Understanding math, machine learning, and data to a satisfactory degree.
For the past five years, one of the most enjoyable things I've done outside of my day job is teaching. From 2020 to 2025, I had the pleasure of teaching a course in the Master of Management Analytics (MMA) program at the Rotman School of Management (UofT). Now that I've wrapped up that course (on to the next one), I decided to package up the material and put it online for posterity. You can find…
For a while now, I've really enjoyed diving deep to understand probability and related fundamentals (see here , here , and here ). Entropy is a topic that comes up all over the place from physics to information theory, and of course, machine learning. I written about it in various different forms but always taken it as a given as the "expected information". Well I found a few of good explanations…
After being busy for the first part of the year, I finally have a bit of time to work on this blog. After a lot of thinking about how to best fit it into my schedule, I've decided to attempt to write shorter posts. Although I do get a lot of satisfaction writing long posts, it's not practical because of the time commitment. Better to break it up into smaller parts to be able to "ship" often rather…
One interesting thing I often think about is the gap between academic and real-world solutions. In general academic solutions play in the realm of idealized problem spaces, removing themselves from needing to care about the messiness of the real-world. Kaggle competitions are a (small) step in the right direction towards dealing with messiness, usually providing a true blind test set (vs. overused…
Unless you've been living under a rock, you've probably heard of large language models (LLM) such as ChatGPT or Bard. I'm not one for riding a hype train but I do think LLMs are here to stay and either are going to have an impact as big as mobile as an interface (my current best guess) or perhaps something as big as the Internet itself. In either case, it behooves me to do a bit more investigation…
After a long digression, I'm finally back to one of the main lines of research that I wanted to write about. The two main ideas in this post are not that recent but have been quite impactful (one of the papers won a recent ICML test of time award). They address two of the topics that are near and dear to my heart: Bayesian learning and scalability. Dare I even ask who wouldn't be interested in the…
Through a couple of different avenues I wandered, yet again, down a rabbit hole leading to the topic of this post. The first avenue was through my main focus on a particular machine learning topic that utilized some concepts from physics, which naturally led me to stochastic calculus. The second avenue was through some projects at work in the quantitative finance space, which is one of the main…
This post has been a long time coming. I originally started working on it several posts back but hit a roadblock in the implementation and then got distracted with some other ideas, which took me down various rabbit holes ( here , here , and here ). It feels good to finally get back on track to some core ML topics. The other nice thing about not being an academic researcher (not that I'm really…
Here's a topic I thought that I would never get around to learning because it was "too hard". When I first started learning about Bayesian methods, I knew enough that I should learn a thing or two about MCMC since that's the backbone of most Bayesian analysis; so I learned something about it (see my previous post ). But I didn't dare attempt to learn about the infamous Hamiltonian Monte Carlo…
A lot of modern machine learning is related to this idea of "compression", or maybe to use a fancier term "representations". Taking a huge dimensional space (e.g. images of 256 x 256 x 3 pixels = 196608 dimensions) and somehow compressing it into a 1000 or so dimensional representation seems like pretty good compression to me! Unfortunately, it's not a lossless compression (or representation).…