As has been a theme in my posts so far, I try to emphasize a reproducible, computational example. In this case, we'll be looking at the "giant component" and how that arises in random graphs.
Apr 4, 2018 · 8 min read
Distributions with SymPy Any good statistics student will need to do some integrals in her / his life. While I generally feel comfortable with simple integrals, I thought it might be worth setting up a workflow to help automate this process!
Jan 30, 2018 · 10 min read
Clustering with K-Means and EM K-means and EM for Gaussian mixtures are two clustering algorithms commonly covered in machine learning courses. In this post, I'll go through my implementations on some sample data.