Two months ago, I wrote a blog post about the start of a new chapter . There, I said that machine learning has changed to an almost-unrecognizable extent, and I really mean it. Yet, AI is also only getting started, and we’re all still figuring it out. There’s been a lot of hype around rapid prototyping, famously by Garry Tan : he has produced 600000+ lines of working Ruby on Rails in a handful of…
This blog post is going to be much shorter than my last one , so I’ll get straight to the point: I’m leaving academia. Given (a) just how theoretical my work has been, with much of it focused on classical methods, and (b) that I have declined several Assistant Professor job offers, including ones with attractive terms, in order to do so, I think this choice is going to come as a big surprise to a…
It’s 2026. I started my previous blog post on AI research, written in 2023, by saying that the hype around ChatGPT had died down somewhat compared to its launch. That turned out to be completely wrong . The hype has not only not died down, I would say it is now larger than it ever has been. The most important factor that has kept the hype alive is the rise of AI-driven software engineering. It…
It’s 2023. Though by now the hype has died down somewhat, it is clear from talking to everyday people that ChatGPT has completely changed the public’s understanding of the capabilities of modern machine learning and artificial intelligence. A year ago, most people would have said that artificial general intelligence is at least a decade away. Today, one could reasonably argue that in its most…
BibTeX has become a universal reference management format in the mathematical sciences. This format is used on arXiv and in virtually all journals and conferences which publish papers. As a result, a significant amount of time is spent managing references within a manuscript. This is not something I like to spend my time on, so in this post, I’ll explore some ways of making the process more…
Markov chains appear everywhere: they are used as a computational tool within Bayesian statistics, and a theoretical tool in other areas such as optimal control and reinforcement learning. Conditions under which a general Markov chain eventually converges to a stationary distribution are well-studied, and can largely be considered classical results. These are, informally, as follows. $\phi$…
The TeX typesetting system is a lovely bit of software: one can easily use it to typeset production-grade documents such as mathematical papers. However, typesetting complex equations can be tedious, learning to use TeX well can involve memorizing a large number of macros, and it can be difficult to understand the meaning of an equation from looking purely at its source. TeX can be made more…
Lots of people, both in the academic and software communities, have personal websites. Building one with today’s frameworks is easier than perhaps at any point in history, yet many people still have websites consisting of an index file inside of a folder hosted by some outdated service. In this post, I describe how this website is built, showcasing software used to make all aspects of developing…
Julia is a wonderful programming language. It’s modern with good functional programming support, and unlike R and Python—both slow—Julia is fast. Writing packages is straightforward, and high performance can be obtained without bindings to a lower-level language. Unfortunately, its plotting frameworks are, at least in my view, not as good as the ggplot package in R. Fortunately, Julia’s…
In my previous posts, I introduced Bayesian models and argued that they are meaningful. I claimed that studying them is worthwhile because the probabilistic interpretation of learning that they offered can be more intuitive than other interpretations. I showcased an example illustrating what a Bayesian model looks like. I did not, however, say what a Bayesian model actually is—at least not in a…
Bayesian statistics provides powerful theoretical tools, but it is also sometimes viewed as a philosophical framework. This has lead to rich academic debates over what statistical learning is and how it should be done. Academic debates are healthy when their content is precise and independent issues are not conflated. In this post, I argue that it is not always meaningful to consider the merits of…
Deep learning is perhaps the single most important breakthrough in statistics, machine learning, and artificial intelligence that has been popularized in recent years. It has allowed us to classify images—for decades a challenging problem—with nowadays usually better-than-human accuracy. It has solved Computer Go, which for decades was the classical example of a board game that was exceedingly…
Welcome to my blog! For my first post, I decided that it would be useful to write a short introduction to Bayesian learning, and its relationship with the more traditional optimization-theoretic perspective often used in artificial intelligence and machine learning, presented in a minimally technical fashion. We begin by introducing an example. Example: binary classification using a fully…